Answers
[tex] {10}^{7} \div {10}^{5} = {10}^{7 - 5} = {10}^{2} [/tex]
13b.) If you're multiplying and the base is the same, then you add the exponents:
[tex] {s}^{2} \times {s}^{3} \times s = {s}^{2 + 3 + 1} = {s}^{6} [/tex]
13c.) This is similar to 13b:
[tex] {6}^{4} \times {6}^{3} \times 6 = {6}^{4 + 3 + 1} = {6}^{8} [/tex]
Related Questions
Jamie owns a sailboat rental company, which has a large variety of sailboats of different sizes. He observed that the speed of the sailboat (with the wind) largely depends on the length of the sailboat, and is approximately one and a half times the square root of its length. Which of the following options represents the relationship between length and speed of a sailboat?
Answers
Answer:C
Step-by-step explanation:
Formula must be S(x) = (1+1/2)√x = 1.5√x, eliminating A and D. Diagram must show that a zero length boat doesn't move, and that boat length four feet goes 1.5×2 = 3 knots. That eliminates B. Check: C says zero feet goes zero knows and 4 feet goes 3 knots.
Answer:
Graph C
Step-by-step explanation:
We know the speed is equal to one and a half times the square root of the length. This means that speed is the dependent variable (y), and length is the independent variable (x).
Since the speed, S(x), is 1.5 times the square root of the length (x), we get the function
S(x) = 1.5√x.
When x = 0, S(x) = 1.5√0 = 1.5(0) = 0. This makes it graph C.
Nathan just bought a car. He models the value, V, in dollars, of the car after t years as V(t)=21,000(0.861)^t. Based on this model, by what percent does the value of Nathan car decrease each year?
Answers
Answer:
Value of the car is decreasing by 13.9% each year.
Step-by-step explanation:
This equation tells us V(t) is the value of the car after a certain time in years, $21,000 is the initial value of the car. What we need to focus on is on the 0.861 part of this equation. This means that the price of the car is worth 0.861 or 86.1% of what it was worth the year prior, this means that the price of the car is decreasing over time. By how much is it decreasing? Well if we consider 1 to mean 100% (since 100 / 100 =1) then we have 100%-86.1%=13.9%. This means that the value of the car is decreasing 13.9% each year.
What is the slope of a line that is parallel to a line with slope of m=-6/5.What is the slope of the line that is perpendicular to a line with a slope of m=6/5.Explain how you know
Answers
Answer:
a) m = -6/5
b) m = -5/6
Step-by-step explanation:
The slopes of parallel lines are the same. The parallel line will have a slope equal to that of the line it is parallel to, -6/5.
__
The slopes of perpendicular lines are the opposite of the reciprocal of one another. The perpendicular line will have a slope that is the negative reciprocal of the slope of the one it is perpendicular to: -1/m = -1/(6/5) = -5/6.
please show work with answer
Answers
∠A ≅ ∠T . . . . given
AX ≅ TX . . . . given
∠AXM ≅ ∠TXH . . . . vertical angles are congruent
ΔAXM ≅ ΔTXH . . . . ASA theorem
MX ≅ HX . . . . CPCTC
___
15.The acronyms that invoke theorems based on two or three sides being congruent are inapplicable in this case.
SSS
SAS
One integer is 9 less than 5 times another. Their product is 18. Find the integers.
Answers
Answer:
x = 3 and x=-6/5
Step-by-step explanation:
x = one integer
y = other integer
One integer is 9 less than 5 times another
x= 5y-9
product is 18
xy = 18
Substitute in for x
(5y-9) *y = 18
Distribute
5y*y -9y = 18
5y^2 - 9y = 18
Subtract 18 from each side.
5y^2 - 9y -18= 18-18
5y^2 - 9y -18 = 0
Using the quadratic formula
-b ± sqrt(b^2 -4ac)
-----------------------
2a
-(-9) ±sqrt(9^2 -4*5*(-18))
--------------------------------------
2(5)
9 ±sqrt(81 +360))
--------------------------------------
10
9 ±sqrt(441)
--------------------------------------
10
9±21
----------
10
x = (9+21)/10 and x = (9-21)/10
x = 30/10 and x = (-12)/10
x = 3 and x=-6/5
Final answer:
The two integers in question are 21 and 6, with 21 being 9 less than 5 times 6, and their product equating to 18.
Explanation:
Finding the Two Integers
The problem states that one integer is 9 less than 5 times another integer, and their product is 18. Let's call the first integer x and the second integer y.
From the problem, we can write two equations:
x = 5y - 9 (One integer is 9 less than 5 times the other)
xy = 18 (The product of the two integers is 18)
Using substitution from the first equation, in the second equation, we replace x with 5y - 9 and solve for y:
(5y - 9)y = 18
This equation leads to a quadratic equation: 5y^2 - 9y - 18 = 0. Factoring the quadratic equation, we find two pairs of numbers that multiply to give -18 and add up to -9: (-6) and 3.
The factors of the equation are (5y + 3)(y - 6) = 0, giving us y = 6 or y = -³/₅. However, since we are looking for integers, we disregard the fraction and only consider y = 6. Plugging y = 6 back into x = 5y - 9, we get x = 5(6) - 9 which simplifies to x = 21.
Therefore, the two integers are 21 and 6.
Diana invests $25,000 in a bank at the beginning of the year. She will receive 7% interest at the end of the year, but she will have to pay a 16% tax on the interest received.
A.) How much interest will Diana earn after she pays the tax?
B.) What percent of Diana's investment is the interest after paying the tax?
Answers
Answer:
A) $1470
B) 5,88%
Step-by-step explanation:
B) Diana will end up with 100% -16% = 84% of the interest she earns, so her effective interest rate is ...
... 7% × 84% = 5.88%
A) Diana's investment earns ...
... 0.0588 × $25000 = $1470
After paying a 16% tax on the interest, Diana will earn $1,470 in interest. This represents 5.88% of her original $25,000 investment.
Diana invests $25,000 in a bank at 7% interest, which she will receive at the end of the year. However, she must pay taxes at a rate of 16% on the interest earned.
First, we calculate the total interest Diana would earn without taxes:
Total Interest = Principal imes Interest Rate
Total Interest = $25,000 imes 0.07 = $1,750.
Next, we calculate the tax on the interest:
Tax on Interest = Interest Earned imes Tax Rate
Tax on Interest = $1,750 imes 0.16 = $280.
Now, we subtract the tax from the total interest to find the interest after taxes:
Interest After Taxes = Total Interest - Tax on Interest
Interest After Taxes = $1,750 - $280 = $1,470.
We find the percentage of the original investment that the interest after taxes represents:
Percent of Investment = (Interest After Taxes / Principal) imes 100
Percent of Investment = ($1,470 / $25,000) imes 100 = 5.88%.
How many hours are in a decade
Answers
Answer:
87600
Step-by-step explanation:
Answer:
87600 hours
Step-by-step explanation:
1 decade = 10 years
1 year = 365 days
1 day = 24 hours
1 decade * 10 years/ 1 decade * 365 days/ 1 year * 24 hours / 1 day
87600 hours
Select the correct answer. Twenty students in Class A and 20 students in Class B were asked how many hours they took to prepare for an exam. The data sets represent their answers. Class A: {2, 5, 7, 6, 4, 3, 8, 7, 4, 5, 7, 6, 3, 5, 4, 2, 4, 6, 3, 5} Class B: {3, 7, 6, 4, 3, 2, 4, 5, 6, 7, 2, 2, 2, 3, 4, 5, 2, 2, 5, 6} Which statement is true for the data sets?
A: The mean study time of students in Class A is less than students in Class B.
B: The mean study time of students in Class B is less than students in Class A.
C: The median study time of students in Class B is greater than students in Class A.
D: The range of study time of students in Class A is less than students in Class B. E: The mean and median study time of students in Class A and Class B is equal.
Answers
Answer:
B: The mean study time of students in Class B is less than students in Class A.
Step-by-step explanation:
To find out why answer B is the right answer, I will give you facts from each option.
Option A is false. The mean study time in Class A is 4.8. Meanwhile in Class B it is 4. For Class A, sum up the 20 study times which is 96 and divide them by 20, you will get 4.8 hours of mean study time. For Class B, the sum of the 20 study times is 80, which divided by 20 will be 4.
Option B is True. See previous explanation.
Option C is False. The median study time in Class B is 4. The median study time in Class A is 4.8,
Option D is False. The range in Class A is from 2 to 8. The range in Class B is from 2 to 7.
Option E is False: The mean and median study time of these classes is different.
Answer:
B: The mean study time of students in Class B is less than students in Class A.
Step-by-step explanation:
Which transformation confirms that rectangle ABCD and rectangle EFGH are similar?
A) Rectangle ABCD is rotated 90° clockwise about the origin and then dilated by a scale factor of 2 with the origin as the center of dilation.
B) Rectangle ABCD is rotated 90° clockwise about the origin and then dilated by a scale factor of 1 2 with the origin as the center of dilation.
C) Rectangle ABCD is rotated 90° counterclockwise about the origin and then dilated by a scale factor of 2 with the origin as the center of dilation.
D) Rectangle ABCD is rotated 90° counterclockwise about the origin and then dilated by a scale factor of 1 2 with the origin as the center of dilation.
Answers
good luck
Answer:
Option D is correct.
Step-by-step explanation:
We are given that,
'Rectangle ABCD is translated to map onto the rectangle EFGH'.
That is, 'Rectangle ABCD is similar to rectangle EFGH'.
So, we see that,
Rectangle ABCD is rotated towards the left and then decreased in size to map onto EFGH.
That is, we have,
Rectangle ABCD is rotated counter-clockwise by 90° about the origin and then dilated by a factor of [tex]\frac{1}{2}[/tex] with the origin as the center of dilation.
Hence, option D is correct.
How do I write Domain and Range in inequality notation?
Answers
Answer:
Domain: (-infinity, infinity) Range: (-infinity, infinity)
Step-by-step explanation:
They are parabolas, therefore you can assume that they go on infinitely. To find range, you must look at your y values. Look for your lowest point. Because the line goes done forever, your beginning mark would be (-infinity.
To find the other part, you look at your positive y values. Look for the highest value. Because this goes on infinitely, the completed version of your notation would be (-infinity, infinity). Be sure to use the infinity symbol though, which looks like an 8 rotated 90 degrees.
To find domain, look at your x values. To begin, look at your left-most values, which would be the negative numbers. Because the line goes on forever to the left, your notation would be (-infinity. To find the other part of domain, look at your positive x values. Because this line goes on infinitely as well, the completed version of your notation would be (-infinity, infinity). Infinity is never bracketed, it is always in parenthesis.
sherrie opened 5 bags of peanuts and counted a total of 75. At this rate, how many peanuts would be in 8 bags.
Answers
Answer:
There should be 120 peanuts
Step-by-step explanation:
We can use ratio's to solve this problem
5 bags
---------------
75 peanuts
5 bags 8 bags
--------------- = ------------------
75 peanuts x peanuts
Using cross products
5x = 75*8
5x = 600
Divide each side by 5
5x/5 = 600/5
x = 120
Answer:
if 5 bags of peanuts = 75peanuts
Then 1 bag will be 15 peanuts beacause 75 divided by 5 is 15
8 bags of peanuts will then be 15 multiply by 8 which is 120 peanuts
Step-by-step explanation:
adam spent 13.10 on supplies for school. book covers cost 1.50 and boxes of mechanical pencils were each 2.80. if he bought seven items total, then how many of each did he buy
Answers
5 book covers and 2 boxes of pencils
Step-by-step explanation:If all 7 were book covers, the cost would be 10.50. The cost is 2.60 more than that. Each box of mechanical pencils costs 1.30 more than a book cover, so there must be 2.60/1.30 = 2 boxes of mechanical pencils (and 5 book covers).
_____
If you want an equation, let p represent the number of pencil boxes. Then 7-p is the number of book covers.
... 1.50(7-p) +2.80p = 13.10
... 1.30p = 13.10 -10.50 . . . . . subtract 10.50, collect terms
... p = 2.60/1.30 = 2 . . . . pencil boxes
... 7-2 = 5 . . . . . book covers
Identify negative angle measure. Select all angles that have a negative measure.
Answers
see attachments below
Step-by-step explanation:In Algebra, angles are measured counterclockwise (CCW), generally using the +x axis as a reference. Thus any angle with an arrow shown in the CW direction will have a negative measure.
Know that clockwise measured angles are negative and anticlockwise measured angles are positive in sign.
Thus,
In first figure first angle is positive, second is negative.In second figure first angle is negative, second is positive.In third figure, first angle is positive, second angle is negative, third angle is positive.How does rotation measure specifies sign of angles?
It is a standard convention used in mathematics that if you measure an angle clockwise(like the clock's hand moves), then the measured angle will be written with negative sign.
If the angle is measured anticlockwise, then the measured angle is written with positive sign.
Thus, by these conclusions, we have:
Thus, In first figure first angle is positive, second is negative.In second figure first angle is negative, second is positive.In third figure, first angle is positive, second angle is negative, third angle is positive.Learn more about sign of angles here:
https://brainly.com/question/11043027
please help me asap!
Answers
Answer:
D) [tex](x-5)^2 + (y-2)^2 = 49[/tex]
Step-by-step explanation:
Center is (5,2) and radius = 7
We use center - radius form of equation of circle
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Where (h,k) represents the center
and r is the radius of the circle
We know center is (5,2) so h= 5 and k =2
r= 7
Plug in all the values
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
[tex](x-5)^2 + (y-2)^2 = 7^2[/tex]
[tex](x-5)^2 + (y-2)^2 = 49[/tex]
x^3-8/x^2+2x+4 divided by (x^2-4)
Answers
The simplified expression is [tex]\( \frac{x - 2}{x + 2} \)[/tex].
To divide the expression [tex]\(\frac{x^3 - 8}{x^2 + 2x + 4}\) by \((x^2 - 4)\)[/tex], you first factor both the numerator and denominator.
Factor the numerator:
[tex]\[ x^3 - 8 \][/tex]
[tex]\[= (x - 2)(x^2 + 2x + 4) \][/tex]
This is based on the difference of cubes: [tex]\(a^3 - b^3 = (a - b)(a^2 + ab + b^2)\), where \(a = x\) and \(b = 2\).[/tex]
Now, factor the denominator:
[tex]\[ x^2 + 2x + 4 \][/tex]
[tex]\[= (x + 2)^2 \][/tex]
The expression becomes:
[tex]\[ \frac{(x - 2)(x^2 + 2x + 4)}{(x + 2)^2} \][/tex]
Now, divide by [tex]\((x^2 - 4)\)[/tex]:
[tex]\[ \frac{(x - 2)(x^2 + 2x + 4)}{(x + 2)^2} \div (x^2 - 4) \][/tex]
Factor [tex]\(x^2 - 4\)[/tex] further:
[tex]\[ x^2 - 4 = (x + 2)(x - 2) \][/tex]
Now, cancel out common factors:
[tex]\[ \frac{(x - 2)(x^2 + 2x + 4)}{(x + 2)^2} \div (x^2 - 4) = \frac{x - 2}{x + 2} \][/tex]
Therefore, the simplified expression is [tex]\( \frac{x - 2}{x + 2} \)[/tex].
Complete question:
Simplify: X^3-8/x^2+2x+4 divided by (x^2-4)
Question: Graph the line defined the equation 8x + 8y = 24
Choose: A,B,C or D!!!
Answers
Answer:
B
Step-by-step explanation:
8x + 8y = 24
-8x on both sides
8y = -8x + 24
Divide by 8 on both
y = -x + 3
Answer:
B
Step-by-step explanation:
(÷8)8x + 8y = 24(÷8)
x + y = 3
y = - x + 3
If x is negative, then the function is decreasing.
y = - x + 3
When x = 0
y = - 0 + 3
y = 3
(0,3)
When y = 0
- x + 3 = 0
- x = - 3
x = 3
(3,0)
Alternative B
I hope I helped you.
Which triangle is similar to triangle SRT?
Answers
Answer:
Triangle PQR
Step-by-step explanation:
PQR I am just adding extra words so I have a higher word count so it accepts my answer :)
The polar form of this is?
Answers
Answer:
2, 120 degrees
Step-by-step explanation:
The first step in finding the polar form is finding the modulus, r
r= sqrt( x^2 + y^2)
r = sqrt( (-1)^2 + sqrt(3)^2)
r = sqrt(1+3)
r= sqrt(4)
r =2
The next step is finding the angle
theta = arctan (y/x)
theta = arctan (sqrt(3)/-1))
theta = arctan (-sqrt(3))
theta = -60
The point (-1, sqrt(3)) is in the 2nd quadrant, but our angle is in the 4th quadrant, so we add 180 degrees
theta = -60 + 180 = 120
theta = 120 degrees
1.2 x 10 to the negative 3rd / 4 x 10 to the 6
Answers
Answer:
[tex]3 \cdot 10^{-10}[/tex]
Step-by-step explanation:
[tex]\dfrac{1.2\cdot 10^{-3}}{4\cdot 10^{6}}=\dfrac{12\cdot 10^{-4}}{4\cdot 10^{6}}\\\\=\dfrac{12}{4}\cdot 10^{-4-6}=3\cdot 10^{-10}[/tex]
I like to adjust the operands so the quotient needs no adjustment. Here that means rewriting the numerator to an equivalent value with a mantissa between 4 and 40.
Which names the tiling
Answers
4, 8, 8
Step-by-step explanation:At each node, three faces meet. One is square (4 sides); the other two are octagons (8 sides). Hence the tiling can be named with three numbers: 4, 8, 8.
Answer:
4, 8, 8
At each node, three faces meet. One is square (4 sides); the other two are octagons (8 sides
Step-by-step explanation:
In rectangle ANHG, whose perimeter is 100, OP, PQ, and QR are congruent and mutually perpendicular and O is the midpoint of AN. If GH = 40 which is PQ?
Answers
Answer:
5
Step-by-step explanation:
The sum of adjacent sides of the rectangle is half the perimeter, 50, so ...
... AH = 50-40 = 10
Then ...
... OP +QR = 10 = 2×OP . . . . . QR ≅ OP
... OP = 5 = PQ . . . . . . . . . . . . PQ ≅ OP
We know the perimeter is the sum of all the sides, and we have two of the sides (40 and 40). We have that the perimeter is equal to 40+40+AG+NH, and since this is a rectangle, NH and AG must be equal. Lets label them as “x” for now.
So 100 = 40 + 40 + x + x
100 = 80 + 2x
2x = 100 - 80
2x = 20
x = 10
So AG and NH are 10. If we look at the three lines in the rectangle, we may notice that if we were to “stack” OP and QR together, we would get the length of AG and NH (which is 10). Since all three lines are congruent (equal), we can label them all as y.
We know OP and QR are equal, and if their sum makes the length of NH or AG, we can say
AG = 2y
10 = 2y
y = 5
And, again, since theyre all congruent, PQ is equal to both OP and QR, so PQ must be 5.
what are the coefficients in the following expression 8x + 5 + 6y
Answers
Answer:
8 5 and 6 are the coefficients
Step-by-step explanation:
For this case we have that by definition, a coefficient is the term that accompanies a variable. If we have the expression given by:
[tex]8x + 5 + 6y[/tex]
The number "5" is a constant.
Thus, two variables, "x" and "y", are observed.
Thus according to the definition, the coefficients are given by "8" and "6" respectively.
Answer:
8 and 6 are the coefficients
A gumball machine has 420 red gumballs. If the red gumballs are 75% of the total number of gumballs, how many gumballs are in the gumball machine?
Answers
Answer:
The answer is 560
Step-by-step explanation:
multiply 420 by .75 for 75%
(420).75=560
The distance it takes a car to come to a complete stop after the brakes are applied is related to the speed that the car is traveling. the stopping distances and speeds are shown in the table.
Which equation represents the data in the table?
A) s=4√d
B) s=0.37d+20 NOT B
C) s=13.7log20
D) s= 1/25d²
Please choose one of the answers provided.
Edit: It is not Choice B
Answers
Answer:
Hence, Option 1 is correct equation [tex]s=4\sqrt{d}[/tex]
Step-by-step explanation:
The distance it takes a car to come to a complete stop after the brakes are applied is related to the speed that the car is traveling. the stopping distances and speeds are shown in the table.
d s
20 17.89
40 25.30
60 30.98
80 35.78
100 40.00
We will check each option for table.
[tex]s=4\sqrt{d}[/tex]
For d=20, Put d=20 into [tex]s=4\sqrt{d}[/tex]
[tex]s=4\sqrt{20}\approx 17.89[/tex]
For d=40, Put d=40 into [tex]s=4\sqrt{d}[/tex]
[tex]s=4\sqrt{40}\approx 25.30[/tex]
For d=60, Put d=60 into [tex]s=4\sqrt{d}[/tex]
[tex]s=4\sqrt{60}\approx 30.98[/tex]
For d=80, Put d=80 into [tex]s=4\sqrt{d}[/tex]
[tex]s=4\sqrt{80}\approx 35.78[/tex]
For d=100, Put d=100 into [tex]s=4\sqrt{d}[/tex]
[tex]s=4\sqrt{100}\approx 40.00[/tex]
All the value of table satisfy the first equation.
Hence, Option 1 is correct equation [tex]s=4\sqrt{d}[/tex]
Tom is 45 and pays $2042 on his mortgage each month while his total take hime pay is $5950 per month. The national average, for those aged 35-64, on housing costs is 35% of income. Compute the percent of Tom's income that he spends on housing.
Answers
Answer:
34.32%
Step-by-step explanation:
Tom is 45 years old.
Tom earning = $5950 per month
Mortgage payment = $2042
Percentage of amount paid towards mortgage in his income = (2042/5950)*100
= 34.32%
Tom pays 34.32% of his income towards mortgage.
The national average of his age group pays 35% of income towards housing.
Thank you.
Please answer ASAP!! which of the following is closest to 0.25 and why?
A) 9/40 B)5/16 C) 9/32 D) 0.28 E) 15/64
Answers
*Functions* Fill in the blank.
The function f(x)=log x is transformed into the equation f(x)=log (1/4x).
The function f(x)=log (1/4x) is a _______ of the parent function by a factor of _______.
A. horizontal stretch
B. horizontal compression
(A and B apply to the first blank, C, D, and E apply to the second blank.)
C. 0.25
D. 1
E. 4
Answers
Answer:
A and C
Step-by-step explanation:
I hope I helped you.
Emily wants to make a rectangular model with a height of one cube
She wants to make the model in exactly 2 different ways. How many connecting cubes could emily use to make the model in only two ways.
Answers
Answer:
Three cubes
Step-by-step explanation:
The cubes have to be indistinguishable and all orientations of one cube are also have to be indistinguishable.
All ways of connecting two cubes result in the same shape. So answer is larger than two.
After connecting two cubes, there are ten faces where the third cube can be attached, and two faces which are connected, accounting for all 12 faces of two cubes.
Of the 10 exposed faces, exactly two are on opposite ends, both leading to the same straight line figure. The other 8 faces all lead to an L shape, and all L shapes can be rotated to be identical.
Hence, three cubes can only make a straight shape or an angled shape.
Four cubes can make a straight shape, a L shape, a Γ shape (but flipping it over through 3 dimensions makes L and Γ identical), a T shape, and a square shape. That is either four or five different objects depending on if they can be lifted from the table. Anyway, it is more than two.
Please Help If You Know How To Do Simple Interest ;3
Worth 15 points each (I think cause I put 30 points)
Answers
Answer:
$5875
Step-by-step explanation:
The simple interest formula for the ending balance is ...
... A = P(1 +rt)
You have principal amount P=5000, interest rate r=0.05, and time t=3.5, so the amount (A) is ...
... A = $5000(1 +0.05·3.5) = $5000·1.175
... A = $5875
A particular leg bone for dinosaur fossils has a mean length of 5 feet with standard deviation of 3 inches. What is the probability that a leg bone is less than 62 inches
Answers
Answer:
The probability of a leg bone measuring less than 62 inches is about 75% (74.86%).
Step-by-step explanation:
To answer this question we can calculate the z-score, then use a table to look up a corresponding percentile using z tables.
The length is a random variable with mean = 60 in and standard deviation of 3 in and we are looking at a particular sample that 62 in long. That sample has the following z value:
[tex]z = \frac{62 - \mu}{\sigma}=\frac{62-60}{3}=\frac{2}{3}\approx0.67[/tex]
The area under the normal distribution curve that corresponds to the z value of 0.67 (using a z table - available on line) is 0.7486. This is the probability that a random sample of a fossil leg length is less that our particular value 62 inches. Roughly speaking, the probability of a leg bone less than 62 in is about 75% (aka 75-th percentile).