Answer:
7,500 in stocks
1,500 in bonds
1,000 in savings
Explanation:
First, let's call x the quantity that you will leave in saving and y the quantity that you will invest in stocks and z the quantity that you will invest in bonds.
Now, we can formulate the following equations:
x + y + z = 10,000
y + z = 9x
y = 5z
Because you have 10,000 in savings, you decide to invest nine times as much as you leave in the account, and you also decide to invest five times as much in stocks as in bonds.
So, we can rewrite the expressions as:
x + y + z = 10,000
-9x + y + z = 0
y - 5z = 0
Now, we can multiply the second equation by -1 and sum this equation with the first one as:
-9x + y + z = 0
(-9x + y + z)*(-1) = 0*(-1)
9x - y - z = 0
Then, the sum is equal to:
x + y + z = 10,000
9x - y - z = 0
10x - 0 - 0 = 10,000
10x = 10,000
x = 10,000/10
x = 1,000
Replacing x on the second equation, we get:
9x - y - z = 0
9*1,000 - y - z = 0
9,000 - y - z = 0
-y - z = - 9,000
Now, we can add the equation with the third one as:
-y - z = - 9,000
y - 5z = 0
0 - 6z = -9,000
-6z = -9000
z = -9000/(-6)
z = 1,500
Finally, using the third equation, the value of y is equal to:
y = 5z
y = 5*1500
y = 7,500
Therefore, you will invest 7,500 in stocks, 1,500 in bonds and you will leave 1,000 in savings.
HELP! I need this ASAP!!A recursive rule for a sequence is given. Find the first four terms of the sequence. f(1) =5 f(n)= f(n-1) +3, where n is an integer and n ≥ 2
f(n) = f(n-1) + 3
substitute n= 2 in the above
f(2) = f (2-1) + 3
= f(1) + 3
= 5 + 3
= 8
substitute n = 3 in the formula
f(3) = f(3-1) + 3
= f(2) + 3
= 8 + 3
= 11
substituite n = 4
f(4) = f(4-1) + 3
= f(3) + 3
= 11 + 3
= 14
The first four terms are 5, 8, 11 and 14
Is it wise to use the rational theorem at the beginning when finding all real roots of polynomial function.
Explanation:
Definition or rational roots theorem:
Rational root theorem is used to find the set of all possible rational zeros of a polynomial function (or) It is used to find the rational roots (solutions) of a polynomial equation
We can actually use the Zeros Theorem and the Conjugate Zeros Theorem together to conclude that an odd-degree polynomial with real coefficients must have atleast one real root (since the non-real roots must come in conjugate algebra Use the rational zeros theorem to find all the real zeros of the polynomial function.
Rational Zero Theorem. If a polynomial function, written in descending order of the exponents, has integer coefficients, then any rational zero must be of the form ± p / q, where p is a factor of the constant term and q is a factor of the leading coefficient.
Hence,
The final answer is TRUE
Find the value of x. Assume that segments that appear to be tangent are tangent. 12, x , 6
The value of x is 16.64.
Given that 14 is tangent to the circle and 9 is a radius, this is a right triangle.
From the figure, we have
Using the Pythagoras theorem,
a^2 +b^2 =c^2
9^2+14^2 =x^2
81+196 = x^2
277 = x^2
By taking the square root of each side, we get
sqrt(277) = sqrt(x^2)
sqrt(277) =x
x = 16.64
Pythagoras theorem:
The Pythagorean Theorem, often known as Pythagoras Theorem, is a crucial concept in mathematics that describes how the sides of a right-angled triangle relate to one another. Pythagorean triples are another name for the sides of the right triangle. Here, examples help to demonstrate the formula and proof of this theorem. In essence, the Pythagorean theorem is used to determine a triangle's angle and length of an unknown side. This theorem allows us to obtain the hypotenuse, perpendicular, and base formulas.
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Could I please get some help on my homework for the next question like this please
we have the equations
x^2+y^2=9
this is the equation of a circle centered at the origin with a radius of 3 units
y=x
this is the equation of a line
therefore
The total points of intersection are 2see the figure below to better understand the problemwhat’s the equation for points (2,13) and (4,6)
The points we have are:
(2,13) and (4,6)
I will label this points as follows:
[tex]\begin{gathered} x_1=2 \\ y_1=13 \\ x_2=4 \\ y_2=6 \end{gathered}[/tex]To find the equation for this line, first we need to find the slope between the points with following slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where m is the slope.
Substituting our known values:
[tex]\begin{gathered} m=\frac{6-13}{4-2} \\ m=\frac{-7}{2} \end{gathered}[/tex]Next, we need to use the point-slope equation:
[tex]y=m(x-x_1)+y_1[/tex]And substitute our values, including the slope:
[tex]y=-\frac{7}{2}(x-2)+13[/tex]Using the distributive property to multiply -7/2 by x and by -2:
[tex]\begin{gathered} y=-\frac{7}{2}x+7+13 \\ y=-\frac{7}{2}x+20 \end{gathered}[/tex]Answer:
[tex]y=-\frac{7}{2}x+20[/tex]The type and number of fish caught in the Charleston Harbor in March was recorded for a month. The results are recorded in the table below. Whatis the probability that the next fish caught is a drum or a flounder? Enter a fraction or round your answer to 4 decimal places, if necessary.Flounder262Number of Fish Caught in MarchBlack DrumBluefish336Red Drum382181Sea Trout190
1) The first thing we need to do in this question, is to find the sample space, i.e. the total number of outcomes, in this case, fishes.
[tex]262+382+181+336+190=1351[/tex]2) Since no one could pick simultaneously two types of fish, then we can tell that these events are mutually exclusive. So, we can write the following:
[tex]\begin{gathered} P(flounder)=\frac{262}{1351} \\ \\ P(black\:drum)=\frac{181}{1351} \\ \\ P(red\:drum)=\frac{382}{1351} \\ \\ P(drum\:or\:flounder)=\frac{262}{1351}+\frac{181}{1351}+\frac{382}{1351}=\frac{825}{1351}\approx0.6107 \end{gathered}[/tex]Note that by "drum" we are including black and red drum.
That is the answer.
Find the amount of each payment R for a t= 18 year loan with principal P = $18,000 and interest rate r = 9% compounded monthly. Round your final answer to two decimal places.
The amount of each payment to 2 decimal places = $90406.80
Explanation:
t = 18 year
Principal = P = $18,000
r = 9% 0.09
Using compound interest formula:
[tex]FV\text{ = P(1 + }\frac{r}{n})^{nt}[/tex]n = number of times it was compounded in a year.
since it is monthly, n = 12
[tex]\begin{gathered} FV\text{ =future value} \\ FV\text{ = 18000(1+ }\frac{0.09}{12})^{12\times18} \end{gathered}[/tex][tex]\begin{gathered} FV=18000(1+0.0075)^{216} \\ FV\text{ = }18000(1.0075)^{216} \\ FV\text{ = 18000}\times5.0226 \\ FV\text{ = 90406.8} \end{gathered}[/tex]The amount of each payment to 2 decimal places = $90406.80
What is the value of the expression below when x = 5 and y 5? 6x — бу
We want to find the value of the given expression;
[tex]6x-6y[/tex]When x=5 and y=5;
Substituting these values in, we have;
[tex]\begin{gathered} 6(5)-6(5) \\ =30-30 \\ =0 \end{gathered}[/tex]Therefore, the answer to this question is zero.
If 5% of a certain number is -62/3
the number is
what is the vertex of y=2(x-3)^2+6 and determine if it’s maximum or minimum value
The general equation of a vertex of a parabola is given by
[tex]\begin{gathered} y=a(x-h)^2+k \\ \text{where} \\ \text{The coordianates of the vertex are} \\ (h,k) \end{gathered}[/tex]If we compare the general equation with that given in question 2
[tex]y=2(x-3)^2+6[/tex]We can infer that
[tex]\begin{gathered} -h=-3 \\ \text{Hence} \\ h=3 \\ \text{Also} \\ k=6 \end{gathered}[/tex]Thus, the vertex is
[tex](h,k)=(3,6)[/tex]To determine if it is maxima or minima, we will use the graph plot
We can observe that we have a minimum value.
Usually, we can determine this also from the value of a.
If a is negative, we have a maxima
If a is positive, we have a minimum
The value of a =2 (Positive)
Hence, we have a minimum
Representing fractions as repeating decimalsConvert the fraction to a decimal:5/6
ok
5/6 = 0.833333 or
The line means that number three is repeated till infinty
How many millimeters are there in 16 meters?A. 160 millimetersB. 1,600 millimetersC. 160,000 millinersD. 16,000 millimeters
It is known that 1 meter = 1000millimeter.
Therefore, 16 meters = 16X 1000 millimeters
16 meters = 16, 000 millimeters.
Hence, option D is the correct answer.
Given: GEFH is a parallelogram with two 35° angles as shown.EF35359GHWhich is the most specific descriptor for GEFH?ParallelogramRhombusRectangleSquare
SOLUTION
The diagram above satifies all the properties of a parallologram
Which are
[tex]\begin{gathered} \text{opposite angle are equal} \\ \text{Opposite sides are equal and parallel} \\ \text{adjacent angle are supplementary} \end{gathered}[/tex]But if from the rule of isoseleses triagle we can conclude that all the side of the figure above are equal
Hence the most specific description for GEFH is
[tex]\text{Rhombus}[/tex]If f(x) = x, the inverse off, f-1 could be represented by
Solution
For this case we have the following function given:
y=f(x)= x
And we want to find the inverse so we can do the following steps:
1) replace y with x
x= y
2) solve for y
y = x
Then the folution would be:
A) f-1 (x) =x
b. Shirley was given the following points and asked to calculate the area, but her graph paper is not big enough. Calculate the area of Shirley's rectangle, and explain to her how she can determine the area without graphing the points. Shirley's points (352, 150), (352, 175), (456, 150), and (456, 175)
The given points are
(352, 150)
(352, 175)
(456, 150)
(456, 175)
Each point represents one vertex of the rectangle.
The points that have the same x-coordinate are in the same vertical line, this means that the diference between the y-coordinates of the point determine the length of the width of the rectangle.
Since is a rectangle both vertical sides are equal.
Using the points
(352, 150)
(352, 175)
You can calculate the width as:
[tex]\begin{gathered} w=y_2-y_1 \\ w=175-150 \\ w=25\text{units} \end{gathered}[/tex]The points that have the same y-coordinate are in the same horizontal line, if you calculate the difference between the x-coordinates of said points, you can determine the length of the rectangle.
Using the points
(456, 150)
(352, 150)
You can calculate the length as
[tex]\begin{gathered} l=x_2-x_1 \\ l=456-352 \\ l=104\text{units} \end{gathered}[/tex]So the rectangle has a length of 104 and a width of 25. Using these values you can calculate the area:
[tex]\begin{gathered} A=wl \\ A=25\cdot104 \\ A=2600\text{units}^2 \end{gathered}[/tex]5. Match the equation with its graph.4x + 8y = 32
In order to find the corresponding graph, let's find two points that are on the line.
To do so, let's choose values of x and then calculate the corresponding values of y:
[tex]\begin{gathered} x=0\colon \\ 0+8y=32 \\ y=\frac{32}{8}=4 \\ \\ x=8\colon \\ 32+8y=32 \\ 8y=0\to y=0 \end{gathered}[/tex]So we have the points (0, 4) and (8, 0).
Looking at the options, the graph that has these points is the fourth graph.
Write the English sentence as an equation in two variables. Then graph the equation.The y-value is three less than twice the X-value.
Given the sentence:
The y-value is three less than twice the X-value.
Let's write the sentence as an equation then graph the equation.
The equation that represents the sentence is:
y = 2x - 3
To graph the eqautaion, let's find and plot three points, then connect the points using a straight edge.
• When x = 1:
Substitute 1 for x and solve for y.
y = 2(1) - 3
y = -1
• When x = 2:
Substitute 2 for x and solve for y.
y = 2(2) - 3
y = 4 - 3
y = 1
• When x = 3:
Substitute 3 for x and solve for y.
y = 2(3) - 3
y = 6 - 3
y = 3
• When x = 0:
y = 2(0) - 3
y = -3
Thus, we have the points:
(1, -1), (2, 1), (0, -3), and (3, 3)
The graph is attached below.
ANSWER:
Equation: y = 2x - 3
Find the value of angle B, rounding to the nearest tenth of a degree.
Law of Cosines.
- For a triangle ABC with sides labeled a,b, and c:
[tex]a^2=b^2+c^2-2bc\cos A[/tex][tex]b^2=a^2+c^2-2ac\cos B[/tex][tex]c^2=a^2+b^2-2ab\cos C[/tex]
Since we are asked to look for angle B, we will use
[tex]b^2=a^2+c^2-2ac\cos B[/tex]Given:
a = 12 cm
b = 8 cm
c = 15 cm
Substituting the given values to our equation:
[tex]b^2=a^2+c^2-2ac\cos B[/tex][tex](8)^2=(12)^2+(15)^2-2(12)(15)\cos B[/tex][tex]64=144+225-(360)\cos B[/tex][tex]360\cos B=369-64[/tex][tex]360\cos B=305[/tex][tex]\frac{360\cos B}{360}=\frac{305}{360}[/tex][tex]B=\cos ^{-1}\frac{305}{360}[/tex][tex]B=32.089[/tex]Since we are asked to round the answer to its nearest tenth, the final answer would be 32.1 degrees.
A figure skater is facing north when she begins to spin to her right. She spins at 2250 degrees. Which direction is she facing when she finishes her spin?
step 1
Divide 2250 degrees by 360 degrees
so
2,250/360=6.25
that means
6 complete circles and 0.25 circle
0.25 circle is equal to 90 degrees and she is facing East
The answer is EastIf figure the skater is facing north when she begins to spin to her right. She spins at 2250 degrees. She faces the east direction when she finishes her spin.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle).
It is given that, a figure skater is facing north when she begins to spin to her right. She spins at 2250 degrees.
Since one rotation of the circle form 360 degree.In order to find the angle when she finishes her spin is,
=2,250/360
=6.25
6.25 shows that 6 complete circles and 0.25 circles and 0.25 circle is equal to 90 degrees and she is facing East.
Thus, if figure the skater is facing north when she begins to spin to her right. She spins at 2250 degrees. She faces the east direction when she finishes her spin.
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Add.−4+ (-4) = Adding negative numbers
Solution
- The solution steps are given below:
[tex]\begin{gathered} -4+(-4)= \\ -4-4=-8 \end{gathered}[/tex]Answer
The answer is -8
Last year, Milan had $10,000 to invest. He invested some of it in an account that paid 6% simple interests per year, and he invested the rest in an account that paid 9% simple interest per year. After one year, he received a total of $840 in interest. How much did he invest in each account?
Let's define the next variables
x: amount of money invested in one account
y: amount of money invested in the other account
Milan had $10,000 to invest, then
x + y = 10000 (eq. 1)
The interest Milan gets after one year are: 0.06x and 0.09y. He received a total of $840 in interest, then
0.06x + 0.09y = 840 (eq. 2)
Isolating x from equation 1:
x = 10000 - y
Replacing this result into equation 2,
0.06(10000 - y) + 0.09y = 840
0.06(10000) - 0.06(y) + 0.09y = 840
600 + 0.03y = 840
0.03y = 840 -600
0.03y = 240
y = 240/0.03
y = 8000
Then,
x = 10000 - y
x = 10000 - 8000
x = 2000
He invested $2000 in the account that paid 6% simple interests per year and $8000 in the account that paid 9% simple interests per year
How many perfect squares less than 1000 have a ones digit of 2,3 or 4?
There are 200 perfect squares less than 1000 that have a ones digit of 2,3 or 4.
To check that perfect squares that have a ones digit of 2,3 or 4 :
First we will check the squares of 0-10 numbers.
[tex]0^{2} = 0[/tex] [tex]1^{2} = 1[/tex] [tex]2^{2} = 4[/tex]
[tex]3^{2} = 9[/tex] [tex]4^{2} = 16[/tex] [tex]5^{2} = 25[/tex]
[tex]6^{2}=36[/tex] [tex]7^{2}=49[/tex] [tex]8^{2}=64[/tex]
[tex]9^{2}=81[/tex] [tex]10^{2}=100[/tex]
As we can see, only 2,8 have the squares which have 2,3 or 4 at ones place.
So, only numbers like 12,18,24,28.........,998 have a ones digit of 2,3 or 4.
Hence, there are 200 perfect squares less than 1000 that have a ones digit of 2,3 or 4.
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Answer: 6
Step-by-step explanation:
We can use brute force for this, because there are 31 numbers to try(32^2 is 1024, which is over 1000).
To begin with, there is no number that ends in 2 or 3 in the first 10 squares. If we move onto the ones digit of 4, we can see that:
2
8
12
18
22
28
Are the only numbers which end in a 4.
We add these up and we get the answer of 6.
4. Suppose that you receive a movie-rental bill for the month that is much higher thanit usually is. Currently you are paying $3.99 for each movie you rent. Switching to asubscription would allow you to watch unlimited movies for only $7.99 per month. However,during a normal month you don't have much time to sit and watch movies. You do not reallywant to waste your money on a monthly subscription. You decide to check your onlinebilling statements and make a probability distribution for the number of movies you mightwatch each month.The results are in the following table:Number of Movies, X 0 1 2 3 4 5Probability, P(X) 0.10 0.15 ? 0.35 0.14 0.13a) What is the probability you will watch 2 movies next month, i.e., P(X=2)?b) What is the probability that you will watch more than 2 movies next month, i.e., P(X<4) orP(X<=3)?c) How much would you expect to spend, on a per-month basis, should you continue to pay foreach movie separately? Explain your answer
For the given table representing the probability distribution, the probability of watching 2 movies is unknown.
The sum of all probabilities should be equal to 1. We can use that to calculate the unknown probability:
Adding all probabilities and equating to 1:
[tex]0.1+0.15+P(x=2)+0.35+0.14+0.13=1[/tex]Solving for P(x=2)
[tex]\begin{gathered} 0.87+P(x=2)=1 \\ P(x=2)=1-0.87 \\ P(x=2)=0.13 \end{gathered}[/tex]Then: A. The probability of watching 2 movies next month is 0.13.
The complete table of probability distribution will look like this:
xP(x)
00.1
10.15
20.13
30.35
40.14
50.13
To calculate the probability of watching more than two movies we need to add the probabilities of watching 3, 4 or 5 movies. Those should be added because those are the cases where more than 2 movies are watched.
[tex]\begin{gathered} P(x>2)=P(x=3)+P(x=4)+P(x=5) \\ P(x>2)=0.35+0.14+0.13 \\ P(x>2)=0.62 \end{gathered}[/tex]Then, B. The probability of watching more than 2 movies is 0.62.
The probability of watching 2 movies is equivalent to P(x>2) or P(x>=3).
On the other hand, to calculate P(X<4) or P(X<=3) we need to add the probabilities of watching 3 movies or less. That is, probabilities of watching 0, 1, 2 or 3:
[tex]\begin{gathered} P(x<4)\text{ or }P(x\le3)=P(x=0)+P(x=1)+P(x=2)+P(x=3) \\ P(x<4)\text{ or }P(x\le3)=0.1+0.15+0.13+0.35 \\ P(x<4)\text{ or }P(x\le3)=0.73 \end{gathered}[/tex]The probability of watching 3 movies or less next month is 0.73.
To estimate how much we would expect to spend per month if we pay for each movie sepparately we need to calculate the expected value of movies per month.
We can estimate that with the probability distribution given in the table.
The expected value is the sum of the products between each event and their probabilities:
[tex]\text{Expected Value}=\sum ^{}_{}x\cdot P(x)[/tex]Let's call EV the expected value:
[tex]\begin{gathered} EV=(0\cdot0.1)+(1\cdot0.15)+(2\cdot0.13)+(3\cdot0.35)+(4\cdot0.14)+(5\cdot0.13) \\ EV=2.67 \end{gathered}[/tex]Then, we should expect to watch about 2.67 movies per month, on average.
I each individual movie costs $3.99, then, the total expenses per month will be:
[tex]2.67\cdot3.99\approx10.65[/tex]Then, C. According to the given probability distribution, we should expect to watch about 2.67 movies per month, on average, and spend in total $10.65 per month. We would be spending more than we would if we selected the unlimited movies plan which costs only $7.99 per month, then, it would be wise to decide to change our subscription to that plan.
measures of relative position
Arranging the diameter in the ascending order,
1.31, 1.31, 1.33, 1.36, 1.43, 1.47, 1.48, 1.49, 1.49, 1.53, 1.53, 1.53, 1.58, 1.68, 1.69.
There are 15 data entry in the given data set.
The 78th percentile can be determined as,
[tex]15\times\frac{78}{100}=11.7[/tex]Thus, the 12th data entry in the ascending order has 78th percentile. 1.53 is the required diameter.
16. Which expression shows how to use the Distributive Property to solve 6 x 349? A) (6 x 300) x (6 x 40) x (6 x 9) B) (6 + 300) + (6 + 40) + (6 + 9) C) (6 x 3) + (6 x 4) + (6 x 9) D) (6 x 300) + (6 x 40) + (6 x 9)
since 349 can be also written as 300+40+9
write the number like so in the multiplication
[tex]6\cdot349=6\cdot(300+40+9)[/tex]apply the distributive property
[tex](6\cdot300)+(6\cdot40)+(6\cdot9)[/tex]The fancy restaurant Mackenzie atel at was having asale so her dinner was 80% of the original cost. Theoriginal cost of her dinner was $20.00. What is the saleprice?
Given data:
The original cost of dinner C=$20.00.
The sale price is 80% of the original cost.
[tex]\begin{gathered} S=\frac{80}{100}(20)_{} \\ =0.8(20) \\ =16 \end{gathered}[/tex]Thus, the final sale price is $16.00.
Can you help me i need the answers
Given that
The figure is given on the coordinate plane. And we have to find the vertices of the figure after a 90-degree clockwise rotation.
Explanation -
So the figure will be rotated from its position clockwise as
Since the given points are J(-9, -8)
K(-2, -8)
L(-2, -3)
M(-9, -3)
After rotating the points will be
J(
K(-7, -3)
L(-2, -3)
M(-2, 4)
when f(x)=-3(2)^-× what is the value of f(-3)
Let the function be,
[tex]f(x)=3\times2^{-x}[/tex]Put -3 for x in the function to find f(-3) implies,
[tex]\begin{gathered} f(-3)=3\times2^{-(-3)} \\ =3\times2^3 \\ =3\times8 \\ =24 \end{gathered}[/tex]Thus, f(-3) is 24.
Two sides of a triangle have the same length. The third side measures 3 m less than twice the common length. The perimeter of the triangle is 17 m. What are the lengths of the three sides? What is the length of the two sides that have the same length? m
Let the common sides have length x, i.e, we have 2 sides measuring x
the third side would measure 2x - 3.
The perimeter = x + x + 2x - 3 = 4x - 3 = 17
so, 4x = 17 + 3 ,
4x = 20
x = 20/4 = 5m
Therefore, the three sides are 5m , 5m and 2( 5 )-3 = 10 - 3 = 7m
A volcano on a recently discovered planet rises to a height of 22.187 mi. Use the table of facts to find the height of the volcano in feet. Round your answer to the nearest tenth.
22.187 mi
1 mi = 5280 ft
22.187 mi = 22.187 x 5280 ft = =117147.36 ft
Answer:
117,147.36 ft