The formula S=C(1+r) models inflation, where C = the value today, r = the annual inflation rate, and S = the inflated value t years from now. a. If the inflation rate is 6%, how much will a house now worth $465,000 be worth in 10 years? b. If the inflation rate is 3%, how much will a house now worth $510,000 be worth in 5 years?
The formula that models inflation is
[tex]S=C(1+r)^t[/tex]C= value today
r= annual inflation rate → usually this value is given as a percentage, but when you input the value in the formula, you have to express it as a decimal value.
S= the inflated value given a determined period of time (t).
a.
r=6%=6/100=0.06/year
C=$465000
t=10 years
[tex]\begin{gathered} S=465000(1+0.06)^{10} \\ S=832744.1789 \end{gathered}[/tex]The price of the house in 10 years at an inflation rate of 6% will be S=$832744.18
b.
r=3%=3/100=0.03/year
C=$510000
t=5years
[tex]\begin{gathered} S=510000(1+0.03)^5 \\ S=437954.3531 \end{gathered}[/tex]The price of the house in 5 years at an inflation rate of 3% will be S=$437954.35
A bottler of drinking water fills plastic bottles with a mean volume of 993 milliliters (mL) and standard deviation of 7 mL. The fill volumes are normally distributed. What proportion of bottles have volumes between 988 mL and 991 mL?
Given data:
Mean: 993mL
Standard deviation: 7mL
Find p(988
1. Find the z-value corresponding to (x>988), use the next formula:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \\ z=\frac{988-993}{7}=-0.71 \end{gathered}[/tex]2. Find the z-value corresponding to (x<991):
[tex]z=\frac{991-993}{7}=-0.29[/tex]3. Use a z score table to find the corresponding values for the z-scores above:
For z=-0.71: 0.2389
For x=-0.29: 0.3859
4. Subtract the lower limit value (0.2389) from the upper limit value (0.3859):
[tex]0.3859-0.2389=0.147[/tex]5. Multiply by 100 to get the percentage:
[tex]0.147*100=14.7[/tex]Then, 14.7% of the bottles have volumes between 988mL and 991mLJada bought an art kit with 50 colored pencils. She and her 3 sisters will share the pencils equally. How many pencils will each person receive? Will there be any pencils left over? If so, how many?
Each will get 16 coloured pencils and 2 will be the left over
Step-by-step explanation:
Give 10 pencil each then add 6 more for each one and the answer will be 16 each and multiple 3×16 =48 and remainder 2
In triangle ABC, AB12, BC18, and m B = 75°. What are the approximate length of AC and measure of A
Length AB = 12cm
BC = 18cm
mB = 75^
5: =3:21 its equivalent ratios
The number that makes the ratios equivalent is 35. Thus, the ratio becomes 5:35 = 3:21
Equivalent ratiosFrom the question, we are to determine the number that will make the two ratios equivalent ratios.
From the given equation,
5: = 3:21
Let the unknown number be x.
Thus,
The equation becomes
5:x = 3:21
Then,
We can write that
5/x = 3/21
Cross multiply
x × 3 = 5 × 21
3x = 105
Divide both sides by 3
3x/3 = 105/3
x = 35
Hence, the number is 35
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fill in the blank with the correct answer. the number _______is divisibel by 2, 3, 4, 5, and 6
a)44
b)180
c)280
d)385
Answer:
b) 180
Explanation:
[tex]180 / 2 = 90\\180 / 3 = 60\\180 / 4 = 45\\180 / 5 = 36\\180 / 6 = 30[/tex]
Hope you have a nice day and a nice Thanksgiving!
A brainiliest would also be nice. thx.
Third-degree, with zeros of 2-i, 2+i and 3 and a leading coefficient of -4
Answer:
Step-by-step explanation:
question will be in picture
f(x) = -5x + 4
What is the value of x when f(x) = 29
To find x, equate -5x + 4 to 29.
-5x + 4 = 29
Next, collect like terms.
-5x = 29 - 4
-5x = 25
Finally divide through by -5 to find the value of x.
[tex]\begin{gathered} \frac{-5x}{-5}\text{ = }\frac{25}{-5} \\ x\text{ = -5} \end{gathered}[/tex]Final answer
x = -5 Option C
Solve x2 + 5x = 0.Step 1. Factor x2 + 5x as the product of two linear expressions.
Taking common factor x:
[tex]x(x+5)=0[/tex]Equal each factor to zero, and solve for x:
[tex]x=0[/tex][tex]\begin{gathered} x+5=0 \\ x=-5 \end{gathered}[/tex]So, the solution is:
[tex]\begin{gathered} x_1=0 \\ x_2=-5 \end{gathered}[/tex]Zero and negative exponentswrite in simplest for without zero or negative exponents10c -²
Explanation
remember some properties of the exponents
[tex]\begin{gathered} a^m\cdot a^n=a^{m+n} \\ (a^m)^n=a^{m\cdot n} \\ a^{-m}=\frac{1}{a^m} \end{gathered}[/tex]Hence,apply
[tex]10c^{-2}=10\cdot c^{-2}=\frac{10}{c^2}[/tex]I hope this helps you
Select all of the true statements about to figure, if a scale factor is 2.
Given: The scale factor is 2 for the given figures
To Determine: The truth statements from the given options
The transformation shown is an enlargement. This means that each of the length of the pre-image multiplied by 2 would give the length of the image
This means
[tex]\begin{gathered} A^{\prime}B^{\prime}=2AB \\ A^{\prime}C^{\prime}=2AC \\ B^{\prime}C^{\prime}=2BC \end{gathered}[/tex]For similar shapes, the angles are congruent and the sides are in proportion of the scale factor
Hence, the following are true statements of the given diagrams
A'C' = 2 AC, OPTION B
If AB = 6, then A'B' = 12, OPTION E
Solve each equation by using the square root property. 2x^2–9=11
We want to solve
2x^2–9=11
First, isolate the portion of the equation that's actually being squared. That is:
2x^2 = 11 + 9
that is equivalent to:
2x^2 = 20
that is equivalent to
x^2 = 20/ 2 = 10
that is
x^2 = 10
Now square root both sides and simplify, that is:
[tex]\sqrt[]{x^2\text{ }}=\text{ }\sqrt[]{10}[/tex]we know that the square root is the inverse function of the function x^ 2, so we can cancel the square :
[tex]x\text{ = }\sqrt[]{10}[/tex]but note that there is always the possibility of two roots for every square root: one positive and one negative: so the final answer is:
[tex]x\text{ = +/- }\sqrt[]{10}[/tex]
what is the median 14,6,-11,-6,5,10
The median of a set of values is the values that divide the set into two subsets, one containing all the values less than the median, and another containing all the values greater than the median.
So, to find the median, let's first rewrite the given values in ascending order:
-11, -6, 5, 6, 10, 14
If the set had an odd number of values, the value in the middle, after rewriting them as we did, would be the median.
Nevertheless, the number of values in this set is even. When this happens, the median corresponds to the mean of the two central numbers.
In this case, the two central numbers are 5 and 6. Their mean is:
(5 + 6)/2 = 11/2 = 5.5
Thus, the median is 5.5.
Can you please help me find the area? Thank you. :)))
The figure shown in the picture is a rectangular shape that is missing a triangular piece. To determine the area of the figure you have to determine the area of the rectangle and the area of the triangular piece, then you have to subtract the area of the triangle from the area of the rectangle.
The rectangular shape has a width of 12 inches and a length of 20 inches. The area of the rectangle is equal to the multiplication of the width (w) and the length (l), following the formula:
[tex]A=w\cdot l[/tex]For our rectangle w=12 in and l=20 in, the area is:
[tex]\begin{gathered} A_{\text{rectangle}}=12\cdot20 \\ A_{\text{rectangle}}=240in^2 \end{gathered}[/tex]The triangular piece has a height of 6in and its base has a length unknown. Before calculating the area of the triangle, you have to determine the length of the base, which I marked with an "x" in the sketch above.
The length of the rectangle is 20 inches, the triangular piece divides this length into three segments, two of which measure 8 inches and the third one is of unknown length.
You can determine the value of x as follows:
[tex]\begin{gathered} 20=8+8+x \\ 20=16+x \\ 20-16=x \\ 4=x \end{gathered}[/tex]x=4 in → this means that the base of the triangle is 4in long.
The area of the triangle is equal to half the product of the base by the height, following the formula:
[tex]A=\frac{b\cdot h}{2}[/tex]For our triangle, the base is b=4in and the height is h=6in, then the area is:
[tex]\begin{gathered} A_{\text{triangle}}=\frac{4\cdot6}{2} \\ A_{\text{triangle}}=\frac{24}{2} \\ A_{\text{triangle}}=12in^2 \end{gathered}[/tex]Finally, to determine the area of the shape you have to subtract the area of the triangle from the area of the rectangle:
[tex]\begin{gathered} A_{\text{total}}=A_{\text{rectangle}}-A_{\text{triangle}} \\ A_{\text{total}}=240-12 \\ A_{\text{total}}=228in^2 \end{gathered}[/tex]The area of the figure is 228in²
First blank transitive propertySubtraction property of equalitySegment additionSubstitution property of equalitysecond blank AB does not equal YZ AC does not equal XZ AB equals YZ AC equals XZ
Given that:
[tex]BC=XY[/tex][tex]AB+BC\ne YZ+XY[/tex]According to the Segment Addition if B lies between A and C, then:
[tex]AB+BC=AC[/tex]In this case, knowing that:
[tex]AB+BC\ne YZ+XY[/tex]And knowing that B lies between A and C, and Y lies between X and Z:
[tex]\begin{gathered} AB+BC=AC \\ YX+XY=XZ \end{gathered}[/tex]Therefore, you can determine that:
[tex]AC\ne XZ[/tex]Hence, the answers are:
- First blank: Third option (Segment addition).
- Second blank: Second option (AC does not equal XZ).
A spinner is shown below. what is the probability that a 5 is spun?
Answer:
The probability that 5 is spun is;
[tex]\begin{gathered} P(5)=\frac{2}{9} \\ or \\ P(5)=22.22\text{\%} \end{gathered}[/tex]Explanation:
Given the figure in the attached image.
We will assume that each of the sectors are of the same size.
The probability of spinning a 5 is equal to the number of sectors with 5 divided by the total number of sectors.
[tex]\begin{gathered} n(5)=2 \\ n(\text{total)}=9 \end{gathered}[/tex]So, the probability that 5 is spun is;
[tex]\begin{gathered} P(5)=\frac{n(5)}{n(\text{total)}}=\frac{2}{9} \\ P(5)=\frac{2}{9} \\ \text{ in percentage;} \\ P(5)=\frac{2}{9}\times100\text{\%} \\ P(5)=22.22\text{\%} \end{gathered}[/tex]Therefore, the probability that 5 is spun is;
[tex]\begin{gathered} P(5)=\frac{2}{9} \\ or \\ P(5)=22.22\text{\%} \end{gathered}[/tex]Martina used a total of 4 3/4 gallons of gas while driving her car. Each hour she was driving, she used 5/6 gallons of gas. What was the total number of hours she was driving?
The number of hours she was driving = 5.7 hours or in fraction 57/10 hours.
What is fraction?
A fraction is a number that represents a part of a whole.
Generally, the fraction can be a portion of any quantity out of the whole thing and the whole can be any specific things or value.
Given, a total gallons is in mixed fraction 4 3/4
can be written as
16+3/4 = 19/4
Let x be the hours she was driving.
The she used 5/6 gallons.
x (5/6) = 19/4
x = 19/4(6/5)
x = 5.7 hours
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true or false the diameter is equal to twice the radius
True, the diameter = twice the radius
A small publishing company is planning to publish a new book. the production cost will include one-time fix costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-timed fixed costs will total $15,756, and the variable costs will be $23.50 per book. With the other method, the one-timed costs will total $48,108, and the variable costs will be $12 per book. For how many books produced will the costs from the two methods be the same?
What we must do is equal both equations like this:
[tex]15756+23.5\cdot x=48108+12\cdot x[/tex]solving for x (numbers of books):
[tex]\begin{gathered} 23.5\cdot x-12\cdot x=48108-15756 \\ 11.5\cdot x=32352 \\ x=\frac{32352}{11.5} \\ x=2813.2=2813 \end{gathered}[/tex]In aproximately 2813 books
For any right triangle, the side lengths of the triangle can be put in the equation a^2+ b^2 = c^2 where a, b, and c are the side lengths. A triangle with the side lengths 3 inches, 4 inches, and 5 inches is a right triangle. Which way(s) can you substitute the values into the equation to make it true? Which variable has to match the longest side length? Why?
It is given that the side lengths of any right triangle can be put in the equation:
[tex]a^2+b^2=c^2[/tex]For a triangle with the side lengths 3 inches, 4 inches, and 5 inches, it can be substituted in two ways that will make the equation true:
Let a=3, b=4, and c=5:
[tex]\begin{gathered} 3^2+4^2=5^2 \\ \Rightarrow9+16=25 \\ \Rightarrow25=25 \end{gathered}[/tex]Hence, the equation is true.
You can also substitute a=4, b=3, and c=5.
This will also give the same result.
Notice that variable c has to match the longest side length.
The reason for this is that equality can only hold if the longest side is the variable at the right, if not there'll be an inequality instead.
Find the image of the given pointunder the given translation.
Answer: P' = (4, 4)
Explanation
As the given point is (8, –3), then the transformation is:
[tex]T(x,y)=(x-4,y+7)=(8-4,-3+7)[/tex][tex]T(x,y)=(4,4)[/tex]Step 1 Step 2 Step 3 Using the figures above, how many small squares will there be in step 4 and step 15? a. Step 4 = b. Step 15 =
Step 4 = 16 squares
Step 15 = 225 squares
1) In the 1st step we can see, 1 square. In the 2nd, 4, and on the third one 9
So there's a sequence, 1, 4, 9
2) We can write the positions and raise them to the 2nd power we can see how it grows:
position (steps) n | 1 | 2 | 3
# squares | 1 | 4 | 9
3) We can derive a formula for that sequence:
[tex]a_n=n^2[/tex]Following this rule, we can find that
Step 4 = 4² = 16 squares
Step 15 = 15² = 225 squares
Find each unknown function value or x value for f(x) = 4x - 7 and g(x) = -3x + 5
Step 1
Find f(2)
[tex]To\text{ do this we substitute for f= 2 in f(x)}[/tex][tex]\begin{gathered} f(x)\text{ = }4x-7 \\ f(2)\text{ = 4(2) -7 = 8 - 7 = 1} \end{gathered}[/tex]Step 2
Find f(0)
[tex]f(0)\text{ = 4(0) -7 = 0 - 7 = -7}[/tex]Step 3
Find f(-3)
[tex]f(-3)\text{ = 4(-3) -7 = -12 -7 = -19}[/tex]Step 4
Find x, when f(x) = -3
[tex]\begin{gathered} f(x)\text{ = -3}--------------(1) \\ f(x)\text{ =4x-7}---------------(2) \\ \text{Equate both equations} \\ -3=4x-7 \\ -3+7\text{ = 4x} \\ 4x\text{ = 4} \\ x\text{ = }\frac{4}{4}=1 \end{gathered}[/tex]Mrs. Cavazos car traveled 192 miles on 6 gallons of gas. Find the unit rate per gallon
To find the unit rate per gallon, we are going to divide 192 by 6
[tex]\frac{192}{6}=32[/tex]The car gets 32 miles per gallon.
KFind the future value and interest earned if $8806.54 is invested for 7 years at 4% compounded (a) semiannually and (b) continuously.(a) The future value when interest is compounded semiannually is approximately $ 11,620.04.(Type an integer or decimal rounded to the nearest hundredth as needed.)The interest earned is approximately $ 2813.5.(Type an integer or decimal rounded to the nearest hundredth as needed.)(b) The future value when interest is compounded continuously is approximately $(Type an integer or decimal rounded to the nearest hundredth as needed.)
Given:
The principal amount = $8806.54
Rate of interest = 4%
Time = 7 years
Required:
Find the future value when interest is compounded continuously.
Explanation:
The future value is calculated by using the formula:
[tex]Future\text{ value = Ae}^{rt}[/tex]Where A = amount
r = rate of interest
t = time period
Substitute the given values in the formula:
[tex]\begin{gathered} Future\text{ value = 8806.54\lparen e}^{0.04\times7}) \\ =8806.54(e^{0.28}) \\ =8806.54\times1.323 \\ =11,651.0524 \\ \approx11,651.05 \end{gathered}[/tex]Interest = 11,651.05 - 8806.54
= 2844.51
Final Answer:
The future value when interest is compounded continuously is approximately $11,651.05.
The earned interest is approximately $2844.51
The two triangles below are similar. Also, m A = 15° and m ZC - 35° as shown below Find m2P, m 2Q, and m ZR. Assume the triangles are accurately drawn
Answer
Angle R = 15°
Angle P = 130°
Angle Q = 35°
Explanation
First noting that the sum of angles in a triangle is 180°.
We first need to calculate the Angle B for the first triangle.
Angle A + Angle B + Angle C = 180°
15° + Angle B + 35° = 180°
Angle B + 50° = 180°
Angle B = 180° - 50°
Angle B = 130°
We are then told to find Angles P, Q and R.
We are told that the two triangles are similar .
Two similar triangles will have the same angle measures.
So, we just need to note the corresponding angles and equate the unknowns.
Triangle ABC is similar to Triangle RPQ
Angle R = Angle A = 15°
Angle P = Angle B = 130°
Angle Q = Angle C = 35°
Hope this Helps!!!
a vector s has the initial point (-2,-4) and terminal point (-1,3) write s in the form s = ai + bj
To write the vector s in the form s=ai + bj, we can use the next formula:
[tex]\vec{s}=(x_2-x_1)\vec{i}+(y_2-y_1)\vec{j}[/tex]Where (x1,y1) are the coordinates of the initial point and (x2,y2) are the coordinates of the terminal point, by replacing these values we have:
[tex]\begin{gathered} \vec{s}=((-1)-(-2))\vec{i}+(3-(-4))\vec{j} \\ \vec{s}=((-1)+2)\vec{i}+(3+4)\vec{j} \\ \vec{s}=(1)\vec{i}+(7)\vec{j} \end{gathered}[/tex]Then the vector s in the form s=ai+bj is: s= 1i + 7j
Simplify: 6-(-9) divided by -9/-4
Answer:
6 2/3
Explanation:
Given the expression:
[tex]\lbrack6-\mleft(-9\mright)\rbrack\div\frac{-9}{-4}[/tex]First, we simplify to obtain:
[tex]=\lbrack6+9\rbrack\div-\frac{9}{-4}[/tex]Note that -9/-4=9/4. The minus sign cancels each other out.
This gives us:
[tex]15\div\frac{9}{4}[/tex]We then change the division sign to multiplication as shown below:
[tex]\begin{gathered} =15\times\frac{4}{9} \\ =\frac{60}{9} \\ =6\frac{6}{9} \\ =6\frac{2}{3} \end{gathered}[/tex]. Connect to Everyday Life In which situation is
a rounded number appropriate? Explain.
The number of
birds in a flock
The number of players on a
football field during a game
The situations that a rounded number is appropriate is both the given situations.
The number of birds in a flock.
The number of players on a football field during a game.
Both the give situation is correct.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The number of birds in a flock.
This will always be a rounded number.
We never say that there are 3.3 birds in a flock
We always say that there are 33 birds in the flock.
The number of players on a football field during a game.
This is always a rounded number.
We never say that there are 3 and a half players or 4.5 players on a football field.
We always say 24 players on a football field.
Thus,
The situations that a rounded number is appropriate is both the given situations.
The number of birds in a flock.
The number of players on a football field during a game.
Both the given situation is correct.
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Answer:
The situations that a rounded number is appropriate is both the given situations.The number of birds in a flock.The number of players on a football field during a game.Both the give situation is correct.What is an expression?An expression is a way of writing a statement with more than two variablesor numbers with operations such as addition, subtraction, multiplication, and division.Example: 2 + 3x + 4y = 7 is an expression.We have,The number of birds in a flock.This will always be a rounded number.We never say that there are 3.3 birds in a flockWe always say that there are 33 birds in the flock.The number of players on a football field during a game.This is always a rounded number.We never say that there are 3 and a half players or 4.5 players on a football field.We always say 24 players on a football field.
I need help solving this logarithmic equation. I need answered step by step,
Okay, here we have this:
We need to solve the following equation for n:
[tex]\log _8n=3[/tex]To solve this equation we will pass the logarithm to its exponential form:
[tex]\begin{gathered} n=8^3 \\ n=8\cdot8\cdot8 \\ n=512 \end{gathered}[/tex]Finally we obtain that n=512.
Answer:
n = 512
Step-by-step explanation:
Solving logarithmic equations:Write logarithmic equations to exponential equation.
[tex]\sf \log_8 \ n = 3\\\\\\ 8^3 = n\\\\[/tex]
n = 8 * 8 *8
n = 512