You bought:
1 notebook
4 eraser
Total Cost = 25.
Now, given Notebook = $5, so
25 - 5 = 20 dollars are left for [4 erasers]
So, each eraser would cost:
20/4 = 6 dollars
Thus,
Each Eraser Cost = $6
Calculating number of periods?How long will an initial bank deposit of $10,000 grow to $23,750 at 5% annual compound interest?
For an initial amount P with an annually compounded interest rate r, after t years the total amount A is is given by:
[tex]A=P(1+r)^t[/tex]Then we have:
[tex]\begin{gathered} \frac{A}{P}=(1+r)^t \\ \ln\frac{A}{P}=t\ln(1+r) \\ t=\frac{\ln\frac{A}{P}}{ln(1+r)} \end{gathered}[/tex]For P = $10,000, A = $23,750 and r = 0.05, we have:
[tex]t=\frac{\ln\frac{23750}{10000}}{\ln(1+0.05)}\approx17.73\text{ years}[/tex]Weights of 2-year-old girls are normally distributed with a mean of 253 lbs, and a standarddeviation of 1.12 lbs. According to this information, what weight would be the 33rd percentile? You must
We have here a case of a normally distributed variable. We can solve this kind of problem using the standard normal distribution, and the cumulative standard normal table (available in any Statistic Book, or on the internet).
We have that we can find z-scores to normalized the situation, and then, using the cumulative standard normal table, we can find the percentile. Then, we have:
[tex]z=\frac{x-\mu}{\sigma}[/tex]In this case, we need to find the raw value, x. We need to find a z-score that represents that before it there are 33% of the cases for this distribution: in this case, the value for z is approximately equal to z = -0.44.
Now, we have the mean (253 lbs), and the standard deviation (1.12 lbs):
[tex]-0.44=\frac{x-253}{1.12}[/tex]And now, we can determine the value, x, which is, approximately, the 33% percentile of this normal distribution:
1. Multiply by 1.12 to both sides of the equation:
[tex]1.12\cdot(-0.44)=\frac{1.12}{1.12}\cdot(x-253)\Rightarrow-0.4928=x-253[/tex]2. Add 253 to both sides of the equation:
[tex]-0.4928+253=x-253+253\Rightarrow252.5072=x\Rightarrow x=252.5072[/tex]Therefore, the weight that would be the 33rd percentile, is, approximately, x= 252.5072 or 252.51lbs (rounding to the nearest hundredth).
1 pointQuestion 5: Which one is NOT a correct description of these angles? *119BThey create a right angle.They are adjacent angles.UΟ Ο Ο ΟO They are complementary angles.O They are supplementary angles.
SOLUTION:
The one that is not a correct description of these anles is tption D. (They are supplementary angles)
EXPLANATION:
Two angles are said to be supplementary if they add up to be 180 and considering the sum of these angles which is 90 (right angle)
this temperature to Fahrenheil. 1.3 If 1 cm'- 1 ml and 1 000 cm -1 4. Determine the following: 1.3.1 How many cm' are in 875 ? 1.3.2 How many t are there in 35,853 cm'?
We will solve it as follows:
1.3.1: We transform liters to cubic centimeters:
[tex]x=\frac{875\cdot1000}{1}\Rightarrow x=875000[/tex]So, there are 875 000 cubic centimeters.
1.3.2: We transfrom cubic centimenters into liters:
[tex]x=\frac{1\cdot35853}{1000}\Rightarrow x=35.853[/tex]So, there are 35.853 liters.
please help! I don't need a huge explanation I was just wondering if my answer is right
In the expression, there are 3 terms so polynomial is trinomial.
In trinomial the highest degree of term
[tex]10y^5[/tex]is 5. So degree of the polynomial is 5.
Anwer:
Trinomial
Degree is 5.
I need to find the composite function with these two equations. I also need to find the domain.
Recall that:
[tex](f\circ f)(x)=f(f(x)).[/tex]Therefore:
[tex](f\circ f)(x)=f(\sqrt[]{x+2})=\sqrt[]{\sqrt[]{x+2}+2}.[/tex]Now, the above function is well defined as long as x+2 remains positive, therefore, it is well defined as long as x is greater or equal to -2.
Answer: The domain is:
[tex]\lbrack-2,\infty).[/tex]The composition is:
[tex](f\circ f)(x)=f(\sqrt[]{x+2})=\sqrt[]{\sqrt[]{x+2}+2}.[/tex]which of the following is equivalent to the expression i^41?
The Solution:
Given:
[tex]i^{41}[/tex]Required:
Find the equivalent of the given expression.
[tex]i^{41}=i^{40}\times i^1=i[/tex]Answer:
[option A]
Simple Interest Practice P5(A)-2135-7-MATH / Simple Interest 2. What was the original amount deposited on an account with a total amount of $80 in the account after 8 years with a 2% interest rate?
The formula to use for solving simple interest rate problems is:
[tex]i=\text{Prt}[/tex]Where
i is interest accumulated
P is the initial, or principal, amount
r is the rate of interest [in decimal]
t is the time
Given,
Total amount in account is 80 [principal plus interest]
rate is 2%
time is 8 years
Let's write:
[tex]\begin{gathered} 80=P+\text{Prt} \\ 80=P(1+rt) \\ 80=P(1+(0.02)(8)) \\ 80=P(1+0.16) \\ 80=P(1.16) \\ P=\frac{80}{1.16} \\ P=68.9655 \end{gathered}[/tex]The amount in the account was around $68.97
simplified (-4+2i)(3-9i)
6 + 42i
Expanding the expression, by using FOIL acronym
(-4+2i)(3-9i)
-12+36i+6i-18i²
-12 +42i -18i² Remember i²= -1
-12 + 42i -18(-1)
-12 + 42i +18
6 + 42i
2) Now we have that complex number in the form a +bi
-
Use a calculator to find θ to the nearest tenth of a degree, if 0° < θ < 360° and sin θ = -0.9945
Solution:
Given:
[tex]\sin \theta=-0.9945[/tex]Using the inverse trigonometric function,
[tex]\begin{gathered} \theta=\sin ^{-1}(-0.9945) \\ \theta=-83.988 \\ \theta\approx-84.0^0\text{ to the nearest tenth} \end{gathered}[/tex]However, since the sine of the angle is negative, it shows that the angle is in the third or fourth quadrant.
Hence, the possible values of the angle are,
[tex]\begin{gathered} \theta=-84+360=276.0^0 \\ \theta=180-(-84)=264.0^0 \end{gathered}[/tex]Therefore, the value of the angle to the nearest tenth of a degree is 264.0 degrees or 276.0 degrees.
Galina runs a bakery, where she sells packages of 4 dozen cookies for $24.96 per package. The amount of money she makes by selling x packages is represented by the function f(x)=24.96x, and her cost for making each package is g(x)=0.04x2+4x+71.If profit is equal to sales minus cost, which function represents her profit, p?
Answer:
p(x) = f(x) - g(x) = -0.04x² + 20.96x - 71
Explanation:
The sales are given by f(x) = 24.96x and the cost are represented by g(x) = 0.04x² + 4x + 71.
Then, the profit is equal to
p(x) = f(x) - g(x)
p(x) = 24.96x - (0.04x² + 4x + 71)
p(x) = 24.96x - 0.04x² - 4x - 71
p(x) = -0.04x² + 20.96x - 71
Therefore, the answer is
p(x) = f(x) - g(x) = -0.04x² + 20.96x - 71
(3,-4); m=6 write an equation in slope intercept form for the line through the given point with the given slope
y= 6x-22
Explanation
Step 1
Let
slope=6
Point (3,-4)
to find the equation in slope intercept form use
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ \text{where} \\ (x_0,y_0)\text{ are the coordinates of the known point} \end{gathered}[/tex]Step 2
Replace,
[tex]\begin{gathered} \text{the know point = (3,-4) so} \\ y-y_0=m\left(x-x_0\right) \\ y-(-4)=6(x-3) \\ y+4=6x-18 \\ \text{substract 4 in both sides} \\ y+4-4=6x-18-4 \\ y=6x-22 \end{gathered}[/tex]I hope this helps you
how to solve 7.-4y=48
solve for y
[tex]\begin{gathered} 7-4y-7=48-7 \\ -4y=41 \\ -\frac{4y}{-4}=\frac{41}{-4} \\ y=-\frac{41}{4} \end{gathered}[/tex]Answer:
y = -41/4 or 10.25
Step-by-step explanation:
7 - 4y = 48
Move 7 across the equals sign to make y stand alone
-4y = 48 - 7
= 41
Divide both sides by the coefficient of y, which is -4
-4y/4 = 41/4
y = -41/4 or 10.25
A principal of S2400 is invested at 8.75% interest compounded annually How much will the investment be worth after 7 years?
Explanation
The question wants us to determine the amount $2400 will yield after 7 years if compounded annually at a rate of 8.75%
To do so, we will use the formula:
[tex]\begin{gathered} A=P(1+r)^t \\ where \\ P=\text{ \$2400} \\ r=8.75\text{ \%=}\frac{8.75}{100}=0.0875 \\ t=7 \end{gathered}[/tex]Thus, if we substitute the values above we will have
[tex]\begin{gathered} A=\text{ \$}2400(1+0.0875)^7 \\ A=\text{ }\$2400\lparen1.0875\rparen^7 \\ A=\text{ \$2400}\times1.79889 \\ A=\text{ \$4317.34} \end{gathered}[/tex]Therefore, after 7 years, the investment will be worth $4317.34
In a direct variation, y = 18 when x = 6. Write a direct variation equation that shows therelationship between x and yWrite your answer as an equation with y first, followed by an equals signSubmit
Compare the ratios in Table 1 and Table 2. Table 1 5 6 10 9 15 12 20 Table 2 7 10 20 21 30 28 40 Which statements about the ratios are true? Check all that apply. The ratio 3:5 is less than the ratio 7:10. Save and Exit Nexd Mark this and return
Table 1
3:5 , 6 : 10 , 9 :15 , 12 : 20
Table 2
7 : 10 , 14 : 20 , 21 : 30 , 28 : 40
Notice that all ratios in each table are equal. Additionally, since:
[tex]\frac{3}{5}=\frac{6}{10}[/tex]And 6<7, then the ratio 3:5 is less than the ratio 7:10.
Therefore, all ratios in table 1 are less than all ratios in table 2.
Some specific comparisons between ratios may apply as well. For example:
The ratio 14:20 (table 2) is greater than the ratio 9:15 (table 1).
Write a similarity relating the two triangles in each diagram.
We know by the figure that angles
A random sample of n= 100 observations is selected from a population with u = 30 and 6 = 21. Approximate the probabilities shown below.a. P(x228) b. P(22.1sxs 26.8)c. P(xs 28.2) d. P(x 2 27.0)Click the icon to view the table of normal curve areas.a. P(x228)(Round to three decimal places as needed.)
Problem Statement
We have been given random sample of 100 observations and we have been asked to find the probabilities of getting certain observed values given the population mean of 30 and a standard deviation of 21.
Method
To solve this question, we need to:
1. Find the z-score of the observations. The formula for calculating the z-score is:
[tex]\begin{gathered} z=\frac{X-\mu}{\sigma} \\ \text{where,} \\ X=\text{ The observed value} \\ \mu=\text{population mean} \\ \sigma=\text{ standard deviation} \end{gathered}[/tex]2. Convert the z-score to probability using the z-score table.
Implementation
Question A
1. Find the z-score of the observations.:
[tex]\begin{gathered} X\ge28 \\ \mu=30,\sigma=21 \\ z\ge\frac{28-30}{21} \\ z\ge-\frac{2}{21} \\ \\ \therefore z\ge-0.0952 \end{gathered}[/tex]2. Convert the z-score to probability using the z-score table.:
Using a z-score calculator, we have the probability to be:
[tex]P(z\ge-0.0952)=0.037938[/tex]This probability is depicted in the drawing below:
If the mean is represented by 0 and the right-hand side of 0 has a probability of 0.5, then the probability of getting greater than or equal to 28, is the addition of the probability 0.037938 gotten above with the 0.5 on the right-hand side of zero.
Thus, the answer to Question A is:
[tex]\begin{gathered} P(X\ge28)=0.037938+0.5=0.537938 \\ \\ \therefore P(X\ge28)\approx0.538\text{ (To 3 decimal places)} \end{gathered}[/tex]
Question B:
[tex]undefined[/tex]The size of a population of bacteria is modeledby the function P, where P(t) gives thenumber of bacteria and t gives the number ofhours after midnight for 0 < t < 10. Thegraph of the function P and the line tangent toP at t= 8 are shown above. Which of thefollowing gives the best estimate for theinstantaneous rate of change of P at t = 8?
Answer: The graph of the P(t) has been provided, we have to find the instantaneous slope of P(t) at t = 8:
[tex]Slope=m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]Therefore we need two y values and two x values, which can be obtained as follows:
[tex]\begin{gathered} t=8 \\ \\ \therefore\Rightarrow \\ \\ x_1=t_1=8-0.1=7.9 \\ \\ y_1=P(t_1)=P(7.9) \\ \\ x_2=t_2=8+0.1=8.1 \\ \\ y_2=P(t_2)=P(8.1) \\ \\ \therefore\rightarrow \\ \\ Slope=\frac{P(8.1)-P(7.9)}{t_2-t_1}\rightarrow(1) \\ \end{gathered}[/tex]Equation (1) corresponds to the third, option, therefore that is the answer.
A worker is getting a 3% raise. His current salary is $35,868. How much will his raise be?
Hello there. To solve this question, we'll simply have to multiply the percent and the salary to find how much will the raise of the worker.
Given his salary: $35,868 and knowing he'll get a 3% raise, we make:
3/100 * 35,868
107,604/100 = 1,07604
Rounding up the answer to the nearest tenth, we have that his raise will be $1,1.
ZABC is a right angle.А2197032°Bс
Given that angle ABC is a right angle, then:
21° + x° + 32° = 90°
x = 90° - 21° - 32°
x = 37°
This corresponds to the option: subtract 21° and 32° from 90°, x = 37°.
x to the 9th power times x to the 5 power
Which one of the following simplifications is incorrect?
Group of answer choices
sqrt(48x^4)*root(4)(16x^10)=8x^4root(4)(3x^2)
sqrt(4x)*sqrt(12x^8)=4x^4sqrt(3x)
sqrt(x^3)*sqrt(xy^4)= x^2y^2
root(3)(64)*sqrt(18)=12sqrt(2)
After simplification, the option 2, [tex]\sqrt{4x}\times \sqrt{12x^8}=4x^4\sqrt{3x}[/tex] is correct option.
In the given question,
We have to find which simplifications is incorrect.
Option 1: [tex]\sqrt{48x^4}\times\sqrt[4]{16x^{10}}=8x^4\sqrt[4]{3x^2}[/tex]
To check whether the given expression is true or not simplifying the left hand side expression.
We simplifying the left hand side by writing it as
[tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}=\sqrt{16\times3\times (x^2)^2}\times\sqrt[4]{(2)^4\times x^{8}\times x^2}[/tex]
[tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}=\sqrt{(4)^2\times3\times (x^2)^2}\times\sqrt[4]{(2)^4\times (x^{2})^4\times x^2}[/tex]
Now simplifying the roots
[tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}=4\times x^2\times\sqrt{3}\times2\times x^2\times\sqrt[4]{ x^2}[/tex]
Now writing it in a simplified form
[tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}=8\times x^{2+2}\times\sqrt{3}\sqrt[4]{ x^2}[/tex]
[tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}=8x^{4}\sqrt{3}\sqrt[4]{ x^2}[/tex]
Hence, the simplified form of [tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}[/tex] is [tex]8x^{4}\sqrt{3}\sqrt[4]{ x^2}[/tex].
So the given statement is wrong.
Option 2. [tex]\sqrt{4x}\times \sqrt{12x^8}=4x^4\sqrt{3x}[/tex]
To check whether the given expression is true or not simplifying the left hand side expression.
We simplifying the left hand side by writing it as
[tex]\sqrt{4x}\times \sqrt{12x^8}=\sqrt{(2)^2\times x}\times \sqrt{3\times4\times (x^4)^2}[/tex]
[tex]\sqrt{4x}\times \sqrt{12x^8}=\sqrt{(2)^2\times x}\times \sqrt{3\times(2)^2\times ({x^4})^2}[/tex]
Now simplifying the roots
[tex]\sqrt{4x}\times \sqrt{12x^8}=2\sqrt{x}\times 2\times x^4\times\sqrt{3}[/tex]
[tex]\sqrt{4x}\times \sqrt{12x^8}=4x^4\sqrt{3x}[/tex]
Hence, the simplified form of [tex]\sqrt{4x}\times \sqrt{12x^8}[/tex] is [tex]4x^4\sqrt{3x}[/tex].
Hence, the option 2 is correct.
Since we get the write answer so we haven't solve the next option.
The next 2 options also can be solved in the way that we use in previous option to solve.
So the option 2 [tex]\sqrt{4x}\times \sqrt{12x^8}=4x^4\sqrt{3x}[/tex] is correct option.
To learn more about the simplification of expression link is here
https://brainly.com/question/14575743
#SPJ1
In the coordinate plane the vertices of angle RST are R(6,-1) S(1,-4) and T(-5,6). Prove that angle RST is a right triangle. State the coordinates of point P such that quadrilateral RSTP is a rectangle. Prove that your quadrilateral RSTP is a rectangle.
We are given coordinates of three points RST and are asked to prove that it forms a Right Triangle.
We kn
2(x+4)=150+ (-2) can u solve
Given equation:
[tex]2(x+4)\text{ = 150 + (-2) }[/tex]Open the bracket:
[tex]\begin{gathered} 2x\text{ + 8 = 150 - 2} \\ 2x\text{ + 8 = 148} \end{gathered}[/tex]Collect like terms:
[tex]\begin{gathered} 2x\text{ = 148 - 8} \\ 2x\text{ = 140} \end{gathered}[/tex]Divide both sides by 2:
[tex]\begin{gathered} \frac{2x}{2}\text{ = }\frac{140}{2} \\ x\text{ = 70} \end{gathered}[/tex]Answer:
x = 70
What is 6 x 1/4 in the simplest form
Answer:
[tex]6\cdot\frac{1}{4}=\frac{3}{2}[/tex]Step-by-step explanation:
Divide 6 by 4:
[tex]6\cdot\frac{1}{4}=\frac{6}{4}=\frac{3}{2}[/tex]Round $43,569.14 the nearest dollar
To find:
Round $43,569.14 the nearest dollar
Solution:
The number after the decimal is less than 50. So, the amount $43,569.14 rounded to the nearest dollar is $43,569.
Thus, the answer is $43569.
Val measures the diameter of a ball as 14 inches. How many cubic inches of air does this ball hold, to thenearest tenth? Use 3.14 forn.The ball holds aboutcubic inches of air.
we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\cdot\pi\cdot r^3[/tex]In this problem we have
r=14/2=7 in ----> the radius is half the diameter
pi=3.14
substitute the given values
[tex]\begin{gathered} V=\frac{4}{3}_{}\cdot(3.14)\cdot(7^3) \\ V=1,436.0\text{ in\textasciicircum{}3} \end{gathered}[/tex]answer is 1,436.0 cubic incheshow to solve this problem
Let
x -----> number of students that preferred vanilla cupcakes
y ----> number of students that preferred chocolate
we know that
x+y=750 -----> equation A
and
2/5=x/y
x=(2/5)y ------> equation B
substitute equation B in equation A
(2/5)y+y=750
solve for y
(7/5)y=750
y=750*5/7
y=536
find the value of x
x=(2/5)(736)
x=214
therefore
the answer is 214 students preferred vanilla cupcakesDirections: Solve the problems below on a separate sheet of paper. You will use a variety of strategies (drawingpictures, building multiple towers, area models, algorithms, and partial products method for division) to solvethe problems. Please submit your answer by writing a complete sentence that expresses the final answer.1. Books are on sale for $8. Peter has $25 in his wallet. How many books can he buy?
books are on sale for $8
Peter has $25 dollar in his wallet
let the numbers of book be x
so,
if a book cost $8
x number of books cost $25
lets put it into mathematical statement
1 = $8
x = $25
lets cross multiply
1 X 25 = 8 X x
25 = 8x
8x = 25
divide both sides by 8
8x/8 = 25/8
x = 25/8
x = 3.125
x = 3 (approximately)
recall, we say x is the numer of books
so,
the number of books peter can by with is $25 in his wallet is 3atement
1