Given:
a.) Two investments are made summing up to 8,800.
b.) For a certain year, these investments yield P1,326 in simple interest.
c.) Part of the investment is allotted for 14% and part for 16%.
Recall: The simple interest formula.
[tex]\text{ I = Prt}[/tex]Where,
I = interest
P = principal amount
r = interest rate
t = time (in year)
Step 1:
P = 8,800
But it's been made into two investments.
Let,
A = investment 1
B = investment 2
We get,
A + B = 8,800 = P (Equation 1)
Step 2:
Part of the investment is allotted for 14% and part for 16%.
Thus,
For investment 1:
Ia = Art = A(14/100)(1) = 0.14A
For investment 2:
Ib = Brt = B(16/100)(1) = 0.16B
We get,
0.14A + 0.16B = 1,326 (Equation 2)
Step 3:
Substitute Equation 1 to Equation 2.
A + B = 8,800
A = 8,800 - B
0.14A + 0.16B = 1,326
0.14(8,800 - B) + 0.16B = 1,326
1,232 - 0.14B + 0.16B = 1,326
0.02B = 1,326 - 1,232
0.02B = 94
0.02B/0.02 = 94/0.02
B = 4,700
Let's now find A.
A + B = 8,800
A + 4,700 = 8,800
A = 8,800 - 4,700
A = 4,100
In Summary:
The amount invested at 14% is 4,100
The amount invested at 16% is 4,700
The mean of the following data values is 32. 19, 23, 35, 41, 42A. True B. False
Remember that mean of a set is another name for the average of that set. To find the mean of a data set, add all the values together and divide by the number of values in the set.
Thus, if we have the following set of values: 19, 23, 35, 41, 42, the mean would be:
[tex]\frac{19\text{ + 23 + 35 + 41 + 42}}{5}=\frac{160}{5}=32[/tex]The correct answer:
Answer:TRUE
Help with question 13 ( the D just represents the word angle )
Using the law of sines, we would have that:
[tex]\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]Solving for C,
[tex]\begin{gathered} \frac{b}{\sin B}=\frac{c}{\sin C}\rightarrow\frac{\sin C\cdot b}{\sin B}=c\rightarrow\sin C\cdot b=c\cdot\sin B \\ \\ \rightarrow\sin C=\frac{c\cdot\sin B}{b}_{}\rightarrow C=\sin ^{-1}(\frac{c\cdot\sin B}{b}_{}) \end{gathered}[/tex]Plugging in the data given,
[tex]\begin{gathered} C=\sin ^{-1}(\frac{(10.3)\cdot\sin (58.8)}{(10.5)}_{}) \\ \\ \Rightarrow C=57 \end{gathered}[/tex]Therefore, we can conclude that:
Sanjay attempts a 50-yard field goal in a football game. For his attempt to be a success, the football needs to pass through the uprights and over the crossbar that is 10 feet above the ground.Sanjay kicks the ball from the ground with an initial velocity of 64 feet per second, at an angle of 34° with the horizontal.Is Sanjay's attempt successful? If not, how many feet too low is the ball?
Let us draw a sketch to understand the situation
We will use some rules here
[tex]\begin{gathered} v_x=vcos\theta=64cos(34) \\ d_x=v_xt=64cos(34)t \end{gathered}[/tex]Since the horizontal distance is 50 yards
Since 1 yard = 3 feet, then
[tex]d_x=50\times3=150feet[/tex]We will use it to find the time t
[tex]\begin{gathered} d_x=150 \\ 64cos(34)t=150 \\ t=\frac{150}{64cos(34)}\text{ s} \end{gathered}[/tex]Now, we will find the vertical distance (h) by using this rule
[tex]\begin{gathered} v_y=vsin\theta=64sin(34) \\ d_y=h=v_yt-\frac{1}{2}at^2=64sin(34)t-\frac{1}{2}(32)t^2 \end{gathered}[/tex]Note that: a is the acceleration of gravity which is 32 ft/s^2
We will substitute t by its value
[tex]h=64sin(34)(\frac{150}{64cos(34)})-16(\frac{150}{64cos(34)})[/tex]We can simplify it by using sin34/cos34 = tan34, and 1/cos34 = sec34
But I will put it on the calculator to find the final answer
[tex]h=55.94\text{ ft}[/tex]Since the height of the crossbar is 10 feet, then
Sanjay's attempt successful
Ashley took 3 minutes to run a distance of 540 meters from point X to point YGrace took 2 minutes to run a distance of 480 meters from point Z to point YA)Find the speed of each girl.B)Which of the two girls ran faster?
First, lets determine the speed of Ashley
d/ t = speed
540meters / 3 minutes
180 meters per minute
Now determine the speed of Grace
d/t = speed
480 meters / 2 minutes
240 meters per minute
Since Grace has the larger number, Grace ran faster
I need help figuring out the answer to this problem can someone help me please ?
So the average decrease will be 50% for the season of 5 weeks as the definition of percent decrease will be "The difference between starting and ending values is the percentage decrease. It displays a percentage loss of value compared to the original regardless of the units. The difference between the initial and final amounts is the amount of decrease".
What is percent decrease?The difference between starting and ending values is the percentage decrease. It displays a percentage loss of value compared to the original regardless of the units. The difference between the initial and final amounts is the amount of decrease. The letter "%" stands for it.
Here,
The percent decrease will be,
48000-24000=24000
24000/48000*100=50%
24000-12000=12000
12000/24000*100=50%
12000-6000=6000
6000/12000*100=50%
6000-3000=3000
3000/6000*100=50%
3000-1500=1500
1500/3000*100=50%
Due to the definition of percent decrease being a season of five weeks, the average decrease will be 50% "The percentage decrease is the difference between the starting and ending values. Regardless of the units, it shows a percentage decline in value relative to the starting point. The amount of decrease is the difference between the initial and final amounts ".
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What is the image of (2,-3) after a 180 degree counterclockwise rotation about the origin?a. (-3, 2) b.(-2, 3) c. (-3, -2)d.(-2,3)
Answer:
b.(-2, 3)
Explanation:
A 180 roration transforms the coordinates of a point according to the following rule.
[tex](x,y)\rightarrow(-x,-y)[/tex]For our point (2, -3), applying the above rule gives.
[tex](2,-3)\rightarrow(-2,3)[/tex]Hence, the coordinates of the image are (-2, 3 ) which is choice B.
Order: ABC 175 mg po. Stock ABC 350 mg po scored tablets. How many tablets would patient take per dose?
The number of tablets that the individual would take per dose would be = 0.5 tablet.
What is a drug?A drug is a substance that is usually prescribed by a physician which when taken has the ability to alter the physiological condition of an individual.
The order or prescribed dosage of the drug ABC = 175mg / dose
The vehicle measurement of the drug = 350mg/tab
If 1 tablet = 350 mg
X tablet = 175 mg
Make X tablet the subject of formula;
X tablet n= 175/350
X tablet = 0.5 tablet or 1/2 tablet.
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Learning Target #1: Creating and Solving Linear Equations11. Short Response #1: The perimeter of a rectangle is 130 ft. The length of the rectangle is 9 feetshorter than it is wide. What are the dimensions of the rectangle? (Hint: P = 2w + 2L) (4 points)Length:Width:
P = 2w + 2L
w = L - 9
C. Two angles are supplementary. One angle measures 2° less than 3 times the other. What are the measures of the two angles?
C.
if x one of the angles, then, the other angle is 3x - 2. Due to these angles are supplementary, you can write:
x + 3x - 2 = 180
by solving for x you obtain:
x + 3x - 2 = 180 simplify like terms left side
4x - 2 = 180 add 2 both sides and divide by 4 both sides
4x = 180 - 2
4x = 178
x = 178/4
x = 44.5
the other angle is then:
3x - 2 = 3(44.5) - 2 = 131.5
Hence, the two angles are 44.5° and 131.5°
A group of workers. an plant 2/3 acres in 7/8 days. Write the unit in acres per day?
To write the unit in acres per day. We have 2/3 acres and 7/8 days:
[tex]\frac{\frac{2}{3}}{\frac{7}{8}}\frac{\text{ acres}}{\text{ days}}=\frac{2\times8}{3\times7}\frac{\text{ acres}}{\text{ days}}=\frac{16}{21}\frac{\text{ acres}}{\text{days}}[/tex]Answer: 16/21 acres per day
A square with an area of 1 square meter is decomposed into 9 identical small squares. Each small square is decomposed into two identical triangles.
A. What is the area, in square meters, of 6 triangles? If you get stuck, draw a diagram.
The area of the 6 required triangles is 1/3m².
What are triangles?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane. The seven different kinds of triangles that can be found in nature—equilateral, right isosceles, obtuse isosceles, acute isosceles, right scalene, obtuse scalene, and acute scalene—must be studied and built.So, one square meter is equal to one huge square.
The larger square has now been divided into nine smaller squares.9 tiny square meters of space equals 1 square meter of space.So, using the unitary method, we can discover a single little square.1 tiny square is equal to 1/9 square meter.Each little square now has two similar triangles on each side of it.Now,
One triangle's surface area equals half that of a small square, or (1/2) (1/9) = 1/18 square meters.Using the unitary approach once more, determine the area of 6 triangles.The area of 6 triangles is equal to the 6 * area of 1 triangle, which is:6 * (1/18) = 1/3 square meter.Therefore, the area of the 6 required triangles is 1/3m².
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if Samantha has 37 green apples and give 4 to her sister and 3 to her bestfriend. How many apples does Samantha have left?
The number of apples that has been left with Samantha is 30 apples which is calculated using subtraction.
Total number of apples that Samantha has = 37 apples
Apples that she gave to her sister = 4 apples
Apples that she gave to her bestfriend = 3 apples
Total apples that she gave will be calculated by using addition.
Total apples that she gave = 4 + 3 = 7 apples
Now, the apples left with her will be calculated using subtraction.
Apples left with her = 37 - 7 = 30 apples.
Therefore, we get that, the number of apples that has been left with Samantha is 30 apples which is calculated using subtraction.
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A spinner with 5 equally sized slices has 2 yellow slices, 2 red slices, and 1 blue slice. Yolanda spun the dial 40 times and got the following results. Answer the following. Round your answer to the nearest thousandth
Given: A spinner with 5 equally sized slices has 2 yellow slices, 2 red slices, and 1 blue slice.
Yolanda spun the dial 40 times and got Yellow 13 times, Red 13 times and Blue 14 times.
Required:
(a) Experimental probability of landing on Blue or Red
(b) Theoretical probability of landing on Blue or Red
(c) What happens when number of spins increases.
Explanation:
(a) Experimental probability =
[tex]Experimental\text{ Probability = }\frac{Number\text{ of trials in which the event occurs}}{total\text{ number of trials}}[/tex]Here, the event is landing on blue or red.
Number of trials in which Blue or Red occurs is 14+13=27
Total number of trials is 40.
So experimental probability is
[tex]\frac{27}{40}=0.675[/tex]Hence, experimental probability is 0.675.
(b) Theoretical probability is
[tex]Theoretical\text{ Probability = }\frac{Favorable\text{ Outcome}}{total\text{ outcome}}[/tex]Here, favorable outcomes for red and blue = 2+1 = 3.
And total possible outcomes = 5
So theoretical probability is
[tex]\frac{3}{5}=0.6[/tex]Hence, theoretical probability is 0.6.
(c) Now, as the number of spins will increase, number of trials will increase and experimental probability will become more and more precise. Hence, it will come closer to theoretical property. So both probabilities will become closer and closer though they might not be equal.
Final Answer:
(a) 0.675
(b) 0.600
(c) Option 1
can u help me fix what i did wrong in the equation
Based on the question, the vertical asymptote is x = -4 and x = 3. This means the denominator cannot have these x-values or else, the function becomes undefined. Hence, from these x-values, we can say that the factors of the denominator are:
[tex](x+4)(x-3)[/tex]Multiplying the factors, we get:
[tex]\begin{gathered} \Rightarrow x^2-3x+4x-12 \\ \Rightarrow x^2+x-12 \end{gathered}[/tex]So, the denominator of our rational function must be x² + x - 12 in order to have those vertical asymptotes.
Another given information is that our x-intercepts are at x = -2 and x = 5. This means that the numerator must be zero at these x-values. Hence, we can say that some factors of the numerator are:
[tex](x+2)(x-5)[/tex]Multiplying these two factors, we get:
[tex]\begin{gathered} \Rightarrow x^2-5x+2x-10 \\ \Rightarrow x^2-3x-10 \end{gathered}[/tex]This means x² - 3x - 10 should be part of our numerator.
Another given information is that the horizontal asymptote is at y = 4. This means that the ratio between the leading coefficients of the numerator and denominator is 4. (since both have the same degree)
So, in order to have a ratio of 4, we will multiply our numerator by 4.
[tex]4(x^2-3x-10)\Rightarrow4x^2-12x-40[/tex]Therefore, our numerator must be 4x² - 12x - 40. And as mentioned above, the denominator must be x² + x - 12. So, the rational function is:
[tex]y=\frac{4x^2-12x-40}{x^2+x-12}[/tex]exponents hwsimplify.
a) -36 b) 36
1) To simplify those expressions let's expand them to better grasp the result:
[tex]\begin{gathered} -6^2=-1\times6^2=-1\cdot36=-36 \\ \end{gathered}[/tex]When the minus sign is accompanying the number without parentheses, we can read it as -1 times the power. That's why -6²=-1 * 36 = -36
b) For the second power we can write out the following:
[tex](-6)^2=(-6)\cdot(-6)=36[/tex]2) Hence, we can state that the answers are -36 and 36
If AC = 66, find the value of x. Round your answer to the nearest tenth if necessary.AB = 8x - 25BC = 9x - 17
We need to represent the segments in a like, like in the following image:
From the image we can see that the sum of the segments AB and BC must be equal to the whole
Write anequivalent expression by distributing thesign outside the parentheses:-(2h + 9.6k) +1
The given expression is
-(2h + 9.6k) +1
Due to the - sign outside the parentheses, every + sign inside the parentheses would be changed to a - sign. Thus, the expression becomes
- 2h - 9.6k + 1
The elevation of a city is positive if the city is above sea level and negative if below sea level.The elevation of New Orleans is -0.3 m.What does an elevation of -0.3 m represent in this situation?
If the elevation of New Orleans is -0.3m, then it is below sea level.
This is because it is a negative number and any
14. Factor x4 + 3x2 - 28.(x2 - 7)(x - 2)(x + 2)(x2 - 2)(x2 + 14)(x2 + 7)(x - 2)(x + 2)(x2 + 4)(x2 - 7)
Answer:
[tex]x^4+3x^2-28=(x^2+7)(x-2)(x+2)[/tex]Step-by-step explanation:
To factorize the expression, we can use a variable substitution. Let's say that z=x^2.
[tex]\begin{gathered} x^4+3x^2-28 \\ z^2+3z-28 \end{gathered}[/tex]Then, to factorize this we need to factor in the form:
[tex](z+\text{?)(z}+\text{?)}[/tex]The numbers that go in the blanks, have to:
*Add together to get 3
[tex]-4+7=3[/tex]*Multiply together to get -28
[tex]-4\cdot7=-28[/tex]So, we get:
[tex]z^2+3z-28=(z-4)(z+7)[/tex]Substitute the equation z=x^2
[tex](x^2-4)(x^2+7)[/tex]Factorizing the perfect square binomial:
[tex]x^4+3x^2-28=(x^2+7)(x-2)(x+2)[/tex]Find the volume of a candy corn, assume they are rectangular pyramids with a length of 8.2 mm, a width of 3.5 mm and a height of 20.1 mm
Given:
Lenght =8.2mm , width = 3.5mm and height = 20.1
The volume of pyramid is given by,
V=1/3 (base area) (height)
As it is rectangular pyramid,
first find area of reactangle . this will be base area for pyramid.
area of reactangle=lenght * weight
[tex]\begin{gathered} A=l\cdot w \\ =8.2\cdot3.5 \\ =28.7\text{ cm}^2 \end{gathered}[/tex]Volume is,
[tex]\begin{gathered} V=\frac{1}{3}\cdot A\cdot h \\ =\frac{1}{3}\cdot28.7\cdot20.1 \\ =192.29\text{ cm}^3 \end{gathered}[/tex]I am needing help on how to this step by step please
The pattern will look like this:
[tex]\begin{gathered} \frac{20}{10}=2=2(10)^0 \\ \frac{20}{10^2}=\frac{2}{10}=2(10)^{-1} \\ \frac{20}{10^3}=\frac{2}{100}=2(10)^{-2} \\ \frac{20}{10^4}=\frac{2}{1000}=2(10)^{-3} \end{gathered}[/tex]The next number will have index of 10 as -4,-5 and so on.
Logarithm 9) solve for P ( in terms of Q)Log (P - Q) = lop P - log Q
we have the expression
[tex]\text{log (P}-Q)=\log P-\log Q[/tex]Applying properties of log right side
[tex]\text{log (P}-Q)=\log (\frac{P}{Q})[/tex]Equate the numbers inside the parenthesis
[tex]P-Q=\frac{P}{Q}_{}[/tex]Solve for P
[tex]P-\frac{P}{Q}=Q[/tex][tex]P\lbrack1-\frac{1}{Q}\rbrack=Q[/tex][tex]P=\frac{Q}{\lbrack1-\frac{1}{Q}\rbrack}[/tex]Simplify
[tex]P=\frac{Q^2}{Q-1}[/tex]classify the systems of equations as consistent dependent, consistent independent,or inconsistent
Recall that:
1) A system of 2 equations is inconsistent if both equations represent different parallel lines.
2) A system of 2 equations is consistent dependent if the equations are equivalent.
3) A system of 2 equations is consistent independent if the slopes of both equations are different.
A) Multiplying the second equation by 2 we get:
[tex]\begin{gathered} \frac{1}{2}y\times2=(x-2)\times2, \\ y=2x-4. \end{gathered}[/tex]Notice that the above equation is the same as the first equation, therefore the equations of the first system of equations are equivalent, then the system is consistent dependent.
B) Notice that the slope of both equations is 4, also, notice that the y-intercept of the first equation is (0,2), and the y-intercept of the second equation is (0,-3), therefore the equations of the system of equations represent different parallel lines, then the system is inconsistent.
C) Notice that the slope of the first equation is 5 and the slope of the second one is 6, therefore the system of equations is consistent independent.
Answer:
A) Consistent dependent.
B) Inconsistent.
C) Consistent independent.
SCS_20-21 Math GR_CFA2 3 Chandler sadelta Naseen an Solana are the theater asks them to the expression shown. Each students answer is shown in 3 Which student answers carece b Doe here anarch
Given:
The expression is,
[tex]\frac{1}{3}(12+3\times6)-5[/tex]The objective is to find which students answer is correct.
By BODMAS rule, the order of arithmetic expression is Bracket, Order of power, Division, Multiplication, Addition, Subtraction.
So as per the rule of BODMAS, first perform the bracket operation.
Inside the bracket, the first operation to be perfoemed in multiplication.
[tex]\frac{1}{3}(12+18)-5[/tex]Now, perform addition inside bracket.
[tex]\frac{1}{3}(30)-5[/tex]Next operation after bracket is division.
[tex]10-5[/tex]Finally by performing the subtracting operation, the answer will be 5.
Hence, the answer of the student naSahar is correct.
Solve. Leave a fraction in your in your answer, if necessary. 45 is what percent of 70.
The following can be written as,
[tex]\frac{45\times100}{70}=\frac{4500}{70}=64.29\text{ \%}[/tex]So 45 is 64.29% of 70.
i need help please, i am desperate. Im fully crying right now so please.
We have a triangular prism.
The volume of a triangular prism is given by,
[tex]V=\frac{1}{2}*b*h*l[/tex]where,
b is the base,
h is the height, and,
l is the length,
for this problem:
b = 3 yd
h = 2 yd
l = 6 yd
Therefore, the volume is,
[tex]V=\frac{1}{2}*3*2*6=18[/tex]Thus, the answer is 18 cubic yards
Write an equation in slope-intercept form that contains the points (2, 8) and (4, 9).
Given two points, the equation of the line in slope form can be obtained using this equation
[tex]\frac{y_2-y_1}{x_2-x_1}\text{ = }\frac{y_{}-y_1}{x_{}-x_1}[/tex]Now we can name the points
x1 = 2, y1 = 8
x2 = 4 , y2 =9
These coordinates can then be substituted into the equation
[tex]\frac{9-8}{4-2}\text{ =}\frac{y\text{ - 8}}{x\text{ - 2}}[/tex][tex]\begin{gathered} \frac{1}{2}\text{ = }\frac{y\text{ - 8}}{x\text{ - 2}} \\ \\ x-2\text{ = 2 (y - 8)} \\ \\ x\text{ - 2 = 2y - 16} \end{gathered}[/tex]x - 2 + 16 = 2y
2y = x - 2 +16
2y = x + 14
Divide both sides by 2
y = x/2 + 14/2
[tex]y\text{ = }\frac{x}{2}\text{ + 7}[/tex]This is the equation in slope-intercept form
where the slope = 1/2
hello I've been stuck on this question and it is a plane trigonometry question hopefully you can help me answer it and thank you for your time
let us start by writing out our parameters
linear velocity v = 50mi/hr
diameter d = 44 in
[tex]\text{Angular Velocity = }\frac{Angle\text{ turned through}}{\text{time}}[/tex]from the diagram above, let the angle turned through be
Bryan invests $500 in an account earning 4% interest that compounds annually. If hemakes no additional deposits or withdrawals, how much will be in the account:1. After 10 years?
Using the compound interest formula:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ _{\text{ }} \\ _{} \end{gathered}[/tex]Where:
P = Principal = 500
r = interest rate = 4% = 0.04
n = Number of times interest is compounded per year = 1
t = time = 10
so:
[tex]\begin{gathered} A=500(1+\frac{0.04}{1})^{10\cdot1} \\ A\approx740.12 \end{gathered}[/tex]Answer:
$740.12
which of the binomials below is a factor of this trinomial? x^2+14x+40A. x-9B. x+10C. x+14D. x^2 + 40
Given the following trinomial expression:
[tex]x^2+14x+40[/tex]To factor the trinomial, we need two numbers:
The product of them = 40
The sum of them = 14
The factors of 40 will be as follows:
40 = 1 x 40 ⇒ sum = 41
40 = 2 x 20 ⇒ sum = 22
40 = 4 x 10 ⇒ sum = 14
40 = 5 x 8 ⇒ sum = 13
so, the numbers will be 4 and 10
The factoring of the expression will be as follows:
[tex]x^2+14x+40=(x+4)(x+10)[/tex]So, the answer will be B. x+10