$613.04
Explanation:Amount invested is the principal
Principal, P = $300
Interest rate, r = 6% = 6/100
r = 0.06
Number of times the interest is compounded per year, n = 4
Time, t = 12
Amount after 12 years, A(12) = ?
Amount formula for compound interest is:
[tex]\begin{gathered} A(t)=P(1+\frac{r}{n})^{nt} \\ \\ A(12)=300(1+\frac{0.06}{4})^{4(12)} \\ \\ A(12)=300(1.015)^{48} \\ \\ A(12)=613.04 \end{gathered}[/tex]In 12 years, the investment will be worth $613.04
please answer the question and please explain in simple way
The x intercepts are determide when you calculated the equation when y=0
To find the x-coordinate of the vertex you have to apply the next formula:
[tex]x=-\frac{b}{2a}[/tex]Where you follow the form of the equation:
[tex]y=ax^2+bx+c[/tex]X-intercep:
1. In this case if we have the equation in the form: x( x - 2) we can know that y=0 when one of the terms is 0:
y=0 when:
x=0x-2=0
x= - 22. y=0 when:
x-4=0
x=4x+5=0
x=-53. y=0 when:
x-1=0
x=1x-5=0
x=5x-coordinate of the vertex:To identify the coeficeints a and b we express the equation in a different form, we have to multiply. Then we can apply the formula to find the x coordinate of the vertex, as follow:
[tex]x=-\frac{b}{2a}[/tex]1.
[tex]y=x(x-2)=x^2-2x[/tex][tex]x=-\frac{(-2)}{2(1)}=\frac{2}{2}=1[/tex]2.
[tex]y=(x-4)(x+5)=x^2+5x-4x-20=x^2-x-20[/tex][tex]x=-\frac{(-1)}{2(1)}=\frac{1}{2}[/tex]3.
[tex]y=(x-1)(x-5)=x^2-5x-x+5=x^2-6x+5[/tex][tex]x=-\frac{(-6)}{2(1)}=\frac{6}{2}=3[/tex]what is the range of the giving relation {(9,1), (9,4) , (9,5) , (9,6)}
ANSWER
EXPLANATION
We are given the relation:
{(9, 1), (9, 4), (9, 5), (9, 6)}
The range of any set of points in
question is in image
r-value being 0.9874, shows that the goodness of fit of the equation is close to 1. This implies that y = 65.18x + 21.43 properly approximates the data.
substitute 32 for x in the equation.
y = 65.18(32) + 21.43
y = 2107.19
Thus, the correct answer is $2107.19 (option A)
Noah bought 15 baseball cards for $9 assuming each baseball card cost the same amount answer the following questions one at this rate how much will the third 30 baseball cards cost explain your reasoning. At this rate how much will 12 baseball cards cost explain your reasoning. Do you think this information will be better represented using a table or a double number line explain your reasoning.
We know that 15 baseball costs $9.
We have to divide to find the unit cost.
[tex]\frac{9}{15}=0.6[/tex]Each baseball card cost 60 cents.
So, for 30 cards, it would cost
[tex]\begin{gathered} 0.6\cdot30=18 \\ 0.6\cdot12=7.2 \end{gathered}[/tex]Hence, 30 baseball cards cost $18, at the same unit price. And 12 baseball cards would cost $7.20.Observe that to get the answers, we just had to multiply the number of cards by the unit price.
There's no need for a table or a number double line because they are used when the amount of data is big enough. It is better to keep it simple.
Which of the following represents vector u = −3i + 8j in component form?
Solution
- The way to write vectors in component form is given below:
[tex]\begin{gathered} u=u_xi+u_yj \\ \text{ In Component form, we have:} \\ u=\langle u_x,u_y\rangle \end{gathered}[/tex]- Thus, we can apply the rule stated above to the question given to us.
- This is done below:
[tex]\begin{gathered} u=-3i+8j \\ \\ \therefore u=\langle-3,8\rangle \end{gathered}[/tex]Final Answer
The answer is
[tex]u=\langle-3,8\rangle\text{ (OPTION 2)}[/tex]refer to the figure to complete thus proportion. c/a = a/?
Here, we want to compare triangles and such write the equivalent ratio on both
Mathematically, if two triangles are similar, the ratio of their sides are fixed
In the triangle consisting of c and a, we can see that c is the hypotenuse( the side facing the right-angle) while a represents the base
Now, in the triangle where we have a as the hypotenuse, we can see that the measure r reresents the base of the triangle
Thus, we can complete the proportion as;
[tex]\frac{c}{a}\text{ = }\frac{a}{r}[/tex]The values of x and y vary directly and one pair of values are given write an equation that relates x and y X=2 y=5
Given:
The values of x = 2 and y = 5
The relation between the values of x and y:
[tex]y=\frac{?}{\square}\text{x}[/tex]Now we need to have y = 5 for x = 2 so let us substitute 5/2 in place of blank space.That is,
[tex]y=\frac{5}{2}x[/tex][tex]\begin{gathered} y=\frac{5}{2}x \\ 5=\frac{5}{2}\times2 \\ 5=5 \end{gathered}[/tex]Hence, the relation gets satisfied.
Hence, the relation is :
[tex]y=\frac{5}{2}x[/tex]While hiking manuel descended 400 meters if manuel started at 1000 meters above sea level which integer represents his elevation now
Let me explain this with the following drawing:
If Manuel started at 1000 meters above sea level and he descended 400 meters, his elevation after this, is 600m above sea level.
So the integer that represents his elevation now is 600.
The length of a rectangle is 4 in longer than its width. If the perimeter of the rectangle is 362 in, find it's area.
The length of a rectangle is 4 in longer than its width, which means
Length = 4 in + width
P = 362 in = 2L + 2W
362in = 2(4 in + W) + 2W = 8in+2W+2W = 8in + 4W
362in = 8in + 4W
Solve for W
362 in - 8in = 4W
354 = 4W
354/4 = W
88.5 = W
Replace W in the Length
Length = 4 in + W
Length = 4 in + 88.5in
Length = 92.5in
The formula for the area is A = Length * Width = L * W
Replace the values and find the area
A = L* W
A = 92.5in * 88.5in
A = 8186.25 in²
(2,-1)(-3,5)1:2find the point that partitions the segment with the two given endpoints with the given ratio
We are given two points
A = (2, -1)
B = (-3, 5)
Ratio = 1:2
Let the ratio be P
Therefore, P is 1:2
Slope = Rise / Run
Rise = y2 - y1
Run = x2 - x1
x1 = 2, y1 = -1, x2 = -3 and y2 = 5
P = 1 / 1+ 3
P = 1/3
The horizontal distance is the same as run
Run = x2 - x1
=-3 - 2
Run = -5
Therefore we have
P x run
1/3 x -5
= -5/3
The distance between P and A on the x - axis is
-5/3 - 2
= -11/3
Rise = y2 - y1
5 - (-1)
= 5 + 1
Rise = 6
1/3 x 6
6/3 = 2
The distance between A and P on the y axis is
2 -(-1)
=2 + 1
= 3
The points are -11/3 and 3
The answer is (-11/3, 3)
write word problem1- correct variable term for the left side2-correct constant term for the left side 3-correct operation between the terms of the left side 4-correct equal sign or inequality symbol 5-correct variable term for the right side6-correct constant term for the right side 7-correct operation between the terms of the right side58×+170>42×+320
For the equation
[tex]58x+170>42x+320[/tex]A word problem could be the following.
Suppose we have a coin whose value we do not know and let us call the value of this coin x. All we know that 58 of these coins plus $170 is greater than 42 of these coins plus $320. This information, when converted into a word problem, gives the above inequality.
What is the image (11,-5) after the Rx=0 • T(11,-5)(-22,-10)(0,-10)(22,10)(0,10)
The original point has coordinates (11,-5)
The transformation applied to this point are Rx=0 * T(11,-5)
First, you have to do the translation T(11,-5), this means that you have to make a horizontal translation 11 units to the right, and a vertical translation 5 units down, following the rule:
[tex](x,y)\to(x+11,y-5)[/tex]So, add 11 units to the x-coordinate and subtract 5 units to the y-coordinate of (11,-5)
[tex](11,-5)\to(11+11,-5-5)=(22,-10)[/tex]Once you've made the translation, you have to reflect the point (22,-10) over the vertical line x=0, this vertical line is the y-axis. This means that you have to reflect the point over the y-axis.
To do this reflection you have to invert the sign of the x-coordinate of the point and leave the y-coordinate the same:
[tex]R_{y-\text{axis}}=(x,y)\to(-x,y)[/tex][tex](22,-10)\to(-22,-10)[/tex]The coordinates of the point after the translation and reflection are (-22,-10), option 1
how many pounds is 19.2 kg
Let's begin by listing out the given information:
[tex]\begin{gathered} 19.2kg\rightarrow lb \\ \end{gathered}[/tex]From general acceptable law, we know that:
[tex]1kg=2.20462lb[/tex]Therefore, 19.2 kg will be converted to pounds using simple proportion as shown below:
[tex]undefined[/tex]Juanita is eight years older than her brother hector. If Juanita is nineteen years old this year, how old is hector
juanita: 19
hector:?
[tex]h+9=j[/tex][tex]h+9=19[/tex][tex]h=19-9=10[/tex]Hector is 10 years
(3m - 2n)³ = (9m² -12mn + 4n²)
For this expression (3m - 2n)³ = (9m² -12mn + 4n²)
1)Let's remember the difference of two cubes
(a -b)³ = a³ -3a²b +3ab²-b³
(3m - 2n)³ = (3m)³ -3 (3m)²(-2n) +3(3m)(-2n)²-(2n)³ = 27m³ -54m²n +36mn²-8n³
27m³ -54m²n +36mn²-8n³ = 9m² -12mn + 4n²
2) Combining Like terms:
27m³ -54m²n +36mn²-8n³ -9m² +12mn+4n² =0
Since we can't get a simpler version of it. Let's keep with that.
Find the axis of symmetry of the graph y = x2 + 8x + 16.
The axis of simetry of a parabola is the vertical line that cross the vertex of the parabola.
So, we need to find the x-value of the vertex:
[tex]\begin{gathered} \text{The general equation of a parabola is:} \\ y=ax^2+bx+c \\ \text{The x-value of the vertex is:} \\ x_v=-\frac{b}{2a} \end{gathered}[/tex]So, in this case a=1 and b=8:
[tex]x_v=-\frac{8}{2\cdot1}=-4_{}[/tex]The axis of simetry is x=-4.
subtract.(9r + 9) - (9r + 3)
Consider the given expression,
[tex](9r+9)-(9r+3)[/tex]Eliminate the parenthesis,
[tex]9r+9-9r-3[/tex]Take the like terms together,
[tex]\begin{gathered} (9r-9r)+(9-3) \\ 0+6 \\ 6 \end{gathered}[/tex]Thus, the value of the expression is 6.
A 150 lb individual weighs how many kg? Round to nearest kilogram.
Take into account that the relation between pounds and kilograms is:
1 kg = 2.204 lb
Then, you can use a conversion factor to determine how many kg are 150 lb, as follow:
[tex]150lb\cdot\frac{1\operatorname{kg}}{2.204lb}\approx68.05\operatorname{kg}[/tex]Hence, 150 lb are approximately 68.05 kg
Find the height of the trapezoid.Base1: 100Base2: 56Leg1: 31Leg2: 31 Please help!!
To find the area of a trapezoid we can use this equation:
[tex]A=A_r+A_{t1}+A_{t2}[/tex]so we have to find the missing sides so:
So the area is:
[tex]undefined[/tex]Write the phrase as an algebraic expression8. the quotient of eight and a number h
the quotient of eight and a number h
we have that
quotient is a division
where
eight is the numerator and h is the denominator
so
8/h
the answer is 8/h
It costs $350 to repair a refrigerator compressor. Compute the QLF for losses incurred as a result of a deviation from a target setting with a nominal tolerance of 60 amps, where a 2-amp variation is acceptable. The mean squared deviation is 1/5
The Quality loss function QLF incurred as a result of a deviation from a target setting is $17.5
How to determine the QLF for the lossesQLF is acronym for quality loss function, this solved using the formula
= kv^2
where
k = constant
v = mean square deviation = 1/5
the constant k is solved by the formula
= c/T^2
where
c = cost of item = 350
T = variation acceptable = 2
= 350 / 2^2
= 87.5
QLF = kv^2\
= 87.5 * 1/5
= 17.5
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A vector has a magnitude of 50 and a direction of 30°. Another vector has a magnitude of 60 and a direction of 150°. What are the magnitude and direction of the resultant vector? Round the magnitude to the thousandths place and the direction to the nearest degree.
Step 1:
Draw the vector diagram
Step 2:
Write the angles to the horizontal axis.
30 degrees to the horizontal axis = 30
150 degrees to the horizontal axis = 180 - 150 = 30
Step 3:
Find the vertical component and the horizontal component of the magnitude.
[tex]\begin{gathered} \text{Horizontal component = Fcos}\theta \\ \text{Vertical component = Fsin}\theta \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} \text{Sum of the vertical component V = 25 + 30 = 55} \\ \text{Sum of the horizontal component H = 43.3 - 51.96 = -8.66} \end{gathered}[/tex]Step 4:
Find the magnitude
[tex]\begin{gathered} \text{Magnitude = }\sqrt[]{V^2+H^2} \\ =\text{ }\sqrt[]{55^2+(-8.66)^2} \\ =\text{ }\sqrt[]{3025+74.9956} \\ =\text{ 56.678} \end{gathered}[/tex]Magnitude = 56.678
Step 5:
Find the direction
[tex]\begin{gathered} \text{Tan}\theta=\text{ }\frac{V}{H} \\ \theta=tan^{-1}(\frac{55}{8.66}) \\ \theta\text{ = 81} \end{gathered}[/tex]Direction = 81
Jane earns £11 400 per year.90169 brs anottoB
After her pay rise she earns £12 198 per year.
What was her percentage pay rise?
The percentage rise of Jane= 7%.
What is percentage ?
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Percentage Increase/ Rise and Decrease/ Fall
The percentage increase is equal to the subtraction of the original number from a new number, divided by the original number and multiplied by 100.
% increase = [(New number – Original number)/Original number] x 100
where,
increase in number = New number – original number
Similarly, a percentage decrease is equal to the subtraction of a new number from the original number, divided by the original number and multiplied by 100.
% decrease = [(Original number – New number)/Original number] x 100
Where decrease in number = Original number – New number
So basically if the answer is negative then there is a percentage decrease.
In the given question , Jane earns initially = £11 400 per year
After rise Jane earns = £12 198 per year.
Percentage rise = [(New number – Original number)/Original number] x 100
Percentage rise = [( 12198 – 11400)/11400] x 100
= [( 798)/11400] x 100= 0.07 × 100 = 7%
So the percentage rise of Jane= 7%.
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Vectors u = −10i + 3j and v = −3i − 7j. What is u − v?
In order to calculate the subtraction of the vectors, we can do the following steps:
[tex]\begin{gathered} u-v\\ \\ =(-10i+3j)-(-3i-7j)\\ \\ =-10i+3j+3i+7j\\ \\ =(-10i+3i)+(3j+7j)\\ \\ =-7i+10j \end{gathered}[/tex]Therefore the correct option is the first one.
Find the distance between the points (-5,4) and (-2,-1)
Answer
√34
Step-by-step explanation
Distance formula
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]where
• d: distance between two points
,• (x₁, y₁): coordinates of the first point
,• (x₂, y₂): coordinates of the second point
Substituting into the formula with the points (-5,4) and (-2,-1), we get:
[tex]\begin{gathered} d=\sqrt{(-2-(-5))^2+(-1-4)^2} \\ d=\sqrt{3^2+(-5)^2} \\ d=\sqrt{9+25} \\ d=\sqrt{34} \end{gathered}[/tex]If Erica teaches 15 fewerthan twice as many as Bo, how many classes does each instructor teach per week?
STEP - BY - STEP EXPLANATION
What to find?
The number each instructor teach per week.
Given:
Total number they teach per week =39
let e = number of classes Erica teaches per week and b = the number of classes Bo teaches per week.
e =2b - 15
Step 1
Form the linear equation.
[tex]b+e=39[/tex]Step 2
Substitute e=2b-15 into the above.
[tex]b+2b-15=39[/tex]Step 3
Collect like term.
[tex]b+2b=39+15[/tex][tex]3b=54[/tex]Step 4
Divide both-side of the equation by 3.
[tex]\frac{3b}{3}=\frac{54}{3}[/tex][tex]b=18[/tex]Step 5
Determine Erica's age.
[tex]\begin{gathered} b+e=39 \\ \\ e=39-b \\ \\ e=39-18 \\ \\ e=21 \end{gathered}[/tex]ANSWER
c. 18 Bo; 21 Erica
Last year. Kareem deposited into an account that paid 4% interest per year and $6000 into an account that paid 9% interest per year. No with withdrawals were made from either account. No rounding needed What was the total interest earned at the end of 1 year? What was the percent interest for the total deposited?
2The points A(2,5), B(6,5), C(5,2) and D(1, 2) are the vertices of a parallelogram.If the parallelogram is translated down two units and right three units, what will bethe coordinates of the final image of point B?
To answer this question, we need to apply the rule of translation to each of the points of the parallelogram. This rule can be expressed as: (x + 3, y -2), that is, the parallelogram is translated down two units and right three units.
Then, we have:
A (2, 5) ---> A'(2 + 3, 5 - 2) ---> A' (5, 3)
B (6, 5) ---> B' (6 + 3, 5 -2 ) ---> B' (9, 3)
C (5, 2) ---> C' (5 + 3, 2 - 2) ---> C' (8, 0)
D (1, 2) ---> D' (1 + 3, 2 -2) ---> D' (4, 0)
Therefore, the coordinates of the final image of point B are B' (9, 3).
A baseball player went up to bat 500 times in a season. He hit the ball 150 times. Find the rate of balls hit to times at bat. Express as a ratio.
To find the answer, we just divide
[tex]\frac{150}{500}=0.30[/tex]As ratio would be
[tex]\frac{150}{500}=\frac{15}{50}=\frac{3}{10}[/tex]Hence, his rate is 3/10, three hits every 10 attempts.Point P(4,-2) undergoes a translation given by (x, y) - (x+3, x-a) , followed by another translation (x, y) - (x-b, x+7) to produce the image of P”(-5,-8). Find the values of a and b and point P’.
Assuming x - a = y - a and x + 7 = y + 7
Original Point P (4, -2)
Translated to Point P' (x + 3, y - a) = (4 + 3, -2 - a) = (7, -2 - a)
Translated to next point P'' = (x - b, y + 7) = (7 - b, -2 - a + 7) = (7 - b, 5 - a) = (-5, 8)
From the above changes, we can see that 7 - b = -5 and 5 - a = 8. Therefore:
[tex]\begin{gathered} 7-b=-5 \\ 7+5=b \\ 12=b \end{gathered}[/tex][tex]\begin{gathered} 5-a=8 \\ 5-8=a \\ -3=a \end{gathered}[/tex]The value of a = -3 and b = 12.
The point P' (7, -2 - a) = (7, -2 - (-3)) = (7, 1). Point P' is at (7, 1).
To check if this is right, let's look at the original point again and its transformations.
P (4, -2) translated to (x + 3, y - a) = (4 + 3, -2 - (-3)) = (7, 1).
P' (7, 1) is then translated to ( x - b, y + 7) = (7 - 12, 1 + 7) = (-5, 8).
As mentioned in the question, P'' is indeed found at (-5, 8).