Answer: 64
Step-by-step explanation:
8x=
8(8)=
8*8=64
Answer:
64
Step-by-step explanation:
To solve this equation, we have to plug 8 into x.
Plug 8 into x and multiply
8(8)
= 64
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Four lines are plotted on the coordinate plane.
Line 1
-10
Line 1
Line 2
Line 3
-10
O Line 4
10
Which line shows a proportional relationship?
Line 2
Line 3
Line 4
Answer:
Line 3
Step-by-step explanation:
Proportional relationship:
• They are straight lines that have a constant slope
• The line must pass through the origin at (0,0)
• The y intercept is zero
The only line passing through the origin at the point (0,0), is Line 3
The line y=x+1 intersects the graph of y=x^2-3x-11 at the points A and B
Find the coordinates of A and B
Answer:
(6, 7) and (-2, -1)
Step-by-step explanation:
if y=x+1 intersects with y=x^2-3x-11
then we need to find x and y such that both of those equations are true.
If y = x + 1 is true and y=x^2-3x-11, then
y - y = x^2-3x-11 - x - 1 is also true
0 = x^2 - 4x - 12
use your preferred method to solve the quadratic equation
0 = (x - 6)(x + 2)
x = 6 or x = -2
now for each x we take y from either equation, but y = x + 1 is simpler.
for x = 6 the coordinates are (6, 7) and for x = -2 the coordinates are (-2, -1)
Money is borrowed at 18% simple interest. after one year, $610.06 pays off the loan. how much was originally borrowed?
The original amount borrowed was $517.
Simple Interest is the method to calculate the interest charged for a given number of years and given rate , in simple interest the principle remains same for each year.
Simple interest =[tex]\frac{P*R*T}{100}[/tex]
where P= principle, R=rate in % , T= time
We know that Amount= Principle+ Simple Interest........(1)
According to the question
Amount=$610.06
Rate=18%
time = 1yr
Substituting the value in equation (1) we get
[tex]610.06=P+\frac{P*18*1}{100}[/tex]
[tex]610.06=\frac{100P+18P}{100}[/tex]
[tex]610.06=\frac{118P}{100}[/tex]
[tex]61006=118P[/tex]
[tex]P=\frac{61006}{118}[/tex]
[tex]P=517[/tex]
Therefore , The original amount borrowed was $517.
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A rock sample containing an isotope with a half-life of 28 million years has an initial mass of 184 grams. how much time has elapsed after three half-lives?
The half life period is the time in which only half of the given population remains. It can be represented through this equation:
[tex]f(t)=a\times(1/2)^{\frac{t}{h}}[/tex]
t = time passeda = y-intercepth = half lifeSolving the QuestionWe're given:
h = 28 million yearsa = 184 grams (this is the initial mass, after 0 time has passed)For most questions like this, we would have to plug these values into the equation mentioned above. However, this question asks for the time elapsed after 3 half-lives.
This can be calculated simply by multiplying the given half-life by 3:
28 million years x 3
= 84 million years
Answer84 million years
Which choice shows 17+14+ 13 rewritten correctly using the commutative
property and then simplified correctly?
Answer:
Could I see the available choices?
Step-by-step explanation:
Answer:
didnt have the choices but any that would have it as the same problem different order
Step-by-step explanation:
17+14+13=13+14+17=14+13+17=14+17+13=17+13+14=13+17+14
-1. 64 as a mixed number in simplest form
Answer:
Step-by-step explanation:
The difference of two natural number is 2. The sum of their squares is 100.Find the numbers.
The required two numbers are 6 and 8.
Let us denote the required numbers by c and d.
Given that the difference between two natural numbers is 2.
If we assume d > c, then d – c = 2
⇒ d = 2 + c → equation 1.
Also given that the sum of their squares is 100.
⇒ c² + d² = 100
⇒ c² + (2 + c)² = 100 (using the value of d from equation 1)
⇒ 2c² + 4c + 4 = 100
⇒ 2c² + 4c = 96
⇒ 2c(c+2) = 96
⇒ c(c+2) = 48
Using the factorization for 48, we get 6 × 8 = 48
⇒ c = 6
⇒ c+2 = 8
⇒ d = 8
Therefore, the required two numbers are 6 and 8.
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Q/R = g/F solve for F
Answer:
the answer is
Step-by-step explanation:
Q/R= G/F
= QF=GR
divide both sides by Q
Q and Q are off so
therefore F= GR/Q
Brittney is 4 years older than Dakota. The variable b stands for Brittney's age. Which expression stands for Dakota's age?
A. 4b
B. 4 - b
C. b + 4
D. b - 4
Choose the graph that depicts one-to-one function
Answer:
Using the horizontal line test, the one to one functions are those which do not intersect with the line more than one time
In the given graphs, the fourth graph represents the one - one fucntion.
Use the concept of graph of fucntion defined as:
Drawing the curve that represents a function on a coordinate plane is known as graphing a function. Every point on the curve will satisfy the function equation if the curve (or graph) reflects the function.
The graph of a one-to-one function is a representation that shows each input value (x) uniquely paired with a corresponding output value (y), with no repetition or overlap in the mapping.
It passes both the vertical line test and horizontal line test, ensuring each input has a distinct output and vice versa.
In the fourth graph:
Apply the vertical line test and we get,
Each input has a distinct output.
Hence,
The fourth graph represents the one-one fucntion.
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find the sum or standard form of 10⁰+9⁰+7⁰+5⁰+3⁰+1¹⁰⁰
Answer:
6
Step-by-step explanation:
10⁰=1
9⁰=1
7⁰=1
5⁰=1
3⁰=1
1¹⁰⁰=1
so,
10⁰+9⁰+7⁰+5⁰+3⁰+1¹⁰⁰=1+1+1+1+1+1=6
Answer:
6
Step-by-step explanation:
We are working with exponents
Any number to the power of 0 is 1
a^0 = 1
1 to a power is 1
10⁰+9⁰+7⁰+5⁰+3⁰+1¹⁰⁰
1 + 1 + 1 + 1 + 1 + 1
6
What formula would you use to find 50 is what percent of 20?
a) p = rb
b) r = p/b
c) i = prt
d) b = p/r
We would use r = p/b formula to find 50 is what percent of 20.
The correct answer is an option (b)
For given question,
we need to find the formula which we use to find 50 is what percent of 20
We make the assumption that 20 is 100% since it is our output value.
Let the value we seek be m.
So, 100 % = 20 ...............(1)
m % = 50 ..............(2)
By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have
[tex]\frac{100\%}{m\%}=\frac{2}{5}[/tex]
So, m = 250%
This means, 50 is 250% of 20
The formula PERCENTAGE p = rb – The result obtained when a number is multiplied by a percent.
The formula BASE ( b = p/r) – The whole in a problem. The amount you are taking a percent of.
The formula RATE (r = p/b) – The ratio of amount to the base. It is written as a percent.
Therefore, we would use r = p/b formula to find 50 is what percent of 20.
The correct answer is an option (b)
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B
Set-up an equation and solve for x.
2x-12
H
C
x+9
12
D
+
|| || ||
0000
Answer:
2x – 12 + 12 = x + 9
2x = x + 9
x = 9
SOLVE SOLVE SOLVE SOLVE
The given expression is simplified as 6x+3y³. Therefore, option A is the correct answer.
The given expression is [tex]\frac{18x^{3}y^{2}+9x^{2} y^{5}}{3x^{2} y^{2} }[/tex].
We need to divide and simplify the given expression.
How to divide binomial by monomial?Division of polynomials by monomial means dividing the polynomials which are written as numerators by a monomial which is written as denominators to find their quotient.
Split the denominators to each numerator and cancel out the common terms and simplify.
Now, [tex]\frac{18x^{3}y^{2}+9x^{2} y^{5}}{3x^{2} y^{2} }=\frac{18x^{3}y^{2}}{3x^{2} y^{2}} +\frac{9x^{2} y^{5}}{3x^{2} y^{2}}[/tex]
=6x+3y³
The given expression is simplified as 6x+3y³. Therefore, option A is the correct answer.
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Suppose that an angle is bisected to form two smaller angles that measure (3+30)° and (5+6)° . What is the measure of the original angle?
°
Based on the angles addition theorem, the measure of the original angle = 44°.
What is the Angles Addition Theorem?The angles addition theorem states that if an angle is bisected to form two smaller angles, then the sum of the measures of the two smaller angles equals the measure of the original angle that is bisected.
Given that the two smaller angles formed when bisected are: (3+30)° and (5+6)°. Based on the angles addition theorem:
The measure of the original angle = (3+30)° + (5+6)°
The measure of the original angle = 33° + 11°
The measure of the original angle = 44°
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Splash city water park has 14 different rides. Each customer goes on an average of 8.4 rides, with standard deviation of 2. The distribution of rides customers go on is normal. What percent of the riders go on more than 10 rides? Round to the nearest percent.
Using the normal distribution, it is found that 21% of the riders go on more than 10 rides.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 8.4, \sigma = 2[/tex]
The proportion of riders that go on more than 10 rides is one subtracted by the p-value of Z when X = 10, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (10 - 8.4)/2
Z = 0.8
Z = 0.8 has a p-value of 0.7881.
1 - 0.7881 = 0.2119 = 21.19% = 21%(rounded to the nearest percent)
21% of the riders go on more than 10 rides.
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nina goes to the neighborhood store to buy 14 rolls of paper towels. if she pays $20.02 in all for the purchase, how much does one roll of paper towels cost?
Answer:
$1.43
Step-by-step explanation:
To find how much one roll of paper towels cost, we have to divide the total purchase ($20.02) by the number of paper towel rolls (14).
20.02 ÷ 14
= $1.43
One paper towel roll costs $1.43
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(3x-5)/4 is less than or equal to -1
How to solve for x?
Step-by-step explanation:
[tex] \frac{3x - 5}{4} \leq1[/tex]
[tex]3x - 5 \leq1 .4[/tex]
[tex]3x - 5 \leq4[/tex]
[tex]3x \leq4 + 5[/tex]
[tex]3x \leq9[/tex]
[tex]x \leq \frac{9}{3} [/tex]
[tex]x \leq3[/tex]
x = {3,2,1,0,...}
TASK 2-Percentages (34 Marks)
Topic: Finding Percentages
1. Suppose you have a grandmother who gives you one cent on your first birthday. The
next year she gives you 3 cents, the following year 9 cents. Each year she triples the
amount she gave the year before until you are 13.
How much money would you have on your 12 birthday? you would have
$154
72
(a) Complete the table below (BMarks)
Birthday
1
2
3
4
5
6
7
8
9
10
11
12
13
Total
Money
1c
3c
9c
27c
81c
$2.43
34 86
39 72
$19 34
338 68
377 36
$154 72
Percentage
3309-44
$309 44
(b) What percentage is the amount of money on your 12th birthday to the total money
given by your grandmother. Your percentage need to be corrected to two decimal
places. You need to show all the steps for your percentage calculation.
Answer:
1; 1
2:3
3:9
4:27
5:81
6:243
7:729
8:2,187
9:6,561
10:19,683
11:59,049
12:177,147
The perimeter of a rectangle is 800 yards. What are the dimensions of the rectangle if the length is 50 yards more than the
width?
Answer:
The length is 225 yd, and the width is 175 yd.
Step-by-step explanation:
Let w = width.
Then the length = w + 50.
perimeter = 2(length + width)
800 = 2(w + 50 + w)
400 = 2w + 50
2w = 350
w = 175
w + 50 = 225
The length is 225 yd, and the width is 175 yd.
Answer:
225 * 175 yards,
Step-by-step explanation:
If the width is x then the length is x+50.
Perimeter = 2(width + length)
800 = 2( x + x + 50)
2x + 50 = 400
2x = 350
x = 175
So, the width is 175 yd and length is 225yd.
Write the equation of the line in slope-intercept form.
It has a coefficient of m = -1 and passes through the point (9, 4).
Answer:
y=-x+13
Step-by-step explanation:
m=-1
m is slope
point is (9, 4)
first use point slope equation
y-y1=m(x-x1)
y-9=-1(x-4)
distribute
y-9=-x+4
isolate the y variable
y=-x+13
The real estate agent's base salary is $21,000. They also receive 5% commission on total sales. How much in total sales do they have to make in order to earn $70,000 in one year?
======================================================
Work Shown:
x = amount of sales
0.05x = five percent of sales to represent commission earned
21,000+0.05x = add on the base salary to get total salary
21,000+0.05x = 70,000
0.05x = 70,000-21,000
0.05x = 49,000
x = (49,000)/(0.05)
x = 980,000
----------
Check:
If the real estate agent sold $980,000 worth of property, then s/he earned 5% of 980,000 = 0.05*980,000 = 49,000 dollars in commission.
The total salary for the year is 21,000+49,000 = 70,000 dollars. The answer is confirmed.
Help me with this please
The correct option is the first one, (1.176*10¹) is 14.7 times larger than (8*10⁻¹)
How many times larger is the first number than the second number?Here we want to see how many times larger is (1.176*10¹) larger than (8*10⁻¹), we can see that both numbers are in scientific notation.
To check that, we just need to take the quotient between the two numbers, we will get:
(1.176*10¹)/(8*10⁻¹) = (1.176/8)*(10¹/10⁻¹)
(1.176/8)*(10¹/10⁻¹) = (1.176/8)*(10¹⁻⁽⁻¹⁾) = (1.176/8)*10² = 0.147*10²
Now, returning to standard notation, we can rewrite:
0.147*10² = 14.7
The correct option is the first one, (1.176*10¹) is 14.7 times larger than (8*10⁻¹)
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Rewrite literal equations.
Solve for m:
e=mc squared.
Answer:
m = e/c
Step-by-step explanation:
The 10th term of arithmetic sequence is three and common difference is three find the third term
Answer:
-18
Step-by-step explanation:
From 3 to 10th term is 7 d's ( d = common difference)
3 - 7d = third term
3 - 7(3) = -18
Jorge Rodriguez earns an annual salary of $48,000. What are his weekly wages?
Answer:
923.08
Step-by-step explanation:
48000/52 weeks
Answer:
923.08
Step-by-step explanation:
There are 52.1429 weeks in a year, so divide.
PLEASE HELP (at least c)
A machinist is required to manufacture a circular metal disk with area 715cm squared
. Give your answers in exact form. Do not write them as decimal approximations.
a) What radius, x , produces such a disk?
b) If the machinist is allowed an error tolerance of ±5cm2 in the area of the disk, how close to the ideal radius in part (a) must the machinist control the radius?
c) Using the ε / δ definition of a limit, determine each of the following values in this context:
f(x)=
a=
L=
ε=
δ=
The 715 cm² area of the disc and the ±5 cm² error tolerance, gives;
a) x = √(715/π) cm
b) The range for the radius is; [√(710/π) cm, √(720/π) cm]
c)
f(x) = π•x²
L = 715 cm²
E = 5 cm
d = √(5/π) cm
How can the variables in the [tex] \epsilon / \delta [/tex] definition of limits be found?Area of the circular metal disk = 715 cm²
a) Required; The disk radius
Let A represent the area of the disk and let x represent the radius, we have;
A = π•x²
Therefore;
x = √(A/π)
Which gives;
x = √(715/π) cm
b) Allowed area error tolerance = ± 5 cm²
The allowed range of values for the area is therefore;
710 ≤ A ≤ 720Which gives;
√(710/π) ≤ x ≤ √(720/π)
c) From the [tex] \epsilon / \delta [/tex] definition of limits, we have;
[tex] \lim\limits_{x → √(715/π)} f(x) = 715 [/tex]
Which gives;
f(x) = A = π•x²
L = 715
|f(x) - L| < E = 5 cm
|x - √(715/π)| < d = √(5/π)
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The table shows the amount a restaurant is donating to a local school based on various dinner bills. Is the amount of donation proportional to the dinner bill? If so, what would be the donation for a dinner bill of $50? If not, explain.
The ratio of the donation to the bill in a table from a similar question is constant, which gives;
The amount donated is proportional to the dinner billIf the dinner bill is $50, the amount donated will be $9How can a professional relationship between the variables be established?The possible values in the table as obtained from a similar question are as follows;
Dinner Bill ($) Donation ($)
25 4.50
30 5.40
35 6.30
40 7.20
Let B represent the dinner bill, and let D represent the donation.
The amount of donation is proportional to the dinner bill if each corresponding value of D/B is constant.
Checking gives;
4.5/25 = 5.4/30 = 6.3/35 = 7.2/40 = 9/50
Which gives;
D/B = 9/50
D = 9/50 × BTherefore
The amount donated is proportional to the dinner billIf the dinner bill is $50, we have;
B = 50
Which gives;
D = 9/50 × 50 = 9
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A basketball player's free throw percentage is 82.5%, or 0.825.
Write this as a fraction.
A. Identify the place value of the last digit in the terminating
decimal. Use this to determine the denominator of the
fraction. The digits to the right of the decimal point are
the numerator of the fraction.
0.825 = 825
Answer:
The 5 is in the thousandths place.
825/1000
Step-by-step explanation:
Simplified this would be 33/40
825/1000 Divide the top and bottom by 25
Evaluate Piecewise Functions, please help asap! Thank you!
Answer:
4, -1, 5, -2
Step-by-step explanation: