Step 1
Given;
[tex]\begin{gathered} Principal=8201 \\ r=2.47=\frac{2.47}{100}=0.0247 \end{gathered}[/tex]Step 2
State the formula for if interest is compound
[tex]A=P(1+\frac{r}{n})^{nt}[/tex][tex]\begin{gathered} A=8201\times2=\text{ \$}16402 \\ 16402=8201(1+\frac{0.0247}{1})^{1\times t} \\ \frac{16402}{8201}=\frac{8201(1+\frac{0.0247}{1})^{1\times t}}{8201} \\ 2=(1+\frac{0.0247}{1})^t \end{gathered}[/tex][tex]\begin{gathered} 2=(1.0247)^t \\ ln2=tln(1.0247) \\ t=\frac{ln2}{ln(1.0247)}=28.4078031 \\ t\approx28\text{ years} \end{gathered}[/tex]Answer; Using interest compounded yearly the time taken for the amount to double is;
[tex]28\text{ years to the nearest whole number}[/tex]Find the area of the rectangle pictured above .2716= units
Recall that the area of a rectangle is given by: length times width.
We need the picture associated with the question to answer this.
So, we apply the are formula we mentioned above, to obtain the area:
Area = length x width
Area = 27 x 16
Area = 432 square units
So please type 432 in the textbox provided.
Apply your understanding of the number line to complete the missing information in the table
SOLUTION
Given the question in the iamge on the question tab;
Explanation:
(1) The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign. For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5. The absolute value of a number may be thought of as its distance from zero along real number line.
(2) Two numbers are opposites if they have the same absolute value but different signs. Eg: 2 is the opposite of -2, their absolute value is 2.
[tex]Considering\text{ our question;}[/tex]
Final answer:
The circle below is centered at the origin and has a radius of 8. What is itsequation?yO A. x²-√2²=8B. x² + y² = 8C. x² - y² = 64D. x² + y² = 64-1010-10810
Answer: The standard form of the circle equation is:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2\rightarrow(1) \\ \\ \\ \\ (h,k)=(x,y)\rightarrow\text{ Center of the circle} \end{gathered}[/tex]According to the equation (1) we can have the following answer:
[tex]\begin{gathered} r=\text{ 8}\rightarrow r^2=8^2=64 \\ \\ (h,k)=(x,y)=(0,0)\text{ }\rightarrow\text{ Center} \\ \\ \therefore\rightarrow \\ \\ (x)^2+(y)^2=64\text{ }\rightarrow\text{ Option\lparen A\rparen} \end{gathered}[/tex]how do i write these problems in exponential form 9. (qt^3)^7
Answer:
q⁷t²¹
Explanation:
To write it in the exponential form, we will use the following properties
[tex]\begin{gathered} (ab)^x_{}=a^x\cdot b^x \\ (a^x)^y=a^{x\cdot y} \end{gathered}[/tex]Therefore, applying the first property, we get:
[tex](qt^3)^7=q^7\cdot(t^3)^7[/tex]Then, we can apply the second property to get:
[tex](qt^3)^7=q^7\cdot t^{3\cdot7}=q^7t^{21}[/tex]So, the answer is:
q⁷t²¹
Joy needs to mix a 10% fungicide solution with a 30% fungicide solution to create 300 milliliters of 21.33 % solution. How many milliliters of each solution must Joy use?
let the 10% fungicide solution be represented by x mm
then 30% fungicide solution will be represented by 300 mm - x mm
since a solution of 300 millimeters is formed,
Then equation =>
10 % of x + 30% of (300 - x) = 21.33 % x 300
=> 0.1 x + 0.3(300 - x) = 0.2133 x 300
=> 0.1x + 90 - 0.3x = 63.99
=> 0.1 x - 0.3x = 63.99 - 90
=> -0.2x = - 26.01
=> 0.2x = 26.01
x= 26.01/0.2
x = 130.05 millimeters
Joy must mix 130.05 millimeters of 10% fungicide solution with (300 - 130.5) milllimeters of 30% fungicide solution to get 21.33% solution.
so Joy must mix 130.05 millimeters of 10% fungicide solution with 169.95 milllimeters of 30% fungicide solution to get 21.33% solution.
Complete the proof of the identity by choosing the Rule that justifies each step.(sec^2x-1) cosx = sin^2x secxTo see a detailed description of a Rule, select the More Information Button to the right of the Rule.
From the question we are to complete the proof
[tex](sec^2x-1)\cos x=\sin ^2x\sec x[/tex]Solving LHS
By applying Pythagorean rule
[tex]1+\tan ^2x=\sec ^2x[/tex]This implies
[tex]\tan ^2x=\sec ^2x-1[/tex]Therefore we have
[tex](\sec ^2x-1)\cos x=\tan ^2x\cos x[/tex]Question 3In the diagram below, paralelines and mare cut by transalWhich pair of angies are vertical angles?25 and 26B22 and 27С21 and 24D23 and 26
Remember that vertical angles don't share any side, they are completely opposite about the vertex.
Having said that, the vertical angles are:
• Angle 2 and angle 3.
,• Angle 1 and angle 4.
,• Angle 5 and Angle 8.
,• Angle 6 and angle 7.
Therefore, the right answer is C.13.List all the subsets of the given set.{lime, pear, starfruit}Choose the answer that lists all of the subsets of {lime, pear, starfruit}.A.{lime}, {pear}, {starfruit}, {lime, pear},{lime, starfruit}, {pear, starfruit}B.{}, {lime}, {pear}, {starfruit}, {lime, pear},{lime, starfruit}, {pear, starfruit},{lime, pear, starfruit}C.{}, {lime}, {pear}, {starfruit}, {lime, pear},{lime, starfruit}, {pear, starfruit}D.{lime}, {pear}, {starfruit}, {lime, pear},{lime, starfruit}, {pear, starfruit},{lime, pear, starfruit}
The correct option is B.{}, {lime}, {pear}, {starfruit}, {lime, pear},
{lime, starfruit}, {pear, starfruit},{lime, pear, starfruit}
STEP - BY - STEP EXPLANATION
What to find?
All subset of a given set.
Given:
{lime, pear, starfruit}
First, we need to not given any set of element n.
The number of subset = 2^n
From the given set, n=3
The number of subset we should have is 2^3 = 8
Now the subsets are:
{}
{lime}
{pear}
{starfruit}
{lime, pear}
{lime, pear}
{pear, starfruit}
{lime, pear, starfruit}
The above are 8 in number, hence the subsets of the given sets.
Therefore, the correct option is . B.{}, {lime}, {pear}, {starfruit}, {lime, pear},
{lime, starfruit}, {pear, starfruit},{lime, pear, starfruit}
Need help asap!..The population of a city is 100,000 and grows at a rate of 4%, four times per year. How big will the population be in 4 years?
Answer:
187,298.
Explanation:
The equation that model the growth in the city is an exponential function with the form:
[tex]P=P_0\cdot(1+r)^t[/tex]Where P0 is the initial population, r is the growth rate and t is the number of quarters because the rate applies four times per year.
So, replacing P0 by 100,000, r by 4%, and t by 16 quarter ( 4 years x 4 quarters), we get:
[tex]\begin{gathered} P=100000\cdot(1+0.04)^{16} \\ P=100000\cdot1.8729_{} \\ P=187,298.1246 \end{gathered}[/tex]Therefore, after 4 years, the population of the city will be 187,298.
To train for a race, Michele jogged6 miles each day before the last two daysbefore the race. She jogged 10 mileseach of those two days. Write anexpression to represent the number ofmiles that Michele jogged in preparationfor the race. Let d represent the numberof days.
6 (d-2)+20
6 miles each day (except for the last 2 days)
10 miles the last 2 days. (10 miles x 2 days = 20 miles)
So the expression is:
6 (d-2) + 10(2)
6 (d-2)+20
Where d is the number of days
2x + 6y = 10x = -1 ,1 ,2y = ?
we have
2x + 6y = 10
For x=-1
substitute the value of x in the expression and solve for y
so
2(-1) + 6y = 10
-2+6y=10
6y=10+2
6y=12
y=2
For x=1
substitute the value of x in the expression and solve for y
so
2(1) + 6y = 10
6y=10-2
6y=8
y=4/3
For x=2
substitute the value of x in the expression and solve for y
so
2(2) + 6y = 10
6y=10-4
y=1
therefore
the values of y are
y=2, 4/3,1
The formula for the area of a rectangle is A = l ∙ w, where A = area, l = length and w = width.A rectangle with a length of 4 millimeters has an area of 44 square millimeters. The width of the rectangle is__millimeters.
Given:
Formula for the area of rectangle is:
[tex]A=l\times w[/tex]Given measurements are:
A=44 square millimeters
l=4 millimeters
The objective is to find: width of rectangle
[tex]\begin{gathered} A=l\times w \\ w=\frac{A}{l} \end{gathered}[/tex]Substituting the values, we get;
[tex]\begin{gathered} w=\frac{44}{4} \\ =11\text{ millimeters} \end{gathered}[/tex]Hence, the width of the recatngle is 11 millimeters.
d) — 4х + 9y = 9x — Зу = -6
The system of equation is:
[tex]\begin{gathered} -4x+9y=9 \\ x-3y=-6 \end{gathered}[/tex]Now we can solve the secon equation for x so:
[tex]x=3y-6[/tex]Now we can replace this value of x in the first equation so:
[tex]-4(3y-6)+9y=9[/tex]and we solve for y so:
[tex]\begin{gathered} -12y+24+9y=9 \\ 24-9=12y-9y \\ 15=3y \\ 5=y \end{gathered}[/tex]Now we can replace y in the first equation to find the value of x so:
[tex]\begin{gathered} x=3(5)-6 \\ x=15-6 \\ x=9 \end{gathered}[/tex][tex]undefined[/tex]The following table represents a grouped frequency distribution of the number of hours spent on the computer per week for 53 students. What percentage of students used the computer less than 11 hours per week? Round your answer to the nearest tenth, if necessary.
Given:
Total number of students = 53
Required: Percentage of students used the computer less than 11 hours
Explanation:
Number of students used the computer less than 11 hours
[tex]\begin{gathered} =5+17 \\ =22 \end{gathered}[/tex]Percentage of students used the computer less than 11 hours
[tex]\begin{gathered} =(\frac{\text{ Number of students used the computer less than 11 hours}}{\text{ Total number of students}}\cdot100)\% \\ =(\frac{22}{53}\cdot100)\% \\ =0.42\% \end{gathered}[/tex]Final AN
look at the image below forr the question please show step by step
Solution:
Given the equation:
[tex]v=\frac{r-s}{2}[/tex]To solve for the variable r,
step 1: Multiply both sides by 2.
This gives
[tex]\begin{gathered} 2\times v=2\times\frac{r-s}{2} \\ \Rightarrow2v=r-s \end{gathered}[/tex]step 2: Add s to both sides of the equation.
Thus, we have
[tex]\begin{gathered} s+2v=r-s+s \\ \Rightarrow r=2v+s \end{gathered}[/tex]Hence, we have
[tex]r=2v+s[/tex]The correct option is
You are playing a game that uses two fair number cubes, If the total on the number cubes la either 11 or 2 onyour next turn, you win the game. What is the probability of winning on your next turn? Express your anawer ana percent, If necessary, round your answer to the nearest tenth,O 91.7%O 8.3%O 5.6%O 0.2%
1) Let's enlist the possible outcomes of two dices:
(1,1) (1,2), (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
There is a total of 36 outcomes
2) Let's bold the favorable outcome, either the sum of the cubes is 11 or 2:
(1,1) (1,2), (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
So there is a total of 3 favorable outcomes:
3) So let's write it as a Probability:
[tex]P=\frac{3}{36}=\frac{1}{12}=0.083[/tex]This can also be written as a percentage multiplying by 100. Hence, the answer is 8.3%
could u please answer in detail?y + 1/4x = 3solve for y
Given the equation :
[tex]y+\frac{1}{4}x=3[/tex]It is required to make the equation in the form :
[tex]y=m\cdot x+b[/tex]So, solve the given equation for y ( make y alone on the left side )
We need to eliminate the term (1/4)x
as the term (1/4)x was added to y , so we need to subtract this term from both sides
So,
[tex]y+\frac{1}{4}x-\frac{1}{4}x=-\frac{1}{4}x+3[/tex][tex]y=-\frac{1}{4}x+3[/tex]What is the combined area of the left and right faces of the prism Tim
The area of the left and right faces are given by:
[tex]A=bh[/tex]for those faces the base is 9 in and the height is 4 in, then their areas area:
[tex]A=9\cdot4=36[/tex]The combined area is their sum, since they are equal we get 72.
Therefore the combined area is 72 squared inches.
Answer:
72 in squared
Step-by-step explanation: I just did the assignment
what is the inverse of cos-¹(-1) on the unit circle
Spinner A and Spinner B below are each to be spun once.If the pointer CANNOT land on the line, how many different outcomes of a numberand a color are possible?A. 18B. 12 C. 9 D. 6
Answer:
A. 18
Explanation:
We can see that there are 6 numbers on spinner A and 3 colors on spinner B. Then, by the rule of multiplication, the number of different outcomes is
6 x 3 = 18
Therefore, the answer is
A. 18
Find the slope of the line through the given points.(-4,7) and (-1,-3)Is the slope increasing or decreasing?
• The following formula can be used to find the slope of a line:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]These points are on the line:
[tex](x_1,y_1);(x_2,y_2)[/tex]Given the following points:
[tex]\mleft(-4,7\mright);(-1,-3)[/tex]Then, you can set up that:
[tex]\begin{gathered} y_2=-3_{} \\ y_1=7 \\ x_2=-1 \\ x_1=-4 \end{gathered}[/tex]Therefore, substituting values into the formula and evaluating, you get:
[tex]\begin{gathered} m=\frac{-3-7}{-1-(-4)} \\ \\ m=\frac{-10}{-1+4} \\ \\ m=-\frac{10}{3} \end{gathered}[/tex]• As you can notice, the slope is negative. Therefore, you can determine that it is decreasing.
Therefore, the answers are:
• Slope of the line:
[tex]m=-\frac{10}{3}[/tex]• It is decreasing.
s rationalized by multiplying the numerator and denominator by what?
Solution:
Given the expression;
[tex]\frac{5}{\sqrt{7}-2}[/tex]Rationalization is done by multiplying the numerator and the denominator by the conjugate.
The conjugate is where we change the sign in the middle of two terms.
Thus, rationalization is done as;
[tex]\frac{5}{\sqrt{7}-2}\times\frac{\sqrt{7}+2}{\sqrt{7}+2}[/tex]CORRECT OPTION:
[tex]\sqrt{7}+2[/tex]The following equation represents the volume of a rectangular prism with a width of winches:V= 2w^3 - 7w^2 +3wa Graph the polynomial on a graphing calculator or an online graphing application. Whatare the 2-intercepts? What do these mean in terms of the situation?b What are the domain and range in terms of the situation? Justify your answers.
SOLUTION
(a) The graph of the function
[tex]V=2w^3-7w^2+3w[/tex]is shown below
From the graph, the two intercepts considered are (0.5, 0) and (3, 0)
They indicate that the width of prism would be 0.5 or 3.0 when the volume of the prism is 0.
(b) The domain are the values for which the x-values, in this case width values are valid. These are points on the graph, where the volume (y-values) would be positive for width (x-values). From the graph, these are x-vaues of 0 to 0.5 or 3 to infinity.
So in interval notation, the domain is
[tex](0,0.5)\cup(3,\infty)[/tex]The range are the values for which the y-values, in this case volume values are valid. Since volume of a prism cannot be negative, so the range is a set of all positive y values
Hence the range is
[tex]y>0[/tex]how do you solve quadratic using square roots?ex: m²=81
we have
m²=81
Apply square roots both sides
[tex]\begin{gathered} \sqrt[]{m^2}=\pm\sqrt[]{81} \\ (m^2)^{(\frac{1}{2})}=\pm(9^2)^{(\frac{1}{2})} \end{gathered}[/tex]simplify
m=(+/-)9are two solutions
because
(-9)^2=81
and
(9)^2=81
Lisa likes to go to one movie per week. She usually spends $12 on herticket and $10 on a drink and popcorn. How much money would shesave in one year if she went on Tuesdays when the price of a ticket washalf off and she didn't have any snacks?
First lets figure out how much she spends in one year. There are 52 weeks in one year
She spends 12 on a ticket and 10 on snacks, or 22 dollars each time
22 * 52 = 1144 dollars in a year.
She decides to go on Tuesday where the ticket is 1/2 prices or 1/2 ( 12) = 6 and no snacks ( 0 dollars)
Her cost is 6 dollars. There are still 52 weeks in a year
6 * 52 = 312 dollars
She saves
1144 - 312 = 832 dollars
WhichdescriOne statistic used to measure a country's wealth is itsgross domestic product (GDP). A higher GDPindicates greater wealth in the country. A researchercompared the GDP per person for 12 countries withthe life expectancy of that country. The data for the 12countries are shown in the scatterplot. The value ofrfor the scatterplot is 0.608.Ο ΤΗThexpo coexcСоexpCountry WealthCou90ex
To answer this question, we can observe that the correlation coefficient for the explanatory variable, GDP, and the response variable, Life Expectancy, is not so weak, r = 0.608, and tend to be a strong correlation coefficient.
It means that both described variables are positively correlated, that is, an increase in the explanatory variable, GDP, implies an increase in the response variable, Life Expectancy.
We can see this from the given graph - if we see the values on the right, we have higher values for life expectancy than, for instance, the first value near the origin of the graph.
Therefore, we can say as we have greater values for GDP, we will expect a higher life expectancy.
In summary, then, we can say that:
"Countries with higher GDPs tend to have higher life expectancies." (last option.)
please help! functions and relations. f(x)= square root of x-4. find the inverse of f(x) and it’s domain.
ANSWER:
[tex]\:D.\text{ }f^{-1}\left(x\right)=\left(x+4\right)^2;x\ge-4[/tex]STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]f(x)=\sqrt{x}-4[/tex]The inverse is the following (we calculate it by replacing f(x) by x and x by f(x)):
[tex]\begin{gathered} x=\sqrt{f^{-1}(x)}-4 \\ \\ \sqrt{f^{-1}(x)}=x+4 \\ \\ f^{-1}(x)=(x+4)^2 \end{gathered}[/tex]The domain would be the range of the original equation, and it would be the range of values that f(x) could take, which was from -4 to positive infinity, that is, f(x) ≥ -4.
Therefore, the domain is x ≥ -4.
So the correct answer is D.
[tex]\:f^{-1}\left(x\right)=\left(x+4\right)^2;x\ge -4[/tex]Write the ratio of the corresponding sides to check if the triangles are equal: example- 2/3=4/5The triangles are similar by what theorem?Write the triangle congruence statement
The ratio of the sides gives
[tex]\frac{20}{8}=\frac{15}{6}[/tex][tex]2.5=2.5[/tex]the ratios of side lengths are the same, and therefore, the triangles are similar.
Now, we are given two side lengths and one angle; thereofre, the triangles are similar by SAS theorem.
find the height of a flagpole which casts a 5.9 M shadow that when the angle of valuation to the sun is 75° round your answer to the nearest tenth
Draw a diagram to visualize the situation:
Notice that φ+θ=90°.
Assuming that the angle φ has a measure of 75°, then:
[tex]\begin{gathered} 75+\theta=90 \\ \Rightarrow\theta=90-75 \\ \Rightarrow\theta=15 \end{gathered}[/tex]Notice that the flagpole and its shadow are the legs of a right triangle. Recall the definition of the tangent of an angle in a right triangle:
[tex]\tan (A)=\frac{\text{Side opposite to A}}{\text{ Side adjacent to A}}[/tex]Then, in this case:
[tex]\tan (\theta)=\frac{h}{5.9m}[/tex]Substitute the value of θ into the equation and isolate h. Then, use a calculator to find the value of h:
[tex]\begin{gathered} h=5.9m\times\tan (15) \\ \Rightarrow h=5.9m\times0.26795\ldots \\ \Rightarrow h=1.5809\ldots m \end{gathered}[/tex]Therefore, to the nearest tenth:
[tex]h=1.6m[/tex]What is the difference between a line and a ray?
we have the following:
Ray:
1. Ray has a starting point and another near the point of the row.
2. You have a starting point but no other ending points. So its length cannot be measured.
3. The symbol for ray is:
[tex]\rightarrow[/tex]Line:
1. There are no end points on a line.
2. There are no end points, so length of a line cannot be measured.
3. The symbol of a line is:
[tex]\leftrightarrow[/tex]