Answers
Let Lydia invest $x
Half of her stock pays 11% dividend.
So mathematically the amount will be
[tex]\frac{x}{2}\times\frac{11}{100}=\frac{11x}{200}[/tex]With the other half, she pays stocks in 14% interest
So mathematically
[tex]\frac{x}{2}\times\frac{14}{100}=\frac{14x}{200}[/tex]Her total annual interest is $420
So
[tex]\frac{11x}{200}+\frac{14x}{200}=420\Rightarrow25x=84000\Rightarrow x=3360[/tex]She invested $3360 in total
And $1680 in each.
Related Questions
I was going back over this and saw i got it wrong what was the right awnser
Answers
ANSWER
E. None of these
EXPLANATION
We want to find the converse of the statement.
A statement is made up of an hypothesis, then a conclusion.
So the converese is found by switching the hypothesis and the conclusion.
The statement given is:
If it is raining then we will go to the beach
The converse of this statement will therefore be:
If we will go to the beach then it is raining
The answer is Option E since the converse is not among the other options.
Describe how to find the anti logarithm of ln x= 2 to the nearest ten-thousandths
Answers
The expression is given as
lnx=2.
ExplanationTo find the antilogarithm of the expression,
To compute the antilogarithm of a natural logarithm, take e to that power.
[tex]lnx=2[/tex][tex]x=e^2[/tex][tex]x=7.389[/tex]AnswerHence the antilogarithm of lnx =2 to the nearest ten-thousandths is 7.3891.
find the volume of the figure below (hint: you may need to find 2 separate volumes and combine them)
Answers
The shape consist of a cone and a cylinder
As such the volume of the shape is the sum of the volume of the two shapes.
The volume of a cone is given as
V = 1/3 Pi R^2H
and that of a cylinder is
V = Pi R^2H
where Pi is a constant 22/7, R is the radius and H is the height
Hence the volume of the figure
=1/3 * 22/7 * 6^2 * 10 + 22/7 * 6^2 * 12
= 22/7 (120 + 432)
= 22/7 * 552
= 1734.86 m^2
explain the structure and creation of regular and semi-regular tessellations
Answers
A regular polygon is repeated to create a tessellation known as a normal tessellation. Recognize that the angles and sides of an ordinary polygon are the same. An equilateral triangle, a rectangular shape, or a hexagon can all be used to create regular tessellations.
Tessellations made from or larger than common polygons are known as semi-regular tessellations. Hexagons and equilateral triangles make up the semi-typical tessellation shown in the image. If we concentrate on the hexagons, we can see that the triangles are rotated around the hexagonal components to generate the pattern. It is a three.3.6 tessellation, as determined by our system for naming tessellations. The hexagon is represented by the six and the trees are the two triangles.
Regular polygons of the same size and shape make up regular tessellations. Multiple regular polygons combine to form semi-regular tessellations. There are only eight ways to arrange regular polygons to produce semi-regular tessellations.
Hence we derived the necessary information.
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The point A(7, -3) is reflected over the point (6, -5) and it's image is pointB. What are the coordinates of point B?
Answers
We have a point A=(7,-3) that is reflected over point C=(6,-5). This means that is refected in an axis that is perpendicular to the segment AC.
The image is point B, and we need to calculate its coordinates.
We can relocate the center of coordinates to point C, do the reflection and then relocate the original center of coordinates.
If now C became the center of coordinates A becomes:
[tex]A^{\prime}=A-C=(7-6,-3-(-5))=(1,2)[/tex]Now, we can reflect it as normal:
[tex]\begin{gathered} (x,y)\longrightarrow(-x,-y) \\ A^{\prime}=(1,2)\longrightarrow B^{\prime}=(-1,-2) \end{gathered}[/tex]Now, we convert this to the original coordinates as:
[tex]B^{\prime}=B-C\longrightarrow B=B^{\prime}+C=(-1+6,-2-5)=(5,-7)[/tex]The point B is (5,-7).
how do I solve x+6y=36
Answers
Answer:
If you're solving for x and y, the answers are there!
Step-by-step explanation:
Hope this helps!
HELP PLEASEEEEEEEEE!!!!!!!! ILL MARK BRAINLIEST
Answers
Answer:
Step-by-step explanation:
here are is answer and the steps it's in the pic below go check it out sorry if it's wrong have a nice day:)
[tex] \frac{3}{2} ln( {4x}^{6} ) - \frac{4}{5} ln( {2m}^{5} ) = [/tex]how do I do this
Answers
Original expression
[tex]\frac{3}{2}\ln 4x^6-\frac{4}{5}\ln 2m^5[/tex][tex]\begin{gathered} \frac{3}{2}\ln 4x^6-\frac{4}{5}\ln 2m^5 \\ \ln (4x^6)^{\frac{3}{2}}-\ln (2m^5)^{\frac{4}{5}}^{} \end{gathered}[/tex][tex]\begin{gathered} \ln (4^{3/2}x^{6\cdot3/2})-\ln (2^{4/5}m^{5\cdot4/5}) \\ \ln (2^{2\cdot3/2}x^9)-\ln (2^{4/5}m^4) \\ \ln (2^3x^9)-\ln (2^{4/5}m^4) \end{gathered}[/tex][tex]\begin{gathered} \ln (\frac{2^3x^9}{2^{4/5}m^4}) \\ \ln (\frac{2^{11/5}x^9}{m^4}) \end{gathered}[/tex]The answer would be
[tex]\ln (\frac{2^{\frac{11}{5}}x^9}{m^4})[/tex]A junk drawer at home contains eight pens for of which work what is the probability that you randomly grab three pens from the drawer and don’t end up with a Penn that works express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth
Answers
Given:
Total no of pens is 8.
No of pens that works =4
No of pens that don't work = 4
[tex]\text{Probability }of\text{ selecting 3 pens }from\text{ the drawer=}\frac{3}{8}[/tex][tex]\text{Probability of selecting }a\text{ pen thta don't work=}\frac{4}{8}[/tex][tex]\begin{gathered} \text{Probability of getting 3 pens from a drawer }and\text{ don't} \\ \text{ end up with a pen }that\text{ work is } \end{gathered}[/tex][tex]=\frac{3}{8}\times\frac{4}{8}[/tex][tex]=\frac{3}{16}[/tex][tex]=0.1875[/tex]What is the initial value and what does it represent?The table shows the total cost of purchasing x same-priced items and a catalog.Total CostNumber of Items Total Cost(x)1$102$143$184$22O $4, the cost per itemO $4, the cost of the catalog$6, the cost per item$6, the cost of the catalogMy
Answers
Duck if the cost of 1 item and the catalog is $ 10 and onwards, the cost for every additional item is $ 4, then:
• The cost per item is $ 4
,• The cost of the catalog is $ 6
I know you are able to select the correct choices.
Thanks for coming, Duck!
Answer:
Step-by-step explanation:
6$ cost of the catalog
The ages of people who attend a local church are normally distributed . The mean age is 39.5 , and the standard deviation is 18. First sketch a normal curve. Then find the probability that that a person chosen at random from this church is ages 21.5 or younger
Answers
Given:
The ages of people who attend a local church are normally distributed.
The mean age = μ = 39.5
And the standard deviation = σ = 18
The sketch of the normal curve will be as follows:
As shown the peak of the curve at the mean value = 39.5
and the distance between the consecutive numbers = 18
now, we will find the probability that a person chosen at random from this church is ages 21.5 or younger
So, we will find P( x < 21.5)
As shown, from the graph:
The answer will be = 0.1587
The students in Mr. Kim's class are discussing how to apply the properties of equality. Juan started with the equation 4 +5 = 9. He multiplied the left side by 3. He said that he could divide the right side by another
Answers
B. 3
1) Let's examine Juan's work
4+5 = 9 Multiplying the left side
(4+5)*3 =9
27 = 9 Divide only the right side by 3
9 = 3 False!
2) Then we can state that
B.
The only way Juan can maintain equality is by multiplying the right side by
3
27= 9
27 = 9 x 3
27 = 27 True!
3) The answer is B and 3.
0.5 is the coefficient of ² in the expression v + 0.5v²
A True
B False
Answers
True, 0.5 is the coefficient of v² in the expression v + 0.5v².
What is a Coefficient?A coefficient is a number or quantity related to a variable. It is usually an integer multiplied by the variable and displayed next to it. Variables that do not have a numerical value are assumed to have a coefficient of one. A coefficient might be positive or negative, real or imaginary, and expressed in decimals or fractions.Given expression is v + 0.5v².
Follow the methods below to find the coefficient of a variable in a term:
Step 1: Encircle the variable and its power whose coefficient we're looking for.
So here we are looking for the coefficient of v²
Step 2: Forget about that variable and think about all the other numbers or variables that were written with it. That is the coefficient.
Hence, the required coefficient is 0.5.
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What is the determinant of H=[ matrix 2&4&9\\ 3&3&1\\ 4&5&3 matrix ]? 15 18 154 169
Answers
Answer:
Step-by-step explanation:
What is the determinant of H=[ matrix 2&4&9\\ 3&3&1\\ 4&5&3 matrix ]? 15 18 154 169Question
What is the determinant of H=[ matrix 2&4&9\\ 3&3&1\\ 4&5&3 matrix ]? 15 18 154 169
Find the slope of the line passing through the points (-6 ,2) and (2,2)
Answers
Answer: 8
Step-by-step explanation:
Laura needs to buy chips and soda for the guests at her party. Each large bag of chips cost $2.40 and each large bottle of soda cost $2.00. She has $48.00 to spend. Part A Create an inequality using two variables to represent this situation. Be sure to explain the meaning of each variable.Part B Which of the following graphs represent the number of chips and soda bottles that Laura can buy? Part C Which combination of bottles of soda and bags of chips can Laura buy?
Answers
Part A.
To write the inequality we have to introduce variables that represent the things Laura needs to buy. For this reason let x be the number of sodas she buys and let y be the number of chips she buys.
Now, we know that each bag of chips cost $2.40 then tha ammount she spends in chips will be
[tex]2.4y[/tex]Following the same reasoning, the ammount she spends in sodas will be
[tex]2x[/tex]The total ammount she spends will be the sum of each ammount, that is:
[tex]2x+2.4y[/tex]Finally, we know that Laura has $48, so she can only spend less or equal this ammount.
Therefore the inequality representing this situation is
[tex]2x+2.4y\leq48[/tex]Part B.
To graph this inequality, first we have to graph the line given by
[tex]2x+2.4y=48[/tex]Doing this we obtained the following graph
Now we need to decide which semi plane represent the solution set of the inequality. Since we have a less or equal sign the right choice is the left one, then the graph of the inequality is
Therefore the graphs representing the number of chips and soda bottles Laura can buy is option B.
Part C.
To determine which combination of bottles of soda and chips Laura can buy we can graph the options we have. Remember that the x-axis represents the soda and the y-axis the chips. Hence the option we have will be equivalent to the points (4,24), (12,8), (16,8) and (28,4). Graphing this points we have
The only option allowed is the one that lies within the shaded region, therefore Laura can buy 12 bottles of soda and 8 bags of chips.
An experimental calculation of the boiling point of olive oil yields 550°F the actual boiling point of olive oil is 570°F use the values in the box below to set a proportion which can be used to find the percent of error in the experimental calculation.
Answers
To calculate the percentage error, the following formula would be applied;
[tex]\begin{gathered} \text{Percentage error}=\frac{|approximate\text{ value-exact value|}}{exact\text{ value}}\times\frac{100}{1} \\ \text{Percentage error}=\frac{|550-570|}{570}\times100 \\ \text{Percentage error}=\frac{20}{570}\times\frac{100}{} \\ \text{Percentage error}=3.50877192 \\ \text{Percentage error}\approx3.5\text{ (nearest tenth of a percent)} \end{gathered}[/tex]ANSWER:
The percentage error, as shown in the calculations above is 3.5 % (to the nearest tenth of a percent)
Petroleum pollution in oceans stimulates the growth of certain bacteria. An assessment of this growth has been made by counting the bacteria in each of 6randomly chosen specimens of ocean water (of a fixed size). The 6 counts obtained were as follows.48, 67, 64, 61, 63, 69Send data to calculatorFind the standard deviation of this sample of numbers. Round your answer to two decimal places.
Answers
σ =6.78
Count, N:6
Sum, Σx:372
Mean, μ:62
The standard deviation(σ) can be calculated using the formula below:
[tex]\sigma=\sqrt[]{\frac{1}{N}\sum ^n_{i=1}(x_i-\mu)^2}[/tex]To calculate Mean( μ);
[tex]\text{Mean}=\frac{48+67+64+61+63+69}{6}[/tex]Mean( μ) = 62
[tex]\sigma=\sqrt[]{\frac{(48-62)^2+(67-62)^2+(64-62)^2+(61-62)^2+(63-62)^2+(69-62)^2}{6}}[/tex][tex]=\sqrt[]{\frac{276}{6}}[/tex][tex]=\sqrt[]{46}[/tex][tex]=6.78[/tex]Therefore, the standard deviation(σ) = 6.78
Can someone help me with this question.
A line passes through the point (-4,-9) and has a slope -5/4 using the Ax+By=C form!!!
Answers
The equation of the line passing through point (-4,-9) and has a slope -5/4 is 5x + 4y = 40
How to find the equation of the linegiven data
A line passes through the point (-4,-9)
slope = -5/4
Ax + By= C
slope = ( y - y1 ) / ( x - x1 )
-5/4 = ( y - 9 ) / ( x - -4 )
-5/4 ( x + 4 ) = ( y - 9 )
-5( x + 4 ) = 4( y - 9 )
-5x + 4 = 4y -36
4 + 36 = 4y + 5x
40 = 4y + 5x
rearranging to suit Ax + By = C
5x + 4y = 40
5x + 4y = 40 is the required equation of the line
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Find three rational numbers between (-6) and (-7)
Answers
Answer: Option (b) 21:18, option(c) 42:36, option(d) 63:54, option(e) 84:62 are equivalent ratios of 7:6
Step-by-step explanation: Hope this helped
Answer: -6 1/4, -6 9/10, -6 11/20
Step-by-step explanation: You find any number in decimals between them, then you covert into fractions if needed.
Find m BDC. B C (-3x + 20° { (-2x + 55) ° D А a. 290 b. 61° c. 25° d. 759
Answers
Let's begin by listing out the information given to us:
We will observe that these two angles are complementary (they sum up to 90 degrees)
[tex]\begin{gathered} m\angle BDC=-3x+20 \\ m\angle CDA=-2x+55 \\ m\angle BDC+m\angle CDA=90^{\circ} \\ -3x+20+(-2x+55)=90 \\ \text{Put like term}s\text{ together, we have:} \\ -3x-2x+20+55=90 \\ -5x+75=90 \\ Subtract\text{ 75 from both sides, we have:} \\ -5x+75-75=90-75 \\ -5x=15 \\ \frac{-5x}{-5}=\frac{15}{-5} \\ x=-3 \\ \\ m\angle BDC=-3x+20=-3(-3)+20 \\ m\angle BDC=9+20=29 \\ \therefore m\angle BDC=29^{\circ} \end{gathered}[/tex]Hence, option A is the correct answer
The expression 1.04 (0.9x) + 50 represents the total cost of a catered meal at a conference.The organizers of the conference were given a reduction in the cost of the catered meal due to the size of the event. Sales tax wascharged on the reduction price The organizers were also charged a set-up fee. The variable x represents the price of catered mealbefore the reduction.
Answers
Answer:
- The set-up fee is $50 ---- True
- The organizers were given a 10% discount on the catered meal. ---- True
Explanation:
Given that the expression that represent the total cost of a catered meal at a conference is;
[tex]1.04(0.9x)+50[/tex]The organizers of the conference were given a reduction in the cost of the catered meal due to the size of the event.
let a represent the percentage discount;
[tex](1-\frac{a}{100})x[/tex]Sales tax was charged on the reduction price;
let b represent the sales tax;
[tex](1+\frac{b}{100})(1-\frac{a}{100})x[/tex]The organizers were also charged a set-up fee.
Let c represent the set-up fee;
[tex](1+\frac{b}{100})(1-\frac{a}{100})x+c[/tex]Comparing to the given equation;
[tex]\begin{gathered} c=\text{ \$50} \\ (1-\frac{a}{100})=0.9 \\ a=10\text{\%} \\ (1+\frac{b}{100})=1.04 \\ b=4\text{\%} \end{gathered}[/tex]So,
discount = 10%
sales tax = 4%
set up fee = $50.
Now let us determine which of the given options are true;
- The cost of the catered meal was less than the set-up fee -- Not enough information, Probably false.
- The sales tax rate was 10% -- false ( sales tax rate is 4%)
- The set-up fee is $50 ---- True
- The organizers were given a 10% discount on the catered meal. ---- True
Mr. Clayton is contemplating which chauffeured car service to take to the airport. The first costs $5 up front and $4 per kilometer. The second costs $15 plus $3 per kilometer. For a certain driving distance, the two companies charge the same total fare. What is the distance? Write a system of equations, graph them, and type the solution.______ kilometers
Answers
Given in the question:
a.) The first costs $5 upfront and $4 per kilometer.
b.) The second costs $15 plus $3 per kilometer.
Let's generate the equation of each of the car service charges,
Let,
y = total cost of service
x = distance traveled
a.) The first costs $5 upfront and $4 per kilometer.
[tex]\text{ y = 5 + 4x}[/tex]b.) The second costs $15 plus $3 per kilometer.
[tex]\text{ y = 15 + 3x}[/tex]Let's determine the driving distance when the two companies charge the same.
We get,
[tex]y_{1st\text{ Company}}=y_{2nd\text{ Company}}_{}[/tex][tex]\text{ 5 + 4x = 15 + 3x}[/tex][tex]\text{ 4x - 3x = 15 - 5}[/tex][tex]\text{ x = 10}[/tex]Therefore, the two companies charge the same at a driving distance of 10 kilometers.
Summary:
1. The system of equations.
y = 5 + 4x
y = 15 + 3x
2. The solution.
x = 10
3. Graphing the system of equations.
At take-off, an airplane weighs 220000 pounds. Convert the weight to tons.
Answers
220000 pounds.
[tex][/tex]The final answer
[tex]110[/tex]help meeee pleasee!!!
thank youu
Answers
Answer:
Domain: A, [1, 7]
Range: [-4, 2]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
help meeeeeeeeee pleaseee !!!!!
Answers
For the functions f(x) and g(x), the two compositions are:
(f o g)(x) = 9x² + 5(g o f)(x) = 3x² + 15How to find the two compositions?Here we have the next two functions:
f(x) = x² + 5
g(x) = 3x
The compositions are:
(f o g)(x) = f( g(x))
So we need to evaluate the function f(x) in g(x), this will give:
(f o g)(x) = f( g(x)) = g(x)² + 5
(f o g)(x) = (3x)² + 5
(f o g)(x) = 9x² + 5
The other composition is:
(g o f)(x) = g( f(x)) = 3*f(x)
(g o f)(x) = 3*(x² + 5)
(g o f)(x) = 3x² + 15
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Find the simple interest.Principal: $6000 Rate: 4% Time in months: 3
Answers
Given:
Principal, P = 6000
Rate, r = 4%
Time, t = 3 months
To find:
The simple interest
Explanation:
Using the simple interest formula,
[tex]SI=P\times\frac{r}{100}\times\frac{t}{12}[/tex]Where t represents the number of months.
On substitution, we get
[tex]\begin{gathered} SI=6000\times\frac{4}{100}\times\frac{3}{12} \\ SI=\text{ \$}60 \end{gathered}[/tex]Final answer:
The simple interest is $60.
use the figure at right. if jk=6x+8 and NO=16, what is the value of x?
Answers
The short line on the sides of the triangle tells us that those sides are equal.
We can see that LN = NJ and
LO = KO
This means that triangle LNO is similar to triangle triangle LJK
LO/NO = (LO + OK)/JK
Given that NO = 16 and JK = 6x + 8, it means that
LO/16 = (LO + OK)/(6x + 8)
Since LO = OK, it means that
LO + OK = LO + LO = 2LO
Therefore
LO/16 = 2LO/(6x + 8)By cross multiplying, it becomes
LO(6x + 8) = 2LO * 16
LO(6x + 8) = 32LO
Dividing both sides of the equation by LO, it becomes
6x + 8 = 32
6x = 32 - 8
6x = 24
x = 24/6
x = 4
4x^2-36 is divided by x+3
Answers
[tex] \frac{4 {x}^{2} - 36 }{x + 3} \\ = \frac{4( {x}^{2} - 9)}{x + 3} \\ = \frac{4(x + 3)(x - 3)}{x + 3} \\ = 4(x - 3) \\ = 4x - 12[/tex]
NOTE THE x+3 in the numerator cancels with the x+3 in the denominator.
The equation to find the constant of proportionality or k is?
2K = Y + X
Y = 2K + X
None of the above
K = Y / X
Answers
The equation to find the constant of proportionality or k is K=Y/X.
The value of the ratio between two proportional quantities, known as the constant of proportionality, is constant. When the product or ratio of two changing amounts gives a constant, that relationship is said to be proportionate. Depending on the kind of proportion between the two specified quantities—direct variation or inverse variation—the proportionality constant's value will vary.
When two variables are proportional to one another either directly or indirectly, their relationship can be expressed as y = kx or y = k/x, where k specifies how the two variables are related to one another. This k is referred to as the proportionality constant.
Hence the equation to find the constant of proportionality or k is
K = Y/X
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