Answer:
After 12 years the investment will be worth $5145.
Step-by-step explanation:
The formula used for compounded interest is:
A = P(1+r/n)^nt
where,
A = future value
P = Principal Amount
r = interest rate
n = no of times interest is compounded
t = time
In the question given:
A=?
P = $2100
r = 7.75% or 0.0775
n = 1
t= 12
A= 2100*(1+0.0775/1)^1*12
A= 2100 *(1+0.0775)^12
A= 2100 *(1.0775)^12
A= 2100 * 2.45
A= 5145
So, after 12 years the investment will be worth $5145.
Gustavo earns 8 dollars per hour plus 10% of his sales. Write an equation that models Gustavo's total earnings, E, when he works x hours and has a total of y sales in dollars. you do not need to solve the equation.
Answer:
e = 8x + 0.1y
Step-by-step explanation:
If Gustavo makes no sales at all, he still gets $8 per hour worked (x). We can model this part with this equation:
e = 8x
But then, if he sells something, he makes extra money.. He makes 10% (0.1) of every sale (y). So the equation becomes:
e = 8x + 0.1y
or you can express it this way:
e = 8x + y/10
which is the same thing just written differently.
A right regular pentagonal prism has a base edge length 14 cm, and height 12 cm. Identify the volume of the prism to the nearest tenth. HELP PLEASE!!
Answer:
4046.56 cm3
Step-by-step explanation:
The base is made by 5 isosceles triangles, with one side of 14 cm, and the opposite angle of [tex] \frac{360} 5 = 72° [/tex]. Each of the other angle is [tex]\frac{180-72} {2} =54°[/tex]. From there, you can calculate the height of each base triangle as in [tex]\frac {h} 7 = tan54[/tex] or 9.634...cm.
Your volume will be [tex]5 * \frac {(14 * 9.634)} 2 * 12 = 4046.56 cm^3[/tex]
Find (ƒ + g)(x) where ƒ(x) = 5x2 + 4, g(x) = 6x2 – x.
(ƒ + g)(x) = 11x2 – x + 4
(ƒ + g)(x) = 11x2 – 4x
To find (ƒ + g)(x) for the given functions ƒ(x) = 5x² + 4 and g(x) = 6x² - x, we add the like terms to get
(ƒ + g)(x) = 11x² - x + 4.
To find (ƒ + g)(x) where ƒ(x) = 5x² + 4, and g(x) = 6x² – x, we simply add the two functions together. We combine like terms to calculate the sum.
By adding the corresponding terms:
The x² terms: 5x² + 6x² = 11x² The x terms: Since there is no x term in ƒ(x), we only have the x term from g(x), which is -x.The constant terms: 4 from ƒ(x) and there is no constant term in g(x).Combining these, we get
(ƒ + g)(x) = f(x) + g(x)
(f + g)(x) = 11x² - x + 4.
Which of the following equations is an example of inverse variation between variables x and y?
A. y = x + 7
B. y = 7x
C. y = x/7
D. y = 7/x
Answer:
D. [tex]y=\frac{7}{x}[/tex]
Step-by-step explanation:
Let y varies inversely with x.
Then we can write the variation equation:
[tex]y\propto \frac{1}{x}[/tex]
We introduce the constant of proportionality, k and obtain the inverse variation equation:
[tex]y=\frac{k}{x}[/tex]
From the given options, the only equation in this form is
[tex]y=\frac{7}{x}[/tex]
In this case, k=7 is the constant of proportionality or constant of variation.
A stove costs $695 will be on sale next week for 20% off its regular price. What is the amount of savings
Answer:
It would be 139$
Step-by-step explanation:
In order to find a percent of a value you first move the decimal place over 2 to the left or divide by 100(percentage is no longer there). In this case it would be .20. You multiply that with the total number(695) and the product is your answer.
Please help me out ‼️
Answer:
7
Step-by-step explanation:
In similar triangles, corresponding elements are proportional. Then we get,
(2x + 1)/(x-1) = 10/4
4(2x +1) = 10(x-1)
8x + 4 = 10x - 10
8x = 10x - 14
2x = 14
x = 7
Hope it helps and if it does, please mark me brainliest...
Answer:
7
both sides are corresponding so triangleABC AB=AC.
Circle M is circumscribed about right triangle ABC with legs 6 meters and 8 meters.
What is the exact circumference of ⊙M
ABC is a right triangle, so AC has length given by
[tex]AC^2=(6\,\mathrm m)^2+(8\,\mathrm m)^2\implies AC=\sqrt{100\,\mathrm m^2}=10\,\mathrm m[/tex]
Then the circumference of circle M is [tex]10\pi\,\mathrm m[/tex].
Can someone help please
Answer:
62 Sunday papers were sold
Step-by-step explanation:
Let x represent the number of Sunday papers sold. Then half that many, or x/2, is the number of Friday papers sold. The total revenue from the sales is the sum of products of quantity and price:
1.50 · x + 0.75 · (x/2) = 116.25
Multiplying by 2, this becomes ...
3.00x +0.75x = 232.50
3.75x = 232.50
Dividing by the coefficient of x gives ...
232.50/3.75 = x = 62
The number of Sunday newspapers sold is 62.
I need help getting started please
Check the picture below.
so, the triangular prism is really 2 triangles and 3 rectangles stacked up to each other at the edges. Let's simply get the area of each shape and sum them up, and that's the area of the prism.
[tex]\bf \stackrel{\textit{two triangles}}{2\left[ \cfrac{1}{2}(\stackrel{base}{6})(\stackrel{height}{5.2}) \right]}+\stackrel{\textit{right-side rectangle}}{(8\cdot 6)}+\stackrel{\textit{left-side rectangle}}{(8\cdot 6)}+\stackrel{\textit{base rectangle}}{(8\cdot 6)} \\\\\\ 31.2+48+48+48\implies 175.2[/tex]
Answer:
The surface area = 175.2 mm²
Step-by-step explanation:
Formula:-
Area of rectangle = lb
Area of triangle = bh/2
It is given a triangular prism.
To find the surface area
Surface area = 3 Rectangle area + 2 triangle area
Rectangle area = 3 * lb
= 3 * 8 * 6
= 144 mm²
Triangle area = 2 * bh/2 = bh
= 6 * 5.2 = 31.2²
Total area = 144 + 31.2 = 175.2 mm²
What is the sum of the geometric sequence -1, 6, -36, ....if there are 7 terms.
A) -39,991
B) -6,665
C) 6,665
D) 39,991
Answer:
A) - 39,991
Step-by-step explanation:
Sum of geometric sequence formula is
[tex]S = a(\frac{1 -r^n}{1-r} )\\a=-1, r=6/(-1)=-6, n=7\\\\S = -1(\frac{1 -(-6)^7}{1-(-6)} )= -\frac{279937}{7} = -39991[/tex]
Answer:
The correct answer option is A) -39,991.
Step-by-step explanation:
We know that the sum of the geometric sequence is given by the formula:
[tex] S _ n = \frac { a _ 1 ( 1 - r ^ n ) } { 1 - r } [/tex]
where [tex]a_1[/tex] is the first term, [tex]r[/tex] is the common ratio and [tex]n[/tex] is the number of terms.
Here,
[tex]a_1 = -1[/tex]
[tex]r = -6[/tex]
[tex]n=7[/tex]
Substituting these values in the above formula to get:
[tex] S _ 7 = \frac { -1 ( 1 - (-6) ^ 7 ) } { 1 - (-6) } [/tex]
S_n = -39,991
Bill is making accessories for the soccer team. He uses 791.86 inches of fabric on headbands for 32 players and 2 coaches. He also uses 273.28 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
There was 23.29 inches used on a headband for each player.
And 8.54 inches used on a wristband for each player.
Step-by-step explanation:To find out how much fabric for headbands and would beused for each player/person you would do
[tex]total \: fabric \: used \: \div \: total \: amount \: of \: people[/tex]
So, if you substitute the values in it is
[tex]791.86÷34=23.29 \: inches \: for \: 1 \: headband. \: [/tex]
And finally, to find how much fabric is used on a wristband for each player/person you would use the same formula.
[tex]273.28 \: \div 32 = 8.54 \: inches[/tex]
Point (-4, 3) lies in Quadrant I II III IV
Answer:
Quadrant II
Step-by-step explanation:
I attached an image of the quadrants system.
You'll see that the scenario where we have a point with a negative X value and a positive Y value, it belongs to Quadrant II.
Quadrant I
Degrees: 0-90
X values: positive (+)
Y values: positive (+)
Quadrant II
Degrees: 90-180
X values: negative (-)
Y values: positive (+)
Quadrant III
Degrees: 180-270
X values: negative (-)
Y values: negative (-)
Quadrant IV
Degrees: 270-360
X values: positive (+)
Y values: negative (-)
Bena bought a bottle of water for $ 1.29 and a pack of gum for $ 1.79.How much did bena give the clerk if she got $6.92 in change
Find the volume of this composite solid.
For this case we have that the figure shown is composed of a cylinder and a cone.
We have that the volume of a cylinder is given by:
[tex]V = \pi * r ^ 2 * h[/tex]
Where:
A: It's the radio
h: It's the height
Substituting the values:
[tex]V = \pi * (5) ^ 2 * 10\\V = \pi * 25 * 10\\V = 250 \pi \ m ^ 3[/tex]
On the other hand, the volume of a cone is given by:
[tex]V = \frac {\pi * r ^ 2 * h} {3}[/tex]
Where:
A: It's the radio
h: It's the height
Substituting the values:
[tex]V = \frac {\pi * (5) ^ 2 * 4} {3}\\V = \frac {\pi * 25 * 4} {3}\\V = \frac {100 \pi} {3} \ m ^ 3[/tex]
Then, the total volume is:
[tex]V_ {t} = 250 \pi \ m ^ 3 + \frac {100 \pi} {3} \ m ^ 3[/tex]
Taking [tex]\pi = 3.14[/tex], we have to:
[tex]V_ {t} = 889.67 \ m ^ 3[/tex]
Answer:
Option D
What is the value of COS H?
Round to four decimal places if needed.
Answer:
Final answer is approx [tex]\cos\left(H\right)=0.4235[/tex].
Step-by-step explanation:
using given information from the attached picture, we need to find the value of cos(H) so let's apply the formula of cosine.
[tex]\cos\left(\theta\right)=\frac{adjacent}{hypotenuse}[/tex]
[tex]\cos\left(H\right)=\frac{GH}{FH}[/tex]
[tex]\cos\left(H\right)=\frac{36}{85}[/tex]
[tex]\cos\left(H\right)=0.423529411765[/tex]
Hence final answer is approx [tex]\cos\left(H\right)=0.4235[/tex].
Using the cosine ratio, the value of cos H to 4 decimal places is: A. 0.4235.
What is the Cosine Ratio?Cosine ratio is expressed as, cos ∅ = adjacent/hypotenuse of a right triangle.
Given:
∅ = H = ?Hypotenuse = 85Adjacent side = 36Therefore:
Cos H = 36/85
Cos H = 0.4235
Therefore, using the cosine ratio, the value of cos H to 4 decimal places is: A. 0.4235.
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Solve the following equation algebraically:
x^2=180
a.
-13.42, 13.42
b.
13.42
c.
-90, 90
d.
-12.42, 12.42
Answer:
A
Step-by-step explanation:
Taking the square root of both sides, you get
[tex]\sqrt{x^2} = \pm\sqrt{180}[/tex]
which simplifies to
[tex]x = \pm\sqrt{180}[/tex]
The square root of 180 is approximately 13.42 and since it is the plus or minus square root, the answer is A, -13.42, 13.42.
Final answer:
The equation x²=180 is solved by taking the square root of both sides, yielding two solutions: x = 13.42 and x = -13.42. Thus, option A is corect.
Explanation:
To solve the equation x² = 180 algebraically, we need to take the square root of both sides of the equation. This gives us two solutions, since both a positive and negative number squared will yield 180. The square root of 180 once calculated is approximately 13.42. Therefore, the two solutions are x = 13.42 and x = -13.42.
4x2+3x=0 please solve this by using quadratic formula
Answer:
x= 0 and x=-3/4
Step-by-step explanation:
[tex]4x^2 + 3x =0[/tex]
We need to solve this equation using quadratic formula.
The quadratic formula is:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
for the type of equation
[tex]ax^2 +bx+c=0[/tex]
So, for our given equation:
a= 4
b= 3
c=0
putting values in the formula
[tex]x=\frac{-3\pm\sqrt{9-0}}{8}\\x=\frac{-3\pm3}{8}\\x=\frac{-3+3}{8}\,and\, x=\frac{-3-3}{8}\\x=\frac{0}{8}\,and\, x=\frac{-6}{8}\\x=0\,and\, x=\frac{-3}{4}[/tex][/tex]
so, x= 0 and x=-3/4.
James wants to pursue a career in engineering whereby he can offer services directly to the public. What certification should he get and who provides this certification?
James needs to obtain a certification of a (______) so that he can offer services directly to the public. The (______) conducts examinations that engineers must pass in order to acquire this certification.
blank 1. fundamental engineer, professional engineer, structural engineer
blank 2. NCEES, NICET, ABET
Answer:
Blank 1. Professional engineer
Blank 2. ABET( Accreditation Board for Engineering and Technology)
What equation/thing is happening to this number to get this solution? My book is just telling me "use a calculator" but it doesn't explain it any further. Please help!
Answer:
Use the square root function on your calculator
Step-by-step explanation:
Look at the third line down, where is says that 936 = AD^2. If you hit the 2nd button on your calculator then the x^2 button, you will get the square root function. After you hit those buttons in that order, you'll get the opportunity to find the square root of 936 by entering it in and hitting "enter" on your calculator. The square root of 936 is 30.59417
Which equation represents the perpendicular bisector of the given line segment?
A) x = 0
B) y = 0
C) y = x
D) x = 10
Answer:
Option D. [tex]x=10[/tex]
Step-by-step explanation:
step 1
Find the midpoint of the given line segment
we know that
The formula to calculate the midpoint between two points is equal to
[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
we have
[tex]A(5,10),B(15,10)[/tex]
substitute the values
[tex]M=(\frac{5+15}{2},\frac{10+10}{2})[/tex]
[tex]M=(10,10)[/tex]
step 2
Find the equation of the perpendicular bisector
we know that
The equation of a perpendicular bisector is equal to the x-coordinate of the midpoint, because is a vertical line (parallel to the y-axis)
therefore
the equation is equal to
[tex]x=10[/tex]
Answer:
10
Step-by-step explanation:
Answer both questions please
1.) The diameter of a circle is 10cm.What is the approximate circumference? Use 3.14 for pi
2.) The radius of a circle is 3 inches. What is the approximate area? Use 3.14 for pi.
Answer:
31.4cm
Step-by-step explanation:
C = 2*pi*r
2r = d
2r=10
r=5
C = 2*5*pi
C = 10*3.14
C = 31.4cm
Find the area of the triangle
Answer:
Step-by-step explanation:
A=BH/2
A=9x12/2
A=54
Answer: 54
Step-by-step explanation:
A = base * height ÷ 2
A = 12 * 9 ÷ 2
A = 108 ÷ 2
A = 54
The midsegment of a trapezoid is 11 cm in length. If one of the trapezoid's bases is 17 cm long, what is the length of the other base?
Answer:
x must be 5
Step-by-step explanation:
Recall that the area formula for a trapezoid is
A = (average of base lengths)(width)
Here we have
17 cm + x
(average of base lengths) = 11 cm = ----------------
2
So 2(11 cm) = 17 cm + x, or
22 cm = 17 cm + x
Then x must be 5.
To find the length of the other base of the trapezoid with a midsegment of 11 cm and one base of 17 cm, use the average property of the midsegment. The calculation reveals the other base is 5 cm in length.
Explanation:The question is about finding the length of the other base of a trapezoid when the length of the midsegment and one of the bases is known. The midsegment of a trapezoid is parallel and equal to the average of the two bases. Therefore, if the midsegment is 11 cm and one base is 17 cm, the other base can be found by setting up the equation:
Midsegment = (Base1 + Base2) / 2
Substitute the known values:
11 = (17 + Base2) / 2
Multiplying both sides by 2 gives:
22 = 17 + Base2
Subtracting 17 from both sides gives:
Base2 = 22 - 17
Base2 = 5
Thus, the length of the other base of the trapezoid is 5 cm.
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each package contains 4 boxes each box contains a 7 pound bag of beans and a bag of rice the bags of rice are all identical
Answer:
28
Step-by-step explanation:
7*4
Answer:
28
Step-by-step explanation:
7*4
A coach is dividing a soccer team of 28 players into groups. If each group has the same number of players, what is the greatest number of groups there can be if each group has no more than 10 players?
Answer:
The only possible groups that could be made if each group have the same number of people is 2 groups of 14 or 4 groups of 7. Since each group cannot have more than 10 people, the only group left is 4 groups of 7.
In ®A shown below, radius AB is perpendicular to chord XY at point C. If XY=24 and AC=5 cm, what is the radius of the circle?
ANSWER
B. 13cm
EXPLANATION
The radius of the circle becomes the hypotenuse of the right triangle formed.
We can use the Pythagoras Theorem to obtain,
AC²+CY²=r²
This implies that,
r²=5²+12²
r²=25+144
r²=169
Take positive square root to get;
r=√169
r=13
AB and AC are two equal chord of a circle, therefore the centre of the circle lies on the bisector of ∠BAC.
OA is the bisector of ∠BAC.
Again, the internal bisector of an angle divides the opposite sides in the ratio of the sides containing the angle.
P divides BC in the ratio 6:6=1:1.
P is mid-point of BC.
OP ⊥ BC.
In △ ABP, by pythagoras theorem,
AB2=AP2+BP2
BP2=36−AP2 ....(1)
In △ OBP, we have
OB2=OP2+BP2
52=(5−AP)2+BP2
BP2=25−(5−AP)2 .....(2)
From 1 & 2, we get,
36−AP2=25−(5−AP)2
36=10AP
AP=3.6cm
Substitute in equation 1,
BP2=36−(3.6)2=23.04
BP=4.8cm
BC=2×4.8=9.6cm
John was born in 1951 and has been contributing to his own retirement plan as well as
Social Security for many years. John was trying to decide if he wanted to retire at 62 years of age rather than at 66 when he would reach full retirement age. According to the Social Security laws, John would receive a 25% reduction in his Social Security if he retired at 62. John went to the Social Security website and discovered that if he retired at 66 he would receive $2,460 a month in retirement from Social Security. How much would he receive if he retired at 62 rather than at 66?
a. $1,650 a month
b. $1,845 a month
c. $1,500 a month
d. $1,745 a month
Answer:
[tex]\boxed{\text{b. \$1845 a month}}[/tex]
Step-by-step explanation:
Amount if retired at 66 = $2460/mo
Less 25 % = 0.25 × 2460 = -615
Amount if retired at 62 = $1845/mo
John would receive [tex]\boxed{\text{\$1845/mo}}[/tex] if he retired at 62.
4. A garden store has the following miscellaneous flower bulbs in a basket.
* 6 amaryllins
* 7 daffodils
* 4 lilies
* 3 tulips
A customer bought 4 bulbs from the basket, one of each type of flower. If the next customer selects 1 of the remaining bulbs at random, which is the closest to the probability that customer will get an amaryllins bulb?
A. 30%
B. 31%
C. 38%
D. 45%
Final answer:
After removing one bulb of each type, the probability of the next customer getting an amaryllins bulb is 5/16, which is 31.25%. Thus, the closest answer provided is 31%, option B.
Explanation:
The question asks for the probability of the next customer getting an amaryllins bulb after four bulbs of different types have been removed from a basket containing miscellaneous flower bulbs. Initially, there were 6 amaryllins, 7 daffodils, 4 lilies, and 3 tulips. Since one bulb of each type was bought by the previous customer, we now have 5 amaryllins, 6 daffodils, 3 lilies, and 2 tulips remaining.
To find the probability of selecting an amaryllins bulb, we divide the number of amaryllins bulbs left by the total number of bulbs remaining:
Probability of selecting an amaryllins = Number of amaryllins bulbs remaining / Total number of bulbs remaining
Probability = 5 / (5 + 6 + 3 + 2) = 5 / 16
To convert this to a percentage, we multiply it by 100: (5 / 16) * 100 = 31.25%
Therefore, the probability is closest to 31%, which corresponds to option B.
It takes Ahmed 50 seconds on his bike to reach his friend's house 250 meters away. What is his average speed?
It takes 5 meters per second.
If you divide 250 by 50 you would get his average speed
The average speed of Ahmed is 5 meters per second.
Important information:
Time taken by Ahmed = 50 secondsDistance = 250 metersWe need to find the average speed of Ahmed.
Average speed:Formula for average speed is:
[tex]\text{Average Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]
Using this formula, the average speed of Ahmed is:
[tex]\text{Average Speed}=\dfrac{250}{50}[/tex]
[tex]\text{Average Speed}=5[/tex]
Thus, the average speed of Ahmed is 5 meters per second.
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The graphs of two cosine functions are shown below.
The function whose graph is B was obtained from the function whose graph is A by one of the following changes. That change was:
the addition of a negative constant
a change in amplitude
a phase shift
a period change
Answer:
"the addition of a negative constant"
Step-by-step explanation:
Please note the following points of functions regarding transformations:
1. If there is a change in amplitude, the function will be compressed/stretched vertically, keeping other variables constant
2. If there is a phase shift, the function would be horizontally transformed
3. If there is a period change, the function would be horizontally compressed/stretched
4. If there is addition of positive/negative constant, the function would shift vertically upward/downwards, respectively.
We can clearly see from the graph that the new function is a vertical downward shift from the original. Hence, looking at the above points, point #4, addition of a negative constant, is correct.