Answer:
9.434 X 10^66
Step-by-step explanation:
2.34 X 10^65 + 9.2 X 10^66 (First, you have to manipulate the exponents to bring them to the same index, i.e. the same power)
We can say that 2.34 X 10^65 = 0.234 X 10^66
Now that the indexes are equivalent, we can proceed to add the two bases together.
0.234 X 10^66 + 9.2 X 10^66
= (0.234 + 9.2) X 10^66
= 9.434 X 10^66
The sum of [tex]\(2.34 \times 10^{65}\)[/tex]and [tex]\(9.2 \times 10^{66}\)[/tex] is[tex]\(9.434 \times 10^{66}\)[/tex]
When adding numbers in scientific notation, it's crucial to align their exponents. In the case of[tex]\(2.34 \times 10^{65}\)[/tex] and [tex]\(9.2 \times 10^{66}\),[/tex] they don't initially share the same exponent. To rectify this, we need to adjust the first number.
First, express[tex]\(2.34 \times 10^{65}\)[/tex]as [tex]\(0.234 \times 10^{66}\)[/tex], moving the decimal point one place to the left. Now, both numbers are in the form[tex]\(A \times 10^{66}\),[/tex]making them compatible for addition.
Next, add the coefficients:[tex]\(0.234 + 9.2 = 9.434\).[/tex]
So, the result is[tex]\(9.434 \times 10^{66}\).[/tex] This number is significantly larger than either of the original numbers. In essence, we're combining a quantity in the tens (0.234) with one in the tens of billions (9.2), resulting in a massive number in the tens of billions of billions (9.434) times 10 raised to the power of 66.
In practical terms, this means that if you were to multiply[tex]\(2.34 \times 10^{65}\)[/tex]by 10 and then add[tex]\(9.2 \times 10^{66}\)[/tex]to it, you would have [tex]\(9.434 \times 10^{66}\)[/tex] as your final answer. This demonstrates the remarkable flexibility and ease of handling extremely large numbers using scientific notation.
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Consider the quadratic function fx=x2-8x-4. What is the value of the leading coefficient
Answer:
1
Step-by-step explanation:
Given
f(x) = x² - 8x - 4
The leading term in the expression is x²
with a coefficient of 1 ← leading coefficient
The leading coefficient of a quadratic function of equation fx=x2-8x-4 is 1.
The leading coefficient of a quadratic function is the coefficient of the x² term. In the quadratic function f(x) = x² - 8x - 4, the leading coefficient is 1 because the coefficient of x² is always assumed to be 1 when not explicitly shown.
8. What is the maximum number of
right angles a triangle can have?
Answer:
1
Step-by-step explanation:
180 = 90 + 90 (F)
you must have 3 angles
Answer:
One.
Step-by-step explanation:
A triangle can only have one right angle because all three angles of a triangle MUST add up to be 180 degrees. That means if there are two right angles then the answer would automatically be over 180.
Example:
90+90+1=181
Therefore, a triangle can only have one right angle
The roots of the function f(x) = x2 – 2x – 3 are shown. What is the missing number?
x = –1 and x = ____
Answer:
x = -1 and x = 3
Step-by-step explanation:
x² – 2x – 3 = (x - 3) (x + 1) = 0
x = 3 or x = -1
Answer:
The roots of the function f(x) = x2 – 2x – 3 are shown. What is the missing number?
x = –1 and x = 3
Step-by-step explanation:
Which is the best description of the graph of the function f(x)=60(1/3)^x?
Answer:
what do you mean the best description?
Step-by-step explanation:
Answer:
: the graph has an initial value of 60, and each successive term is determined by multiplying by 1/3
Step-by-step explanation:
f(xequal 6 [1/nitial value x=0, f(x) = 60*[1/3]^0 = 60*1 = 60x=1 ⇒f(1) = 60*[1/3]x=2 f(2) = 60*[1/3]^2 = f(1) * [1/3]x = n f(n) = 60*[1/3]^n=60*[1/3]^(n-1)*[1/3] = f(n-1)*[1/3]
There are 870 boys and 800 girls in a school.
The probability that a boy chosen at random studies Spanish is 2/3
The probability that a girl chosen at random studies Spanish is 3/5
a) Work out the number of students in the school who study Spanish.
b) What is the probability, as a fraction in its simplest form, that a student
chosen at random from the whole school does not study Spanish?
Answer: a) 1060, b) [tex]\dfrac{61}{167}[/tex]
Step-by-step explanation:
Since we have given that
Number of boys = 870
Number of girls = 800
Probability that a boy chosen studies Spanish = [tex]\dfrac{2}{3}[/tex]
Probability that a girl chosen studies Spanish = [tex]\dfrac{3}{5}[/tex]
So, the number of boys in the school who study Spanish would be
[tex]\dfrac{2}{3}\times 870=290\times 2=580[/tex]
So, the number of girls in the school who study Spanish would be
[tex]\dfrac{3}{5}\times 800\\\\=3\times 160\\\\=480[/tex]
So, total number of students who study Spanish would be :
[tex]480+580=1060[/tex]
b) What is the probability, as a fraction in its simplest form, that a student
chosen at random from the whole school does not study Spanish?
Number of students who do not study Spanish would be:
[tex](870+800)-1060\\\\=1670-1060\\\\=610[/tex]
So, the probability of students who does not study Spanish would be :
[tex]\dfrac{610}{1670}=\dfrac{61}{167}[/tex]
Hence, a) 1060, b) [tex]\dfrac{61}{167}[/tex]
There are 1060 students who study Spanish in the school. The probability that a student chosen at random from the whole school does not study Spanish is 610/1670.
Explanation:To work out the number of students in the school who study Spanish, we need to find the number of boys and girls who study Spanish and add them together. The probability that a boy chosen at random studies Spanish is 2/3. So the number of boys who study Spanish is 870 * (2/3) = 580. The probability that a girl chosen at random studies Spanish is 3/5. So the number of girls who study Spanish is 800 * (3/5) = 480. Therefore, the total number of students who study Spanish is 580 + 480 = 1060.
To find the probability that a student chosen at random from the whole school does not study Spanish, we subtract the probability that a student does study Spanish from 1. The probability that a student does study Spanish is 1060 (students who study Spanish) divided by 1670 (total number of students in the school). Therefore, the probability that a student does not study Spanish is 1 - (1060/1670) = 610/1670, which is already in its simplest form.
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A water sprinkler sends water out in a circular pattern. How many feet away from the sprinkler can it spread water if the area formed by the watering pattern is 1,808.64 square feet? Use 3.14 for pi.
Answer:
The sprinkler can spread water in a radius of 24 feet.
Step-by-step explanation:
Since the sprinkler sends water in a circular pattern in order to find the distance at which it can spread the water we need to find the radius of the circle. The area of the circle is said to be 1808.64 and it's formula is given by:
area = pi*r²
1808.64 = 3.14*r²
r² = 1808.64/3.14 = 576
r = sqrt(576) = 24 feet
The sprinkler can spread water in a radius of 24 feet.
Ms. Johnson skates 19.7 miles in 2.8 hours. Estimate her speed in miles per hour.
Answer: 7.04mph
Step-by-step explanation:
[tex]d=19.7mi\\t=2.8h\\v=?[/tex]
Formula:
[tex]d = v*t\\v=\frac{d}{t}\\v=\frac{19.7mi}{2.8h}\\ v=7.04mph[/tex]
Does coordinate x or coordinate y represent a greater number?
Answer:
It depends
Step-by-step explanation:
There is no problem attached and it depends on the problem.
Answer:
MOSKAUStep-by-step explanation:
what is the slope between the points (4,-1) and (-4,3)?
The formula for slope is [tex]\frac{rise}{run} = \frac{y2-y1}{x2-x1}[/tex].
Subtract y1 from y2. (y1= -1, y2 = 3)
3 - -1 = 4
Now subtract x1 from x2. (x1 = 4, x2 = -4)
-4 -4 = -8
Divide the difference between the y coordinates by the difference between the x coordinates.
[tex]\frac{4}{-8}[/tex] or 4 ÷ -8 = -0.5
Answer:The slope between the two points is -0.5.
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The graph of f(x) = (0.5)x is replaced by the graph of g(x) = (0.5)x − k. If g(x) is obtained by shifting f(x) down by 5 units, then what is the value of k?
Step-by-step explanation:
k is the variable for the translations on the Y-axis so if u move the graph 5 units down then k would be 5
Answer:
k=5
Step-by-step explanation:
5. A bag contains 4 green marbles and 5 white marbles. Suppose a marble is
randomly selected. What are the odds in favor of picking a white marble?
A 4 to 5
OB 5 to 4
c 4 to 9
D
5 to 9
Answer:
d
Step-by-step explanation:
A carpenter finds that the measure of an angle formed between a vaulted ceiling and one wall is 67°. How many degrees is the supplement of this angle?
Answer:
113 degrees
Step-by-step explanation:
To find the supplement angle, subtract 67 degrees from 180 degrees
180 - 67 = 113 degrees
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What is the cube root of b^27
Answer:
b^9
Step-by-step explanation:
We can only subtract or add roots to each other but if we are cubing we can divide them by 3.
the fish Casey caught are listed below.
8 8 12 11 10 8 10 9
Casey catches one more fish that is 13 inches long. Which measure will remain the same when the 13-inch fish is included in the list of fish lengths?
(Highlight the correct answer)
Mean
Median
Mode
Range
Help, can anybody solve the below
Answer:
1) -3/4
2) 2/3
3) -4/5
4) -1/4
13) 2
14) 0
15) -2/3
16) -3
hope this helps
How many solutions are there to the equation below?
13x + 195 = 13(x+15)
O
A. 1
OB. o
c. infinitely many
A new statue with a circular base is being unveiled in a downtown park. The statue's base has a radius of 15 feet. What is the area of the base? Round your answer to the nearest whole number. Use 3.14 for π.
The area of the circular base is 707 square feet, calculated using the formula A = πr², where π is 3.14 and the radius is 15 feet.
Explanation:The question asks for the area of a circular base of a statue with a given radius. This is a question of geometry, and the formula for the area of a circle is A = πr², where A represents the area and r represents the radius. In this case, the radius given is 15 feet.
To calculate the area, we insert the value of the radius into the formula, so it becomes A = π(15)². Since we are asked to use 3.14 for π, the calculation becomes: A = 3.14 * 15², which equals 706.5 square feet.
However, since we have been asked to round to the nearest whole number, the final answer would be 707 square feet.
To find the area of the circular base of the statue, we can use the formula A = πr^2, where A is the area and r is the radius. In this case, the radius is given as 15 feet. Plugging this value into the formula, we get:
A = 3.14 * 15^2 = 3.14 * 225 = 706.5 square feet
Rounding to the nearest whole number, the area of the base is approximately 707 square feet.
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Parallel lines e and f are cut by transversal b.
Horizontal and parallel lines e and f are cut by transversal b. At the intersection of lines b and e, the uppercase right angle is (2 x + 18) degrees. At the intersection of lines b and f, the top right angle is (4 x minus 14) degrees and the bottom right angle is y degrees.
What is the value of y?
16
50
130
164
Answer:
130
Step-by-step explanation:
e // f
2x + 18 = 4x - 14
2x = 32
x = 16
y = 180 - (4x - 14) = 180 - (64 - 14) = 130
Using the congruency of the top-right angles, it is found that the value of y is of 130.
---------------------
When two parallel lines are cut by a transversal, the top-right angles are congruent, that is, they have the same measure.In this question, their measures are of (2x + 18)º and (4x - 14)º. Thus, with this, we can find x:[tex]4x - 14 = 2x + 18[/tex]
[tex]2x = 32[/tex]
[tex]x = \frac{32}{2}[/tex]
[tex]x = 16[/tex];
Thus, the measure of the top right angles is given by, in degrees: [tex]4x - 14 = 4(16) - 14 = 64 - 14 = 50[/tex]---------------------
The top-right and the bottom-right angles are supplementary, that is, the sum of their measures is 180º.The measure of the top-right angle is of 50º.The measure of the bottom-right angle is of y.Thus:
[tex]y + 50 = 180[/tex]
[tex]y = 130[/tex]
The value of y is of 130.
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A person invested $690 in an account growing at a rate allowing the money to double
every 7 years. How much money would be in the account after 3 years, to the nearest
dollar?
The amount of money in the account after 3 years would be $828.
Explanation:To determine the amount of money in the account after 3 years, we need to find the number of times the money doubles in a period of 3 years, given that it doubles every 7 years. To find this, we divide 3 by 7 to get the number of doubling periods which is approximately 0.4286. Since the money doubles every 7 years, we multiply the initial investment of $690 by 2 raised to the power of 0.4286 to find the final amount.
Using the formula A = P(1+r)^n, where A is the final amount, P is the initial investment, r is the interest rate per period, and n is the number of periods, we have P = $690, r = 100% (as the money doubles), and n = 0.4286. Substituting these values into the formula, we get A ≈ $827.84. Hence, the amount of money in the account after 3 years, to the nearest dollar, would be $828.
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Final answer:
To calculate the future value of an investment that doubles every 7 years after 3 years, we use the exponential growth formula with an annual interest rate determined by the Rule of 70, resulting in approximately $918.
Explanation:
To determine how much money will be in the account after 3 years given that the amount doubles every 7 years, we can use the formula for exponential growth. The formula is A = P(1 + r/n)nt, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (as a decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
Since the money doubles every 7 years, the effective annual interest rate 'r' that would cause this can be found using the Rule of 70. The Rule of 70 states that to find the number of years required to double the money at a given interest rate, you divide 70 by the annual interest rate. Here, we have that number already (7 years), so we can rearrange to find the interest rate: rate = 70 / time to double. Therefore, the interest rate is 70 / 7, which equals 10% or 0.10 as a decimal.
However, we are looking for the amount after 3 years, not 7. Thus, we need to adjust our formula to account for this shorter time period:
A = P(1 + r)^t
A = 690(1 + 0.10)^3
A = 690(1.331)
A ≈ $918
So, after 3 years, the investment would grow to approximately $918, to the nearest dollar.
is 4 pounds greater than 96 ounces
Answer:
No
Step-by-step explanation:
there are 16 ounces in a pound. 4*16 is is 62.
The label on a jacket said it was 80% wool, 14% nylon, and x% other fibers. What is the value of x?
Answer:
6%
Step-by-step explanation:
80%-14%=x%
every % = %
80%-14%=94%
100%-94%=6%
Answer:
6%
Step-by-step explanation:
80% + 14= 94.
94 is 6 digits away from 100, so the answer is 6%.
The senior class had 100 T-shirts to sell to raise money. They sold 52 T-shirts at $7.75 each. Then they sold the rest for $9.25 each. How much money did they collect overall?
$775.00
$847.00
$925.00
$853.00
Answer:
$847.00
Step-by-step explanation:
First you multiply 52 by $7.75
This gives you $403
Then you subtract 52 from 100 to find the remainder of shirts
This gives you 48
So then you multiply 48 by $9.25
This gives you $444
Then you add $444 and $403 giving you $847.00
Answer:
The answer is B: 847
Step-by-step explanation:
52 x 7.75 = 403
100 - 52 = 48
48 x 9.25 = 444
444 + 403 = 847
The rule is applied to ΔFGH to produce ΔF"G"H".
What are the coordinates of vertex F" of ΔF"G"H"?
(4, –1.5)
(4, –0.5)
(–1.5, 4)
(–0.5, 4)
ITS TIMED. I REALLY NEED HELP!!!
Answer:
(4, –1.5)
Step-by-step explanation:
Mr. Key just his phone bill for the year. The total cost of the bill was $120
What is the unit rate that he paid each month?
O
$12/month
$10/month
O
$1440/year
O
$1/month
Answer:
$10/month
Step-by-step explanation:
9-2: MathXL for School: Practice & Problem Solving KT EDIT
Assignment is past due
9.2.10
Question Help
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement
"And" probabilities can always be determined using the formula P(A and B)=P(A)- P(B).
Choose the correct answer below.
O A. This statement is false, "And" probabilities can only be determined using the formula P(A and B)=P(A). P(BIA).
O B. This statement is false. "And probabilities can be determined using the formula P(A and B) = P(A). P(B) only if A and B are independent. Otherwise, they
can be found using the formula P(A and B)=P(A). P(BIA).
O C. This statement is true.
O D. This statement is false, "And" probabilities can always be determined using the formula P(A and B) = P(A) + P(B).
Answer:the way you put this answer is not readable sorry.
Step-by-step explanation:
The statement is false; the formula to determine "And" probabilities varies depending on whether events are independent or dependent.
Explanation:The statement "And" probabilities can always be determined using the formula P(A and B) = P(A) - P(B) is false. The correct method to determine the probability of two events A and B occurring together, also known as the conjunction, depends on whether the events are independent or dependent. If A and B are independent, the formula is P(A and B) = P(A) × P(B). However, if A and B are dependent, you must use the formula P(A and B) = P(A) × P(B|A), where P(B|A) represents the conditional probability of B given that A has already occurred.
A room is 12 feet wide. A scale model of the room has a scale of 1 in = 6 ft. What is the width
of the room in the model?
A:6 in
B:2ft
C:1ft
D:2in
Final answer:
To determine the room's width in a scale model, use the scale conversion ratio of 1 in = 6 ft. The width in the model is calculated to be 2 inches.
Explanation:
A room is 12 feet wide. A scale model of the room has a scale of 1 in = 6 ft,
To find the width of the room in the model, we use the scale conversion ratio: 1 inch on the model represents 6 feet in reality. Since the room is 12 feet wide, the width in the model would be 2 inches (12 feet ÷ 6 feet per inch = 2 inches).
A toy rocket launched into the air has a height (h feet) at any given time (t seconds) as h=- 16t^2 + 160t until it hits the ground. At what time(s)is it at a height of 9 feet above the ground?
Name the quadrilateral with the most specific name that will describe it.
A) parallelogram
B) isosceles trapezoid
C) square
D) rectangle
Answer: a) parallelogram
Step-by-step explanation:
Top side and bottom side are same lengths/parallel
Angles in a quadrilateral add up to 360 degrees
105+75*2=360
Final answer:
The most specific name for the quadrilateral described is a (C) square because it has equal sides and all right angles, which is more specific than a rectangle, isosceles trapezoid, or a parallelogram.
Explanation:
The question asks to name the quadrilateral with the most specific name. The answer is (C) square. A square is a special type of rectangle with all sides of equal length, which is itself a type of parallelogram. A square is more specific than a rectangle, isosceles trapezoid, or a generic parallelogram because a square has all the properties of these shapes but also has equal sides and all right angles.
consider the following pair of equations:
x + y = -2
y= 2x + 10
if the two equations are graphed at what point do the lines representing the two equations intersect
Answer:
The lines representing these equations intercept at the point (-4,2) on the plane.
Step-by-step explanation:
When we want to find were both lines intercept, we are trying to find a pair of values (x,y) that belongs to both equations, which means that it satisfies both equations at the same time.
Therefore, we can use the second equation that gives us the value of y in terms of x, to substitute for y in the first equation. Then we end up with an equation with a unique unknown, for which we can solve:
[tex]x+y=-2\\x+(2x+10)=-2\\x+2x+10=-2\\3x+10=-2\\3x=-2-10\\3x=-12\\x=\frac{-12}{3} \\x=-4[/tex]
Next we use this value we obtained for x (-4) in the same equation we use for substitution in order to find which y value corresponds to this:
[tex]y=2x+10\\y=2(-4)+10\\y=-8+10\\y=2[/tex]
Then we have the pair (x,y) that satisfies both equations (-4,2), which is therefore the point on the plane where both lines intercept.
Look at the following graph of the given equation. Determine whether the equation is a function. Explain why or why not.
y = 2 x + 2
On a coordinate plane, points are at (negative 1, 0), (0, 2), (1, 4), (2, 6).
Answer:
Yes this is a function
Step-by-step explanation:
y = 2x + 2
0 = 2(-1) + 2
0 = -2 + 2
0 = 0
Yes
2 = 2(0) + 2
2 = 0 + 2
2 = 2
Yes
4 = 2(1) + 2
4 = 2 + 2
4 = 4
Yes
6 = 2(2) + 2
6 = 4 + 2
6 = 6
Yes
The equation y = 2x + 2 is a function, because each 'x' value corresponds to a single 'y' value, as per the mathematical definition of a function.
The graph of the equation y = 2x + 2 does indeed represent a function. In mathematics, a function is defined as a relation in which each input (or 'x' value) corresponds to exactly one output (or 'y' value). In the given coordinate pairs, you will notice that each individual 'x' value (such as -1, 0, 1, and 2) corresponds to a single 'y' value. Furthermore, the equation itself, y = 2x + 2, will always yield a single 'y' value for each 'x' value you substitute into it. This aligns with the definition of a function. Hence, the equation y = 2x + 2 is a function.
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