The amount that was invested at 9% is $10303 , and at 6% is $1032 .
In the question ,
it is given that
total amount invested is $11335 .
let the amount invested at 9% be "x" .
so , the interest earned from 9% part is 0.09x
and let the amount invested at 6% be "y" .
the interest earned from 6% part is 0.06y
So , the equation is x + y = 11335 .
x = 11335 - y
Also given that interest earned from 9% amount exceeds the interest earned from 6% by $865.35 .
So , according to the question
0.09x = 0.06y + 865.35
On substituting x = 11335 - y in the above equation , we get
0.09(11335 - y) = 0.06y + 865.35
1020.15 - 0.09y = 0.06y + 865.35
0.09y + 0.06y = 1020.15 - 865.35
0.15y = 154.8
y = 154.8/0.15
y = 1032
and x = 11335 - 1032
x = 10303
Therefore , The amount that was invested at 9% is $10303 , and at 6% is $1032 .
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Passes through (8,8) with slope 11/6
Given:
point (8,8).
slope 11/6
The slope intercept form is,
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept.
we know that m=11/6 so subistute in the equation.
[tex]y=\frac{11}{6}x+b[/tex]Now, let us plug in the point in the equation to find the value of b that is the y-intercept.
[tex]undefined[/tex]What is the answer to this equation?
Answer:
D 7.5
Step-by-step explanation:
n + n-3 + 2n-4 = perimeter ≥ 37
4n-7≥37
4n≥30
n≥7.5
O is the center of the regular hexagon below. Find its perimeter. Round to the nearest tenth if necessary.
To solve this problem, we have to find the side length and multiply it by the number of sides of the figure.
To find the length side we will use the following formula:
[tex]ap=\sqrt[]{I^2-(\frac{I^{}}{2})^2}\text{.}[/tex]Where ap is the length of the apothem, and I is the side length.
Substituting the given values, we get:
[tex]10=\sqrt[]{I^2-(\frac{I}{2})^2}.[/tex]Solving the equation for I, we get:
[tex]\begin{gathered} \\ I=\frac{2\times10}{\sqrt[]{3}}. \end{gathered}[/tex]Therefore, the perimeter of the hexagon is:
[tex]6I=6\times\frac{2\times10}{\sqrt[]{3}}\approx69.3\text{ units.}[/tex]Answer:
[tex]69.3\text{ units.}[/tex]Write the rate as a fraction in the simplest form $1680 for 8 weeks 236 miles on 12 gallons of gasoline
The question asked to write the rate as a fraction in simplest form
[tex]\text{ \$1,680 for 8 w}eeks[/tex]To write the above relation in a fraction, we will have
[tex]\begin{gathered} =\frac{1680}{8} \\ \end{gathered}[/tex]Dividing to the lowest term, we will have
[tex]\begin{gathered} =\frac{210}{1} \\ whichis\text{ \$210 for 1 we}ek \end{gathered}[/tex]The question asked to write the rate as a fraction in simplest form
[tex]236\text{ miles on 12 gallons of gasoline}[/tex]To write the above relation in a fraction, we will have
[tex]=\frac{236}{12}[/tex]To express as a fraction in its lowest terms will be
[tex]\begin{gathered} =\frac{59}{3} \\ \text{which represents 59 miles for 3 gallons} \end{gathered}[/tex]9.5.35 Assigned Media An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 300 feet of antique picket fencing are to be used to enclose the garden, find the dimensions of the garden What is the length of the garden? The length of the garden is
Answer:
• The dimensions of the garden are 90 feet by 60 feet.
,• The length of the garden is 90 feet.
Explanation:
Let the length of the garden = l
The width is exactly two-thirds of the length, Width = (2/3)l
If 300 feet of antique picket fencing are to be used to enclose the garden, this means that the perimeter of the proposed garden is 300 feet.
[tex]\begin{gathered} \text{Perimeter}=2(\text{Length}+\text{Width)} \\ 300=2(l+\frac{2}{3}l) \end{gathered}[/tex]Next, solve the equation for the length, l:
[tex]\begin{gathered} \frac{300}{2}=l+\frac{2}{3}l \\ 150=\frac{5l}{3} \\ l=150\times\frac{3}{5} \\ l=90\text{ feet} \end{gathered}[/tex]The length of the garden is 90 feet.
Next, we determine the width.
[tex]\begin{gathered} \text{Width}=\frac{2}{3}l \\ =\frac{2}{3}\times90 \\ =2\times30 \\ =60\text{ feet} \end{gathered}[/tex]The dimensions of the garden are 90 feet by 60 feet.
Write 5.8% as a fraction in lowest terms.
Answer:
[tex]5.8\text{ \%}\rightarrow\frac{29}{500}[/tex]Explanation: We have to write 5.8% In fraction in lowest terms:
This percent number essentially is:
[tex]5.8\text{ \%=}\frac{5.8}{100}[/tex]Therefore we can write it as:
[tex]\frac{5.8}{100}=\frac{5.8\times10}{100\times10}=\frac{58}{1000}[/tex]In lowest terms, this would be:
[tex]\frac{58}{1000}=\frac{29}{500}[/tex]Which calculation and answer show how to convert 13 to a decimal?
when evalueatong the expression 13/15,
13 serves as the dividend and
15 is the divisor
Divisor is always placed outside the division sign and the dividend inside.
According to the option, you can see that 15 which is the divisor is placed outside and 13 is placed inside.
check the diagram below:
Option A is the correct answer in this case
James is putting a frame around a rectangular photograph. The photograph is 12 inches long
and 10 inches wide, and the frame is the same width all the way around. What will be the
area of the framed photograph? (Hint: use "x" as your variable.)
Polynomial:________
=_________
=_________
=_________final answer in standard form.
PLEASSEEEEEE i need know this asap
Answer:
The area is 4x² + 44x + 120Step-by-step explanation:
GivenDimensions of rectangle are 12 in and 10 in,Width of the frame is x.To find The area of the framed photographSolutionDimensions of the framed photograph are:
12 + 2x and 10 + 2xArea of the framed photograph is:
A = lwA = (12 + 2x)(10 + 2x) = 12*10 + 12*2x + 10*2x + 2x*2x = 120 + 24x + 20x + 4x²= 4x² + 44x + 120The measures of the angles of a triangle are shown in the figure below. Solve for x.
44°
61°
(8x+11)°
Earl Miller, a customer of J. Crew, will pay $400 for a new jacket. J. Crew has a 60% markup on selling price. What is the most that J. Crew can pay for this jacket?
If Earl Miller, a customer of J. Crew, will pay $400 for a new jacket. J. Crew has a 60% markup on selling price. The most that J. Crew can pay for this jacket is $160.
How to find the total payment?Given parameters:
Cost of new jacket = $400
Markup = 60%
Now let find the amount that was paid for the jacket using this formula
Amount = Cost of new jacket × ( 1- markup)
Let plug in the formula
Amount = $400 × ( 1 - .60 )
Amount = $400 × .40
Amount = $160
Therefore we can conclude that the amount of $160 was paid the most.
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An elevator car starts on the second floor of a building 27 feet above the ground. The car rises 4.2 feet every second on its way up to the 15th floor. Assuming the car doesn’t slow down or make any stops , how long will it take the car to reach a height of 102 feet above the ground?
17.86 seconds
Explanation:The starting point of the elevator car = 27 feet above the ground
The endpoint point of the elevator car = 102 feet above the ground
The total distance traveled by the elevator car = 102 feet - 27 feet
The total distance traveled by the elevator car = 75 feet
Time taken by the elevator car to rise 4.2 feet = 1 second
Time taken by the elevator car to rise 75 feet = 75/4.2 seconds
Time taken by the elevator car to rise 75 feet = 17.86 seconds
Therefore, it takes the car 17.86 seconds to reach a height of 102 feet above the ground
can u find a b and c its parallelogramthank u
To answer this question, we need to remember two theorems of parallelograms:
1. If a quadrilateral is a parallelogram, the two sets of its opposite angles are congruent:
2. The consecutive angles of parallelograms are supplementary (they sum 180 degrees):
Then, with this information, we have that:
[tex]97\cong m\angle c\Rightarrow m\angle c=97[/tex]And also, we have that the diagonal forms two congruent triangles, and the sum of internal angles of a triangle is equal to 180, then, we have:
[tex]m\angle c+26+m\angle b=180\Rightarrow97+26+m\angle b=180\Rightarrow m\angle b=180-97-26[/tex]Then, we have:
[tex]m\angle b=180-123\Rightarrow m\angle b=57[/tex]Then, using that the consecutive angles of parallelograms are supplementary (they sum 180 degrees), we have:
[tex]97+m\angle a+m\angle b=180\Rightarrow97+m\angle a+57=180\Rightarrow m\angle a=180-97-57_{}[/tex]Thus, we have that the measure for angle a is:
[tex]m\angle a=180-154\Rightarrow m\angle a=26[/tex]In summary, we have that (all the measures in degrees):
m< a = 26
m< b = 57
m< c = 97
Which sample size will produce the widest 95% confidence interval, given asample proportion of 0.5?A. 40B. 70C. 60D. 50
The confidence interval depends on the margin of error. When finding the margin of error, the z score corresponding to the 95% confidence level would be multiplied by the square root of the product of the estimated proportion of success and failure divided by the sample size. The greater the sample size, the smaller thie value that would be gotten from this operation. The smaller the sample size, the greater the value that would be gotten from this operation. A greater value would give a bigger margin of error. Thus, the confidence interval would be wider. Hence, the correct option for the sampe size is
A. 40
How to solve this problem? (the answer is 262 Hz). i want to know the step by step on how to solve the equation given. if it helps, i am a grade 10 student. (YES, this is a MATH problem)
The frequency of middle C = 262 Hz
Explanation:The formula for calculating the frequency, F hertz, of a note n seminotes above the concert pitch is:
[tex]F\text{ = 440(}\sqrt[12]{2})^n[/tex]This can be re-written as:
[tex]F=440(2^{\frac{n}{12}})[/tex]Middle C is 9 semitones below the concert pitch
That is, n = -9
To find the frequency of middle C, substitute n = -9 into the equation for F
[tex]\begin{gathered} F=440(2^{\frac{-9}{12}}) \\ F\text{ = 440(}0.5946) \\ F\text{ = }261.62\text{ Hz} \\ F\text{ = 262 Hz (to the nearest hertz)} \end{gathered}[/tex]The frequency of middle C = 262 Hz
Using the completing-the-square method, rewrite f(x) = x2 − 8x + 3 in vertex form. (2 points)
A) f(x) = (x − 8)2
B) f(x) = (x − 4)2 − 13
C) f(x) = (x − 4)2 + 3
D) f(x) = (x − 4)2 + 16
By using the completing the square method, f(x) = x² − 8x + 3 in vertex form is: B. f(x) = (x − 4)² − 13.
The vertex form of a quadratic equation.In this exercise, you're required to rewrite the given function in vertex form by using the completing the square method. Mathematically, the vertex form of a quadratic equation is given by this formula:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.
In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:
f(x) = x² − 8x + 3
f(x) = x² − 8x + (8/2)² - 13
f(x) = x² − 8x + (4)² - 13
f(x) = x² − 8x + 16 - 13
f(x) = (x² − 8x + 16) - 13
f(x) = (x − 4)² − 13
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I need a math wiz to explain this to me, are you a math wiz?
SOLUTION
The questions is outside scope
Simplify [tex]{({4e}^{ - 8x})}^{0.5} [/tex]with no negative exponents. thanks!
Explanation
Given the following expression
[tex]\begin{gathered} \text{Simplify (4 }e^{-8x})^{\frac{1}{2}} \\ \text{This expression can be written as} \\ (4\cdot\text{ }e^{-8x})^{\frac{1}{2}} \\ \text{Splitting the expression, we can have the below expression} \\ (4)^{\frac{1}{2}}\cdot(^{}e^{-8x})^{\frac{1}{2}} \\ \text{According to the law of indicies} \\ x^{\frac{1}{2}}\text{ = }\sqrt[]{x} \\ \text{Hence, we have the following expression} \\ \sqrt[]{4\text{ }}\cdot\text{ (}e^{-8x\cdot\text{ }\frac{1}{2}}) \\ 2\cdot\text{ }e^{-4x} \\ 2e^{-4x} \\ \text{Therefore, the simplified form is 2}e^{-4x} \\ \frac{2}{e^{4x}} \end{gathered}[/tex]In the picture below, measure 1 is 5x-14 degrees and measure 3 is 2x+10 degrees. Find measure 2.
SOLUTION:
Step 1:
In this question, we have the following:
In the picture below, measure 1 is (5x-14) degrees and measure 3 is (2x+10) degrees.
Find the measure of 2.
Step 2:
From the diagram, we can see that angles 1 and 3 are vertically opposite and they are also equal.
Based on this fact, we can see that:
[tex]\begin{gathered} \angle\text{1 = }\angle3 \\ (\text{ 5 x- 14 ) = ( 2x + 10 )} \\ \text{collecting like terms, we have that:} \\ 5x\text{ - 2x = 10 + 14} \\ \text{3 x = 24} \end{gathered}[/tex]Divide both sides, we have that:
[tex]\begin{gathered} x\text{ =}\frac{24}{3} \\ \text{x = 8 } \end{gathered}[/tex]Then, we put x = 8 into the equation for Angle 1 , we have that:
[tex]\angle1=(5x-14)=5(8)-14=40-14=26^0[/tex][tex]\angle3=(2x+10)=2(8)+10=16+10=26^0[/tex]Hence, we can see that Angles 1 and 3 are equal.
Step 3:
From the diagram, we can see that:
we can see that angles 2 and 4 are vertically opposite and they are also equal.
Recall that angles 1 and 3 are also vertically opposite and they are also equal.
Therefore, we can see that:
[tex]\begin{gathered} \angle2\text{ = p} \\ \angle4\text{ = p} \\ \angle1\text{ = }26^0 \\ \angle3=26^0 \\ \text{Then, we have that:} \\ p+p+26^0+26^{\text{ 0 }}=360^0\text{ ( Sum of angles at a point)} \\ 2p+52^0=360^0 \\ 2p=360^0-52^0 \end{gathered}[/tex]Divide both sides by 2, we have that:
[tex]\begin{gathered} 2p=308^0 \\ p\text{ =}\frac{308^0}{2} \\ p=154^0 \end{gathered}[/tex]CONCLUSION:
[tex]\begin{gathered} \operatorname{Re}call\text{ that }\angle2\text{ = p} \\ \text{Then, we have that:} \\ \angle2=154^0 \end{gathered}[/tex]Please I really need help. I just need the answer no steps
Explanation
The question wants us to obtain the margin of error
A margin of error tells you how many percentages points your results will differ from the real population value.
The formula to be used is
To do so, we will have to list out the parameters to be used
[tex]\begin{gathered} standard\text{ deviation=}\sigma=13.8 \\ sample\text{ size=n=18} \\ confidence\text{ level=}\gamma=80\text{ \%} \end{gathered}[/tex]The next step will be to find the z-score value for a confidence level of 80%.
From the statistical table, we have
[tex]Z_{\gamma}=1.28[/tex]So, we can input the given data obtained into the formula
So we will have
[tex]\begin{gathered} MOE=1.28\times\sqrt{\frac{13.8^2}{18}} \\ \\ MOE=1.28\times\frac{13.8}{\sqrt{18}} \\ \\ MOE=1.28\times3.2527 \\ \\ MOE=4.16344 \end{gathered}[/tex]So the margin of error (M.E.) = 4.163 (To 3 decimal places)
19. Write in algebraic terms: six times a number, minus five times the number, plus eight.
Let the number be a
6a x 5a + 8
During a food drive, a local middle school collected 3,195…
Answer:
100 cans
Explanation:
• The total number of canned food items collected = 3,195
,• The number of classrooms that participated = 28
To estimate the number of items each classroom donated, divide 3195 by 28.
[tex]\frac{3195}{28}\approx\frac{3000}{30}=100[/tex]Note: Round to a whole number since the number of cans cannot be a decimal.
Each class donated about 100 cans.
Solve the following system of linear equations using elimination. x-y=5 -x-y=-11
Elimination Method : In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.
The given system of equation :
x - y = 5 ( 1 )
- x - y = - 11 ( 2 )
Add the equation ( 1 ) & ( 2 )
x - y + ( -x - y ) = 5 + ( -11 )
x - y -x - y = 5 - 11
x - x - y - y = -6
0 - 2y = - 6
y = -6/( -2)
y = 3
Substitute the value of y = 3 in the equation ( 1)
x - y = 5
x - 3 = 5
x = 5 + 3
x = 8
Answer : x = 8, y = 3
what is equivalent to 2^4 x 4^2?
Given an indices shown below
[tex]2^4\text{ }\times4^2^{}[/tex]Addition method of indices
The second power need to be split into the power of 2
[tex](2^4\text{ }\times2^2)2^2)[/tex]Hence the equivalent is Option B
- 2/3 (x+12)+2/3 x=-5/4 x+2
We will have the following:
[tex]-\frac{2}{3}(x+12)+\frac{2}{3}x=-\frac{5}{4}x+2\Rightarrow-\frac{2}{3}x-8+\frac{2}{3}x=-\frac{5}{4}x+2[/tex][tex]\Rightarrow-\frac{2}{3}x+\frac{2}{3}x+\frac{5}{4}x=2+8\Rightarrow\frac{5}{4}x=10[/tex][tex]\Rightarrow5x=40\Rightarrow x=8[/tex]So, the value of x is 8.
4. The temperature in Baguio is 18.6℃, while Manila the temperature is 31.5℃. How much warmer is it in Manila than Baguio?A. 12.6℃B. 12.7℃C. 12.9℃D. 13℃
Given:
The temperature in Baguio is 18.6℃.
The temperature in manila is 31.5℃.
To find:
The differene bin temperature etween imanila and aguio.
Explanation:
The difference between manila and Baguio's temperature s
[tex]31.5^{\circ}C-18.6^{\circ}C=12.9^{\circ}C[/tex]Thus, manila is 12.9 degrees Celcius warmer than Baguio.
Final answer:
anila is 12.9 degrees Celcius warmer than Baguio.
What is the product of V3 and 7V30 in simplest radical form?
Determine the product of two expressions.
[tex]\begin{gathered} \sqrt[]{3}\times7\sqrt[]{30}=7\sqrt[]{30\cdot3} \\ =7\sqrt[]{3\cdot3\cdot10} \\ =7\cdot3\sqrt[]{10} \\ =21\sqrt[]{10} \end{gathered}[/tex]So answer is,
[tex]21\sqrt[]{10}[/tex]what are the three terms and 4x - 2y + 3
Solution
We have the following expression:
[tex]4x-2y+3[/tex]Here we have 3 terms:
[tex]4x,\text{ -2y and 3}[/tex]Variable terms:
[tex]4x,-2y[/tex]Constant term
[tex]3[/tex]a company loses $5,400 as the result of manufacturing defect. each of the 8 owners have agreed to pay an equal amount, x, to pay for the loss. How much each owner paid?
Explanation:
If 'x' is the amount each owner will pay, there are 8 owners and the total amount to pay is $5,400 the equation to solve is:
[tex]8x=5,400[/tex]Solving for x:
[tex]x=\frac{5,400}{8}=675[/tex]Answer:
Each owner has to pay $675
A line passes through the point (-6,1) and has a slope of -5/2
Write an equation in slope - intercept form for this line .
Answer: [tex]y=-\frac{5}{2}x+16[/tex]
Step-by-step explanation:
The equation in point-slope form is [tex]y-1=-\frac{5}{2}(x+6)[/tex]. To find the equation in slope-intercept form, isolate [tex]y[/tex].
[tex]y-1=-\frac{5}{2}(x-6)\\\\y-1=-\frac{5}{2}x+15\\\\y=-\frac{5}{2}x+16[/tex]
Be sure to include the correct unit in your answer
The fence required is:
[tex]388.3125ft^2[/tex]Explanation:For the farmer to build an accurate fence, he needs to know the area of the rose garden. The area is the sum of the area of the rectangle and the area of the semicircle.
The area of the rectangle is:
[tex]\begin{gathered} A=wl \\ =15ft\times20ft \\ =300ft^2 \end{gathered}[/tex]The area of the semicircle is:
[tex]\begin{gathered} A=\frac{\pi}{2}r^2 \\ \\ \text{Where r is the radius }=\frac{15}{2}=7.5ft,\pi=3.14 \\ \\ A=\frac{3.14}{2}(7.5)^2=88.3125ft^2 \end{gathered}[/tex]The area of the rose garden is:
[tex]300ft^2+88.3125ft^2=388.3125ft^2[/tex]