We have the following:
Using the data above, how many people would be expected to live in Japan if the proportion of people to square miles were the same in Japan as in the United States?
If the factors of a polynomial are x-4 and x-5, which value of x make that polynomial 0?
Given a polynomial of factors below,
[tex]f(x)=(x-4)(x-5)[/tex]To find the values of x at f(x) = 0, substitute for f(x) into the equation above,
[tex]\begin{gathered} (x-4)(x-5)=0 \\ x-4=0 \\ x=4 \\ x-5=0 \\ x=5 \\ x=4\text{ and 5} \end{gathered}[/tex]C is the right option
one to the sixth power
sixth power is the exponent of 1.
To obtain the result, multiply 1 by itself 6 times:
1x1x1x1x1x1=1
1^6 = 1
Which of the following choices best describes the expression 2/3 (3/4x - 3/2)A: equivalent to 1/2x - 1B: equivalent to x - 1/2C: not equivalent to 1/2x - 1 or x - 1/2
distributing:
[tex]\begin{gathered} \frac{2}{3}\cdot\frac{3}{4}x-\frac{2}{3}\cdot\frac{3}{2}= \\ =\frac{1}{2}x-1 \end{gathered}[/tex]the expression is equivalent to 1/2x - 1
Figure WXYZ is a rhombus.
Complete the statements below about angle X and angle Y.
x + z = 180 (Because it is a Rhombus and angles across from each other equal 180)
x = 97
y = 83
A bank features a savings account that has an annual percentage rate of 4.1 % with interestcompounded monthly. Zach deposits $3,000 into the account.How much money will Zach have in the account in 1 year?Answer = $Round answer to the nearest penny.What is the annual percentage yield (APY) for the savings account?%. Round to the nearest hundredth of a percent.APY=
It is given that the amount invested is $3000 with an interest rate of 4.1% compounded monthly.
It is required to find the amount in 1 year and the annual percentage yield.
The formula for Compound Interest is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where:
• A= final amount
,• P= amount invested initially
,• r= interest rate
,• n= number of times interest is compounded in a year
,• t= number of years
Substitute P=3000, r=4.1%=0.041, n=12 (compounded monthly), and t=1 into the formula:
[tex]A=3000(1+\frac{0.041}{12})^{12(1)}\approx\$3125.34[/tex]The formula for the Annual Percentage Yield is given as:
[tex]APY=(1+\frac{r}{n})^n-1[/tex]Substitute r=0.041, n=12 into the formula:
[tex]APY=(1+\frac{0.041}{12})^{12}-1\approx0.0418=4.18\%[/tex]Answers:
Amount = $3125.34
APY = 4.18%
Write an nth term of arithmetic sequence -5,-2,1,4
Henry started the school year with 3 packages of pencils. He used 4 pencils each week. If a school year is 36 weeks, during which week will he run out of pencils?
We know that
• Henry started with 3 packages of pencils.
,• He used 4 pencils each week.
,• The school year is 36 weeks.
Assuming that each package of pencils has 8, he would have
[tex]3\cdot8=24[/tex]Henry has 24 pencils in total. But he uses 4 pencils each week, so let's divide
[tex]\frac{24}{4}=6[/tex]Therefore, Henry will run out of pencils in week 6.The quotient of forty three abs a number m
Explanations:
Answer:
In 2 years, Ariel wants to buy a bicycle that costs 1,000.00. If she opens a savings account that earns 9%interest compounded quarterly, how much will she have to deposit as principal to have enough money in 2 years to buy the bike?
Let's first list down the information given in the scenario:
a.) In 2 years ariel wants to buy a bicycle that costs 1,000.00
b.) She opens a savings account that earns 9% interest compounded quarterly
Question: How much will she have to deposit as principal to have enough money in 2 years to buy the bike?
To be able to determine the principal amount Ariel will need to deposit, let's use this formula for Compound Interest:
[tex]\text{ A = }P(1\text{ + }\frac{\frac{r}{n}}{100})^{nt}[/tex]Where:
A = Is the final amount/ cost of the bicycle = 1,000
n = Number of times the interest is being compounded = 4
r = Interest rate = 9%
t = No. of periods elapsed/ No. years the principal money be deposited
P = Principal amount/ amount to be deposited
Let's now find the principal amount:
[tex]\text{ A = }P(1\text{ + }\frac{\frac{4}{n}}{100})^{nt}\text{ }\rightarrow\text{ 1,000 = }P(1\text{ + }\frac{\frac{9}{4}}{100})^{4(2)}[/tex][tex]\text{1,000 = }P(1\text{ + }\frac{2.25}{100})^8\text{ }\rightarrow\text{ 1,000 = }P(1\text{ + }0.0225)^8\text{ }\rightarrow1,000=P(1.0225)^8[/tex][tex]\text{ P = }\frac{1,000}{(1.0225)^8}\rightarrow\text{ P = }\frac{1,000}{1.19483114181}[/tex][tex]\text{ P = 836.93835 }\cong\text{ 836.94}[/tex]Therefore, Ariel must deposit a principal amount of 836.94 for her to be able to buy the bike in 2 years.
A rectangle or televisions length is 3 inches more than twice its width the perimeter of the television is 144 inches what is the width of the television
The width of the television is 23 in.
What is rectangle?A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles. The opposite sides of a rectangle are equal and parallel.
Given that, A television's length is 3 inches more than twice its width the perimeter of the television is 144 inches
Perimeter of a rectangle = 2(length+width)
According to question,
l = 3+2w
Therefore,
Perimeter = 2(w + 3+2w) = 144
3w + 3 = 72
3w = 69
w = 23
Hence, The width of the television is 23 in.
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6. A basketball coach purchases bananas for the players on his team. Thetable shows total price in dollars. P. of n bananas. Which equation couldrepresent the total price in dollars for n bananas?number of bananastotal price in dollars74.13B47295.31105.90O P = 0.596O P = 5.90-0.59O P = 590//O Pan0.59
,Given the table of values we can find the equation that will represent the total price in dollars for the bannana by using the equation of a line.
Explanation
The equation of a line is given as
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1}[/tex]We can then remodel the equation above to fit the given table of values. This would give;
[tex]\frac{p_2-p_1}{n_2-n_1}=\frac{p-p_1}{n-n_1}[/tex]Next, we will pick some random points to represent the variables in the equation
[tex]\begin{gathered} p_1=4.13;p_2=4.72 \\ n_1=7;n_2=8 \end{gathered}[/tex]Then we insert the variables into the formula.
[tex]\begin{gathered} \frac{4.72-4.13}{8-7}=\frac{p-4.13}{n-7} \\ \frac{0.59}{1}=\frac{p-4.13}{n-7} \\ p-4.13=0.59(n-7) \\ p-4.13=0.59n-4.13 \\ p=0.59n+4.13-4.13 \\ p=0.59n \end{gathered}[/tex]Answer: The equation is given as p = 0.59n
The function fx) = 110(1.004)* models the population of rabbits, inthousands, in a state x years after 1990. What is the approximatepopulation of the rabbits in 2012?A 115,000aora8. 120,000Input ->-1990C 310,085,000aayo338,550,000TE
The following function models the population of rabbits, in thousands, in a state x years after 1990.
[tex]f(x)=110\cdot(1.004)^x[/tex]What is the approximate population of rabbits in 2012?
Count the number of years after 1990 to 2012.
That's 22 years so we have x = 22
Let us substitute x = 22 into the above function
[tex]\begin{gathered} f(22)=110\cdot(1.004)^{22} \\ f(22)=110\cdot(1.091796) \\ f(22)=120.09756 \end{gathered}[/tex]That is approximately 120 thousands or 120,000
Change 0.005 to equivalent fraction. ANS. _________.
You can identify that the following is a Decimal number:
[tex]0.005[/tex]In order to convert a Decimal number to an Equivalent fraction, you can follow the steps shown below:
1. You need to write the Decimal number 0.005 as the numerator of the fraction and the denominator must be 1:
[tex]=\frac{0.005}{1}[/tex]2. Now you can multiply the numerator and the denominator by 1,000, in order to remove the decimal places of the numerator (notice that it has three decimal places):
[tex]=\frac{0.005\cdot1,000}{1\cdot1,000}=\frac{5}{1,000}[/tex]3. Finally, you have to reduce the fraction. Notice that you can divide the numerator and the denominator by 5. Then, you get:
[tex]=\frac{1}{200}[/tex]The answer is:
[tex]\frac{1}{200}[/tex]If logx = -5, what is x?A. -0.00001B. 0.00001C. 0.00005D. -0.00005
Hello there. To solve this question, we have to remember some properties about logarithms.
Given the logarithmic equation:
[tex]\log(x)=-5[/tex]We want to determine the value of x.
For this, remember the following rule:
[tex]\text{ For }a,\,b\in\mathbb{R}^+\text{ and }b\cancel{=}1,\text{ }\log_b(a)=c\Rightarrow a=b^c[/tex]Such that, in this case, the logarithm has base 10, therefore
[tex]x=10^{-5}[/tex]This power of 10 can be easily found :
[tex]x=0.00001[/tex]It has 5 digits after the decimal place, being the fifth digit a 1.
This is the answer contained in the option B.
Use elimination to solve eachsystem of equations3x - y = -56x - 2y = 8
Solution
We are given the pair of simultaneous equation
[tex]\begin{gathered} 3x-y=-5\ldots\ldots\ldots\ldots\ldots(1) \\ 6x-2y=8\ldots\ldots\ldots\ldots\ldots\ldots(2) \end{gathered}[/tex]we solve using elimination method
equation (1) x 2
[tex]\begin{gathered} 6x-2y=-10\ldots\ldots\ldots\ldots\ldots(1) \\ 6x-2y=8\ldots\ldots\ldots\ldots\ldots\ldots(2) \end{gathered}[/tex]Equation (2) - equation (1)
We have
[tex]\begin{gathered} (6x-6x)+(-2y+2y)=8-(-10) \\ 0=18 \end{gathered}[/tex]Which is impossible because 0 (zero) can never be equal to 18
Therefore, the simultaneous is not consistent or it degenerate and thus, there is no solution
A survey was given to a random sample of 1750 voters in the United States to askabout their preference for a presidential candidate. Of those surveyed, 28% of thepeople said they preferred Candidate A. Determine a 95% confidence interval for thepercentage of people who prefer Candidate A, rounding values to the nearest tenth.
A 95% confidence interval for the percentage of voters who choose Candidate A is (0.3,0.3).
Given that,
1750 American voters were chosen at random to participate in a poll on their presidential candidate preferences. 28% of those polled indicated they favored Candidate A.
We have to find determine a 95% confidence interval for the percentage of voters who choose Candidate A.
We have a sample size=1750
28% preferred candidate A.
Margin of error = Z[tex]\sqrt{P(1-P)/n}[/tex]
Where, z=1.96 at 95%
P=0.28
n=1750
ME = 1.96[tex]\sqrt{0.28(1-0.28)/1750}[/tex]
ME = 1.96[tex]\sqrt{0.28(0.72)/1750}[/tex]
ME = 1.96[tex]\sqrt{0.2016/1750}[/tex]
ME = 1.96[tex]\sqrt{0.000152}[/tex]
ME = 0.021
For confidence interval is
CI= 0.28±0.021
CI= (0.28+0.021,0.28-0.021)
CI = (0.301, 0.259)
For the nearest tenth,
CI = (0.3,0.3)
Therefore, A 95% confidence interval for the percentage of voters who choose Candidate A is (0.3,0.3).
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Points A(-2,-3),B(-2,4),and C(3,6) are three vertices of parallelogram ABCD. Opposite sides of a parallelogram have the same length. Draw the parallelogram in the coordinate plane and label the coordinates of the fourth point.
Given:
Points A(-2,-3),B(-2,4),and C(3,6) are three vertices of parallelogram ABCD.
As we know, the opposite sides of the parallelogram are parallel and congruent
To draw the parallelogram, we will draw the points and connect the sides
AB, AC, and BC
then, draw two lines parallel to AB from C and BC from A, the intersection will give the point D
The graph of the parallelogram will be as shown in the following picture
As shown the coordinates of the fourth point D = (3, -1)
I can send photo, which expressions are equivalent to 18x - 6? select all that apply
ANSWER:
The equivalent expressions are
[tex]\begin{gathered} 6\cdot(3x-1) \\ 2\cdot(9x-3) \\ 16.4x-6+1.6x \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]18x-6[/tex]If we factor we have:
[tex]\begin{gathered} 6\cdot(3x-1) \\ 2\cdot(9x-3) \end{gathered}[/tex]if we separate the value we have
[tex]16.4x-6+1.6x=18x-6[/tex]Myra has a remote control toy boat.she runs the toy boat on a lake at a constant speed. The graph of a function representing the toy boats distance, y , in feet , from the shore of the lake after X seconds includes the points (1,8) and (1.5, 10.1)
Given
the constant speed.
the points 1 (1,8)
Point 2 (1.5, 10.1)
Procedure
y=mx+b
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ m=\frac{8-10.1}{1-1.5} \\ m=\frac{-2.1}{-0.5}=4.2 \end{gathered}[/tex][tex]\begin{gathered} y=mx+b \\ 8=4.2(1)+b \\ 8-4.2=b \\ 3.8=b \end{gathered}[/tex]the equation is: y=4.2x+3.8
The statements that are true are:
B. The rate of the change of the function is 4.2
D. The toy boat's speed on the lake is 4.2 feet per second
E. the toy boat is originally 3.8 feet from the shore of the lake
Darnell is running a short experiment on probability. He chooses one block at random from each of the two groups shown below. What is the probabilitythat he will choose a Z from Group 1 and a T from Group 2?
Answer
P(Z and T)= 8/121
Explanation
The total out come in group 1 = 11
The number of z = 4
Probability of picking a Z in group 1 = 4 / 11
Group 2
The total out comes = 11
Number of T outcomes = 2
Probability of picking a T = 2/11
Therefore, P( Z and T) = P(Z) x P(T)
P(Z and T) = P(Z) x P(T)
P(Z) = 4/11
P(T) = 2/11
P(Z and T) = 4/11 x 2/11
P(z and T) = 8/121
Therefore, the probability of picking a Z and aT is 8/121
A company is making building blocks. What is the length of each side of the block? V=1 ft3 The length of each side is
The length of the block = 1ft.
The volume of the length of the side of blocks = 1ft^3
The 3 on the one feet means raised to power 3.
So, 1ft raised to power 3:
[tex]1ft^3\text{ = 1ft }\times\text{ 1ft }\times\text{ 1ft}[/tex]To get the length, we would assume the block is a cube
The volume of a cube = length^3
1 ft^3 = length^3
[tex]\begin{gathered} \text{cube root both sides:} \\ \sqrt[3]{1ft^3}\text{ = }\sqrt[3]{length^3} \\ \text{length = }\sqrt[3]{(1\text{ft}}\times1ft\times1ft) \\ \text{length = 1ft} \end{gathered}[/tex]Hence, the length of the block = 1ft.
volume= {1}{3} * \pi * r ^{2}* hHELPsolve for H
Explanation
[tex]Volume=\frac{1}{3}\pi r^2h[/tex]Step 1
multiply each side by 3
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h \\ V\cdot3=\frac{1}{3}\pi r^2h\cdot3 \\ 3V=\pi r^2h \end{gathered}[/tex]Step 2
divide both sides by
[tex]\pi r^2[/tex][tex]\begin{gathered} 3V=\pi r^2h \\ \frac{3V}{\pi r^2}=\frac{\pi r^2\text{ h}}{\pi r^2} \\ h=\frac{3V}{\pi r^2} \end{gathered}[/tex]If a normally distributed data set has a mean of81 and a standard deviation of 6, which of thefollowing represents approximately 95% of thedata?
95% of the data is represented as 69 to 93 (option G)
Explanation:Given:
mean of data = 81
standard deviation = 6
To find:
The option that represents 95% of the data
To determine the right option, we will apply the empirical rule (68-95-99.7%):
68% of the data will fall within 1 standard deviation
95% of the data will fall within 2 standard deviation
99.5% of the data will fall within 3 standard deviation
[tex]\begin{gathered} 2\text{ standard deviation is represented as:} \\ \mu\text{ }\pm\text{ 2\sigma} \\ where\text{ \mu = mean, \sigma = standard deviation} \end{gathered}[/tex]substitute the values:
[tex]\begin{gathered} μ\pm2σ\text{ = 81 }\pm\text{ 2\lparen6\rparen} \\ =\text{ 81 }\pm\text{ 12} \\ 81\text{ }\pm\text{ 12 means 81 - 12 , 81 + 12} \\ =\text{ 69, 93} \\ This\text{ means 95\% of the data is represented from 69 to 93 \lparen option G\rparen} \end{gathered}[/tex]Decide whether enough information is given to prove that △RSV≅△UTV. If so, state the theorem you would use.
In the diagram we are given that angle S = angle T
We are given that side SV = side TV
We know that vertical angles are equal so angle RVT = angle UVT
WE have 2 angles and the included side so we can use the ASA Congruence theorem which states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
There is enough information to use the ASA Congruence Theorem.
how many 3/8 are in 3
We can see that there are 24/8 in 3 units, so we have then that there are 8 times 3/8 in 3 units.
So, the answer is there are 8 times.
Donna earns a commission. She makes 3.5% of the amount she sells. Yesterday she sold a $800 recliner. How much was her commission.
Amount sold = $800
Commission = 3.5%
To calculate the commission amount, multiply $800 by the commission percentage in decimal form (divided by 100)
800 x (3.5/100)= 800 x 0.035 = $28
The results of an experiment that Lacey is doing are recorded in the table below.Day Number of Amoeba1 2^1 2. 2^23 2^3How many amoebas will be present on the fourth day?216, 6, 46 and 4 are different answers.
This problem is about geometric sequence, which is a sequence formed by multiplying (or dividing) a constant factor.
In this case, we can observe that each new day has greater power, specifically, its exponent increases by one. This is because each day, the number of amoebas increases by a multiplying factor of 2.
Having said that, we can deduct that the fourth day is going to have a power with exponent 4, because as we said before, each day the exponent increases by 1.
So, the power of the fourth day is
[tex]2^4=16[/tex]Therefore, the right answer is 16, the last choice.Solve the following system of equations. How many solutions are there? x + y = 2 5x + 5y = 10 a) There is no solution. b) There are infinite solutions. c) There is one solution.
we are given the following system of equations:
[tex]\begin{gathered} x+y=2,\text{ (1)} \\ 5x+5y=10,\text{ (2)} \end{gathered}[/tex]Equation (2) can be rewritten dividing by 5 on both sides as:
[tex]\frac{5x}{5}+\frac{5y}{5}=\frac{10}{5}[/tex]Solving the operations:
[tex]x+y=2,\text{ (2)}[/tex]Since equation (2) is the same equation as equation(1), this means that the system has infinite solutions.
The figure below is an isosceles trapezoid:KLIK = 12x - 34IL = 4x - 10X =Blank 1:
From the definition, it must have symmetry in the present figure. It seems to be a vertical line going through the middle of the drawing. From this, we can say that:
[tex]\begin{gathered} IK=JL \\ 12x-34=4x-10 \end{gathered}[/tex]Now, we can solve it.
[tex]\begin{gathered} 12x-34=4x-10 \\ 12x-4x=34-10 \\ 8x=24 \\ x=\frac{24}{8} \\ x=3 \end{gathered}[/tex]