suppose that you have a 10,000 in a rather risky investment recommend by your financial advisor during the first year your investment decreases by 50% of its original value during the second year your investment at the end of year 1 increases by 60%. Weiser tells you that there must have there must have been a 10% overall increase of your original $10,000 investment. Is your financial advisor using percentages Properly? If Not, what is your actual gain or loss of your original $10,000 investment?
The financial advisor is NOT using percentages properly, because the 60% increase would multiply the new value after one year, and not the initial value.
So first let's find the investment after one year:
[tex]\begin{gathered} 10000-50\text{\% of 10000} \\ =10000-0.5\cdot10000=10000-5000=5000 \end{gathered}[/tex]Then, we have an increase of 60%, so:
[tex]\begin{gathered} 5000+60\text{\% of 5000} \\ =5000+0.6\cdot5000=5000+3000=8000 \end{gathered}[/tex]The final value is 8000, which is lesser than the original value, so we have a loss.
The percentual loss is:
[tex]\frac{10000-8000}{10000}=\frac{2000}{10000}=0.2=20\text{\%}[/tex]I can only send this at first. I will send you a picture of the work problem with the choices for the blanks.
Concept
Area of the shaded part
= Area of the outer square - Area of the inner square
Next,
Area of the outer square = Length x Length = 5 x 5 = 25
Area of the inner sqaure = Length x Length = 2 x 2 = 4
Final answer
The area of the shaded part = 25 - 4
= 21 inches square
two 5 in by 1.5 in and two 2 in by 1.5 in
1.5
2 in and 5 in
zachs orange paint is made by mixing 3 cups of red for every 5 cups of yellow. we know that Zach brought 24 cups of red paint. how many cups of yellow paint must he get to make his orange paint mixture?
For the information given in the statement you have
[tex]\frac{\text{number of cups of red paint}}{\text{ number of cups of yellow paint}}=\frac{3}{5}[/tex]Then
[tex]\frac{3}{5}=\frac{24\text{ cups of red paint}}{\text{ x cups of yellow paint}}[/tex]Solving for x
[tex]\begin{gathered} \frac{3}{5}=\frac{24}{x} \\ \text{Apply cross multiplication} \\ 3\cdot x=24\cdot5 \\ 3x=120 \\ \text{ Divide by 3 into both sides of the equation} \\ \frac{3x}{3}=\frac{120}{3} \\ x=40 \end{gathered}[/tex]Therefore, he must get 40 cups of yellow paint to make his orange paint mixture.
How long will it take for an investment to triple if interest is compounded continuously at 7%
Step-by-step explanation:
Question:
How long will it take an investment to triple, if the interest is
7
%
and compounded quarterly?
Future Value:
You have to find time that will it take an investment to triple. The amount is compounded quarterly so, n=4. Substitute all values into the formula,
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Answer and Explanation:
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PLEASE HELP!! pleaseAlthough she's only in middle school, Tameka loves to drive go-carts! Her favorite place to drive go-carts, Drivers Delight, has 3 circular tracks. Track 1 has a radius of 60 feet. Track 2 has a radius of 85 feet. Track 3 has a radius of 110 feet. A. Compute the circumference of Track 1. B. Compute the circumference of Track 2. C. Compute the circumference of Track 3.D. Driver's Delight is considering building a new track. They have a circular space with a diameter of 150ft. Compute the circumference of the circular space
A. Circumference of Track 1 = 2π r
= 2 x 3.14 x 60
=376.8 feet
B.Circumeference of track2 = 2π r
= 2 x 3.14 x 85
=533.8 feet
C.Circumference of track3 = 2π r
=2 x 3.14 x 110
=690.8 feet
D.Circumference of the circular space = 2π r
Diameter was given to be 150 ft
but radius(r) is half the diameter. Hence radius = 150ft/2 = 75 ft
Circumference of the circular space = 2x 3.14 x 75
=471 feet
Sort the cards so that each group adds up to 100%
Answer:
Add the 20%, 0.40 and the 40/100 chart
Add the 1/10, the 0.10, and the 80/100 chart
And finally, add the 6%, the 4/100 chart, and the 90/100
Which of the following is an example of a theorem? A. the areas of two congruent figures are equal. B. the area of a square is the square of the length of its side. C. the area of a rectangle is the product of its base and height. D. the area of a rectangle is the sum of all its non-overlapping parts
Theorem is a statement that can be proved or that is proven to be true.
Option A is a theorem because it is proven that the area of two congruent figures are equal.
Option B is a theorem because the area of a square is the square of the length of its side.
[tex]\begin{gathered} A_{square}=l\times l \\ A_{square}=l^2 \end{gathered}[/tex]Option C is a theorem because the area of a rectangle is the product of its base and height.
[tex]\begin{gathered} A_{rec\tan gle}=b\times h \\ A_{rec\tan gle}=bh \end{gathered}[/tex]Thus, A, B and C are CORRECT
given (10,5) and (x,-10), find all x such that the distance between these two points is 17. separate multiple answers with a comma.
x = (2, 18)
Explanation:Given the points (10, 5) and (x, -10)
The distance between these points is:
[tex]\begin{gathered} D=\sqrt[]{(x-10)^2+(-10-5)^2} \\ \\ =\sqrt[]{(x-10)^2+(-15)^2} \\ \\ =\sqrt[]{(x-10)^2+225} \end{gathered}[/tex]The distance is given to be 17, so
[tex]\begin{gathered} \sqrt[]{(x-10)^2+225}=17 \\ \\ (x-10)^2+225=17^2 \\ (x-10)^2=17^2-225 \\ (x-10)^2=289-225 \\ (x-10)^2=64 \\ x-10=\pm\sqrt[]{64}=8 \\ x=\pm8+10 \\ x=8+10=18 \\ OR \\ x=-8+10=2 \end{gathered}[/tex]x = 2 or x = 18
a grain silo has a cylindrical shape. its radius is 9ft, and height is 52ft. what is the volume of the silo?use the value of 3.14 for pieround to the nearest whole number
Given:
Radius = 9 ft
Height = 52 ft
Volume of cylindrical (silo) is:
[tex]\text{Volume}=\pi r^2h[/tex][tex]\begin{gathered} r=9 \\ h=52 \\ \pi=3.14 \end{gathered}[/tex][tex]\begin{gathered} \text{Volume}=\pi r^2h \\ =3.14\times(9)^2\times52 \\ =3.14\times81\times52 \\ =254.34\times52 \\ =13225.68 \end{gathered}[/tex]Nearst whole number is 13226
Can you help me with circumference and rotations?A Bicycle tire has a diameter of 62 cm, What is the distance the bicycle travels in 10 revolutions, round your answer to the nearest cm
Given:
[tex]\begin{gathered} D_{\text{iamteter of the tire}}=62cm \\ N_{\text{umber of revolution}}=10revolutions \end{gathered}[/tex]To Determine: The distance travelled
The distance travel in 1 revolution is the circumference of the tire.
The circumference of a circle is calculated by the formula below
[tex]\begin{gathered} C_{\text{ircumference of a circle }}=2\pi r \\ 2r=d \\ \text{Therefore} \\ C_{\text{ircumference of a circle }}=\pi d \end{gathered}[/tex]Substituting for diameter in the formula to get the distance travelled in 1 revolution as below
[tex]D_{is\tan ce\text{ travelled in 1 revolution}}=\pi\times62cm=62\pi cm[/tex]Therefore the distance in 10 revolution would be
[tex]\begin{gathered} D_{is\tan ce\text{ travelled in 10 revolutions}}=10\times62\pi cm \\ D_{is\tan ce\text{ travelled in 10 revolutions}}=620\pi cm=1947.787cm \\ D_{is\tan ce\text{ travelled in 10 revolutions}}\approx1948cm \end{gathered}[/tex]Hence, the distance travelled by the bicycle in 10 revolutions to the nearest cm is 1948cm
Abel owns a dog walking business. He walks12 dogs every day of the week. If Abel walks2.6 miles each day, how many miles does hewalk in one week?
Abel walks 2.6 miles each day of the week.
The week has 7 days.
So, to calculate how many miles he walks in one week we simply have to multiply the number of miles that he walks per day (2.6) by the number of days in a week (7).
2.6 miles per day x 7 days = 2.6 x 7 = 18.2 miles a week.
Chip Ahoy
The number of chocolate chips in an 18-ounce bag of
Chips Ahoy! chocolate chip cookies is approximately
normally distributed with a mean 1262 chips and a
standard deviation of 118 chips according to a study
by cadets of the U.S. Air Force Academy. (Why are
they studying chocolate chip cookies?}
What percent of bags has between 1026 and 1380 chocolate chips? Write your percent without the percent sign.
What percentage of the 18-ounce bags of chips ahoy! Cookies contains fewer than 1144 chocolate chips? Write the percent without the percent sign.
What percentage of the 18-ounce bags of chips ahoy! Cookies contains more than 1498 chocolate chips? Write the percent without the percent sign.
Using the normal distribution, it is found that:
81.85% of bags has between 1026 and 1380 chocolate chips.15.87% of the bags contain fewer than 1144 chocolate chips.2.28% of bags contain more than 1498 chocolate chips.Normal Probability DistributionThe z-score of a measure X of a variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the fraction presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation of the number of chips are given as follows:
[tex]\mu = 1262, \sigma = 118[/tex]
The proportion of bags that has between 1026 and 1380 chocolate chips is the p-value of Z when X = 1380 subtracted by the p-value of Z when X = 1026, hence:
X = 1380:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (1380 - 1262)/118
Z = 1
Z = 1 has a p-value of 0.8413.
X = 1026:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (1026 - 1262)/118
Z = -2
Z = -2 has a p-value of 0.0228.
0.8413 - 0.0228 = 0.8185.
Hence the percentage is 81.85%.
The proportion that has fewer than 1144 chips is the p-value of Z when X = 1144, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (1144 - 1262)/118
Z = -1
Z = -1 has a p-value of 0.1587.
Hence the percentage is of 15.87%.
The proportion that has more than 1498 chips is one subtracted by the p-value of Z when X = 1498, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (1498 - 1262)/118
Z = 2
Z = 2 has a p-value of 0.9772.
1 - 0.9772 = 0.0228
Hence the percentage is of 2.28%.
More can be learned about the normal distribution at https://brainly.com/question/4079902
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Graph the line with the equation y = 2x - 1.
A line is uniquely defined by two points.
Since the points (0, -1) and (1, 1) lie on the graph (since they satisfy the equation), you can draw the line through these points.
Classify the triangle as acute, right , or obscure and classify it as equilateral , isosceles , or scalene
Step 1:
What is an isosceles triangle?
What is Isosceles Triangle? A triangle with two sides of equal length is an isosceles triangle.
Step 2: What is an acute angle?
An acute angle is an angle that measures between 90° and 0°.
Step 3:
The figure is an acute isosceles.
Final answer
Acute Isosceles
Graph the line that passes through the point: (1,-1) and is parallel to another line whose slope is 1.
The line that passes through the point (1,-1) and is parallel to another line whose slope is 1 will be y = x-2.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that line that passes through the point (1,-1) and is parallel to another line whose slope is 1.
The standard from the equation is,
y = mx + c
The equation with slope 1 is,
y = x +c
For the y-intercept, the value of y is -1.
-1 = 1(1) + c
-1 = 1+c
c = -2
Substitute the value of the slope, m as -1 and c as -2 we get,
y = 1x-2
y = x-2
Learn more about the straight line here:
brainly.com/question/3493733
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I need help defining variables and changing them into an inequality.
Enrollment in finite mathematics plus enrollment in calculus is less than 300.
The first step in solving a word problem is identifying the variables. The variables in any algebraic expression is the unknown value, and to solve it we usually assign a letter to represent it (x and y being the most commonly used).
In the question above, we already know that the number of student enrollees is less than 300 and not equal to 300 (might as well be just 20, we do not know) but we do know that it is NOT EQUAL TO 300, but less than.
Also we do not know the number of those enrolled for finite mathematics, so we shall call that f. Those that enrolled for calculus we shall call c. Since both categories are less than 300, the two variables f and c can now be written as an inequality which reads,
f plus c is less than 300
That is;
f + c ⊂ 300
6) Rotate clockwise around the origin 270°270°AYRSх6-2TQ QWhat is the rule? (x,y) → (Q' (_)R' (_)S'(__)T'(___)
we know that
The rule for a rotation by 270° about the origin is (x,y)→(y,−x)
so
we have
R(-5,0) -------> R'(0,5)
S(-3,0) ------> S'(0,3)
T(-1,-3) ------> T'(-3,1)
Q(-6,-3) ----> Q'(-3,6)
step 2
Graph the image
Plot the ponts of the image
using a graphing tool
please wait a minute to draw the figure
PLEASE HELP!! Fill in the gaps to factorise the expression below
3) Rotate counterclockwise around the origin180°180°Ay41NН.2.4xK44What is the rule? (x,y) - (___)H(__)l'(_,J'(___)K'(__)
We have the next points
H(-4,1)
I(-2,2)
J(-1,-2)
K(-4,-4)
The rule to rotate 180° counterclockwise
[tex](x,y)\rightarrow(-x,-y)[/tex]with rule, we can find the points
H'=(-(-4),-1)=(4,-1)
I'=(-(-2),-2)=(2,-2)
J'=(-(-1),-(-2))=(1,2)
K'=(-(-4),-(-4))=(4,4)
so the answer is
H'=(4,-1)
I'=(2,-2)
J'=(1,2)
K'=(4,4)
we can graph them they are the points in red
How can each type of sequence be helpful in everyday situations? Provide an example and the corresponding equation for each type.
Answer:
The two types of the sequence include
1) Arithmetic sequence
2) Geometric sequence
An arithmetic sequence is an ordered set of numbers that have a common difference between each consecutive term. For example in the arithmetic sequence 3, 9, 15, 21, 27, the common difference is 6. An arithmetic sequence can be known as an arithmetic progression.
The Nth term of an arithmetic sequence is given below as
[tex]\begin{gathered} T_n=a+(n-1)d \\ \text{Where,} \\ a=\text{first term} \\ n=Num\text{mber of terms} \\ d=\text{common difference}=T_2-T_1=T_3-T_2 \end{gathered}[/tex]A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
The Nth term of a geometric sequence is given below as
[tex]\begin{gathered} U_n=ar^{n-1} \\ \text{Where,} \\ a=\text{first term} \\ r=\text{common ratio=}\frac{t_2}{t_1}=\frac{t_3}{t_2} \end{gathered}[/tex]Real life illustrations of the types of sequence
Sequences are useful in our daily lives as well as in higher mathematics. For example, the interest portion of monthly payments made to pay off an automobile or home loan, and the list of maximum daily temperatures in one area for a month are sequences.
Example: arithmetic sequence
A boy building a tower with blocks uses 15 for the bottom row. Each row has 2 fewer blocks than the previous row. Suppose that there are 6 rows in the tower. Find a for n = 6
The number of blocks in each row forms an arithmetic sequence with a₁ = 15 and d= −2. The formula to be used is an = a₁ + (n − 1)d.
[tex]\begin{gathered} t_n=a+(n-1)d \\ T_6=15+(6-1)(-2) \\ T_6=15+5(-2) \\ T_6=15-10 \\ T_6=5 \end{gathered}[/tex]Hence,
On the sixth row, he will have 5 blocks left
Example: geometric sequence
A country's population is growing in such a way that each new generation is 1.5 times as large as the previous generation. Suppose there are 100 insects in the first generation. How many will there be in the fifth generation?
Here,the common ratio r=1.5
[tex]U_n=a(1.5)^{n-1}[/tex]4 divided by 48.03 Long Division
Answer: 12.00705
Step-by-step explanation:
The answer is 3(sign)2 I need help with the work
First, notice that the two sides of the right triangle are equal, then, using the pythagorean theorem,we get:
[tex]\begin{gathered} 6=\sqrt[]{x^2+x^2}=\sqrt[]{2x^2} \\ \Rightarrow\sqrt[]{2}x=6 \\ \Rightarrow x=\frac{6}{\sqrt[]{2}}\cdot(\frac{\sqrt[]{2}}{\sqrt[]{2}})=\frac{6\sqrt[]{2}}{2}=3\sqrt[]{2}_{} \\ x=3\sqrt[]{2} \end{gathered}[/tex]therefore, x = 3*sqrt(2)
2a + 3b when a=2 and b=4
Answer:
16
Step-by-step explanation:
[tex]2a+3b \\ \\ =2(2)+3(4) \\ \\ =4+12 \\ \\ =16[/tex]
Answer:
Step-by-step explanation:
2a+3b when a=2 and b=4
2a 2*2 =4
3b 3*4=12
=12+4=16
=2a+3b= 16 :)
Mena is making a hamster house. She cuts a hole for a window that has side lengths of 5 inches and 3 inches. Which drawing plan shows the correct rectangular opening? On these graphs, each unit represents 1 inch. 10 B(1,8) C (48) A. 6 5 4 3 2 1 A (1,2) D (4.2) 1 2 3 4 5 6 7 8 9 10 F (7.8) 10 9 E (3.8) 8 7 B. N00 1 H (3,2) G (7.2) 1 2 3 4 5 6 7 8 9 10
We need a rectangle with one side 5 units long and another side 3 units long
The correct option is:
Solve x^2-6+58=0 please fast I need help
Answer:
No real solutions.
Step-by-step explanation:
When solving this equation, you have to figure out if the two sides of an equation equal each other.
Solve.
x^2-6+58 = 0
Answer: No real solutions.
This is due to the fact that x^2-6+58 does not equal 0.
Hope this helps!
Btw, if this is correct, could I have Brainliest? Thanks!
In AWXY, WY is extended through point Y to point Z, YWX = (3x + 17), XYZ = (10x – 5), and WXY = (3x - 2). Find WXY.
Let's draw the figure to better understand the scenario:
To be able to get the measure of ∠WXY, we will be using the relationship of the interior angles of a triangle.
The sum of all interior angles of a triangle is 180°. Therefore we can say,
[tex]\text{ }\angle YWX\text{ + }\angle WXY\text{ + }\angle XYW=180^{\circ}[/tex]The formula or measure of ∠XYW isn't given. However, we observed that ∠XYW and ∠XYZ are pairs of Supplementary Angles. This means that the sum of two angles is equal to 180°.
We get,
[tex]\text{ }\angle XYW\text{ + }\angle XYZ=180^{\circ}[/tex]Therefore,
[tex]\text{ }\angle XYW\text{ }=180^{\circ}\text{ - }\angle XYZ[/tex]We will use this to complete the formula of the sum interior angles, substituting ∠XYW = 180° - ∠XYZ.
[tex]\text{ }\angle YWX\text{ + }\angle WXY\text{ + }\angle XYW=180^{\circ}[/tex][tex]\text{ }\angle YWX\text{ + }\angle WXY\text{ + (}180^{\circ}-\angle XYZ)=180^{\circ}[/tex]Substituting the given formulas of each angle, let's find x.
[tex]\text{ }\angle YWX\text{ + }\angle WXY\text{ + (}180-\angle XYZ)=180^{\circ}[/tex][tex](3x+17)+(3x-2)+(180-(10x-5)^{})=180^{\circ}[/tex][tex]\text{-4x + 200 = 180}[/tex][tex]\text{-4x = 180 - 200 = -20}[/tex][tex]\frac{\text{-4x}}{-4}\text{ = }\frac{\text{-20}}{-4}[/tex][tex]\text{ x = 5}[/tex]Let's substitute x = 5 to ∠WXY = 3x - 2 to find its measure.
[tex]\angle WXY=3x-2=\text{ 3(5) - 2}[/tex][tex]\text{ = 15 - 2}[/tex][tex]\angle WXY=13^{\circ}[/tex]Therefore, the measure of ∠WXY = 13°.
Please helpppppppppp
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simplifying with like terms; 3x^2 + 5x - 2x^2
Simplifying,
[tex]\begin{gathered} 3x^2+5x-2x^2 \\ \rightarrow3x^2-2x^2+5x \\ \rightarrow x^2+5x \end{gathered}[/tex]See attached pic. I am confused on how to answer A with the correct number of significant figures.
Recall one of the rules for significant figures
A final zero or trailing zeros in the decimal portion ONLY are significant
24.00 mg has four significant figures
2,4, 0 and 0
24.00 mg when converted to grams is 0.024 g
0.024 only has 2 significant figures, therefore we need to add 2 more zeroes at the end of 4
0.024 g → 0.02400 g
Juan is designing an exercise room in his house. How many square feet of rubber flooring will he need to cover the floor? The product is sold in whole square yards. How many square yards should he buy? Explain. 10 ft 3 ft 9 ft 13 ft The total area of the exercise room is 103 ft. This is also the total amount of rubber flooring that Juan must have. (Type a whole number.) The number of square yards equivalent to this total area is 11.4 square yards. (Round to the nearest tenth as needed.) Since rubber flooring is sold in whole sq. yards, Juan must purchase exactly square yards.
The amount of rubber flooring will be the area of the floor.
We can calculate the area as the sum of two rectangles:
Then, the area is:
[tex]A=10\cdot4+9\cdot7=40+63=103ft^2[/tex]We can convert this area into square yards as:
[tex]A=103ft^2\cdot(\frac{1\text{ yd}}{3\text{ ft}})^2=103\cdot\frac{1}{9}\text{ yd}^2\approx11.44\text{ yd}^2[/tex]As we have to purchase a whole number of square yards, we will buy the next integer greater than 11.44, that is 12 sq yd.
Answer:
The floor area is 103 square feet.
This is equivalent to 11.44 square yards.
He has to purchase 12 square yards of rubber floor.
