Given that Tom invested $4500 in an investment paying 10% compounded quarterly for 3 years.
We have to find the interest for the given time period.
We know that the formula of amount on a principal P, rate r per annum, time t years where interest is compounding quarterly is:
[tex]A=P(1+\frac{r}{4})^{4t}[/tex]Here, P = 4500, r = 0.1 and t = 3. So,
[tex]\begin{gathered} A=4500(1+\frac{0.1}{4})^{4(3)} \\ =4500(1+0.025)^{12} \\ =4500(1.025)^{12} \\ =4500(1.3448) \\ =6051.6 \end{gathered}[/tex]So, the amount we get is $6051.6.
Now, it is known that the interest is the difference between the amount and the principal. So,
[tex]\begin{gathered} \text{ interest}=\text{ amount-principal} \\ =6051.6-4500 \\ =1551.6 \end{gathered}[/tex]Thus, the interest is $1551.6.
Sarah Meeham blends coffee for Tasti-Delight. She needs to prepare 190 pounds of blended coffee beans selling for
$4.55 per pound. She plans to do this by blending together a high-quality bean costing $5.50 per pound and a cheaper
bean at $3.50 per pound. To the nearest pound, find how much high-quality coffee bean and how much cheaper coffee
bean she should blend.
She should blend lbs of high quality beans.
(Round to the nearest pound as needed.)
By solving an equation we can say that Sarah needs to blend a total of 96 pounds of coffee beans.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, the total pounds Sarah needs to blend:
Let the number of pounds by 'x'.Now form an equation as:
5.50x + 3.50x = 190 × 4.55Then, solve equation for 'x' as follows:
5.50x + 3.50x = 190 × 4.559x = 864.5x = 864.5/9x = 96 pounds
Therefore, by solving an equation we can say that Sarah needs to blend a total of 96 pounds of coffee beans.
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Which is an x-intercept of the continuous function in thetable?O (-1,0)O (0, -6)O (-6, 0)O (0, -1)
The x-intercept happens when:
[tex]f(x)=0[/tex]Therefore, the x-intercepts for that functions are:
[tex]\begin{gathered} x=-1 \\ x=2 \\ x=3 \end{gathered}[/tex]Answ
3/4 divided by 3/5 how do you work the problem
We copy the first number, change the division sign to multiplication, then flip the second fraction
Cancel the three's
If you want to simplify the improper fraction, divide the numerator by the denominator
5/4 = 1 1/4
Can someone do it for me please
Step-by-step explanation:
13.
a/7 + 5/7 = 2/7
a/7 = 2/7 - 5/7 = -3/7
a = -3
14.
6v - 5/8 = 7/8
6v = 7/8 + 5/8 = 12/8
v = 12/8 / 6 = 2/8 = 1/4
15.
j/6 - 9 = 5/6
j - 54 = 5
j = 5 + 54 = 59
16.
0.52y + 2.5 = 5.1
0.52y = 5.1 - 2.5 = 2.6
y = 2.6/0.52 = 5
17.
4n + 0.24 = 15.76
4n = 15.76 - 0.24 = 15.52
n = 15.52/4 = 3.88
18.
2.45 - 3.1t = 21.05
-3.1t = 21.05 - 2.45 = 18.6
t = 18.6/-3.1 = -6
How do I do this, I’m unsure how to go about it
Given:
[tex]\sqrt{\frac{6}{x}}\cdot\sqrt{\frac{x^2}{24}}[/tex]Simplify:
[tex]=\sqrt{\frac{6}{x}}\cdot\frac{\sqrt{x^2}}{\sqrt{24}}=\sqrt{\frac{6}{x}}\cdot\frac{x}{2\sqrt{6}}[/tex]Apply the properties of fractions:
[tex]=\frac{\sqrt{\frac{6}{x}}x}{2\sqrt{6}}[/tex]Simplify:
[tex]=\frac{\frac{\sqrt{6}}{\sqrt{x}}x}{2\sqrt{6}}=\frac{\sqrt{6}\sqrt{x}}{2\sqrt{6}}[/tex]Eliminate common terms:
[tex]=\frac{\sqrt{x}}{2}[/tex]Answer:
[tex]\frac{\sqrt{x}}{2}[/tex]hours worked. pay2. 12.504. 25.006. 37.508. 50.00write a function rule for the table
The Function is the equation of a line
Step1: we pick any two-point in the of the table and substitute them into the formula below
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1_{}}{x_2-x_1}[/tex](y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)
Let us pick the point (4,25) and (8,50)
where
[tex]x_1=[/tex]I just want to go to sleep but I need the answer to this question
The average rate of change of a function f(x) from x1 to x2 is given by:
[tex]\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]In this case we need the first three seconds so x1=0 and x2=3.
Calculate the values of the function at x=0 and x=3 to get:
f(0)=150 and f(3)=0.
Substitute these values into the formula for average rate of change:
[tex]\begin{gathered} \frac{f(3)-f(0)}{3-0} \\ =\frac{0-150}{3} \\ =\frac{-150}{3} \\ =-50 \end{gathered}[/tex]Hence the avearage rate of change of the function for the first three seconds is -50.
Note that the negative sign shows that the function is decreasing in the time interval (first three seconds).
Hi I need help with question 3 :) . Directions: For each real world situation, write and solve a system of equations . Give the solution as either an ordered pair or list what each variable is worth . Then explain what the solution means in terms of the situation
3.
We know that Hobby Land sells art supplies two different ways.
We can represent the situation with a system of equations
[tex]\begin{cases}x+y=139\ldots(1) \\ 4x+7y=781\ldots(2)\end{cases}[/tex]Where x is the cost of one easel and y represents the cost of one paint set.
Now, we must solve the system of equations.
We can multiply equation (1) by -4
[tex]\begin{gathered} -4(x+y)=-4(139) \\ -4x-4y=-556\ldots(3) \end{gathered}[/tex]Then, we can add (3) + (2)
[tex]\begin{gathered} -4x-4y=-556 \\ 4x+7y=781 \\ -------------- \\ 3y=225 \end{gathered}[/tex]Now, we can solve the equation for y
[tex]\begin{gathered} 3y=225 \\ y=\frac{225}{3}=75 \end{gathered}[/tex]Finally, to find x we can replace the value of y in the equation (1)
[tex]\begin{gathered} x+75=139 \\ x=139-75=64 \end{gathered}[/tex]So, the cost of one easel is $64.
Solution as either an ordered pair:
- (64, 75).
Write 6.5123 x 10^8 in standard
The standard form is a standard method of writing numbers such that we have it in the form:
[tex]a\times10^b[/tex]where
[tex]0Therefore, 6.5123 x 10^8 in standard form is:[tex]6.5123\times10^8[/tex]simplify 3p x 5q x 2
30pq=3p×5q=15pq×2=30pq
Suppose the graph of
y
=
f
(
x
)
is stretched vertically by a factor of
3
, reflected across the
x
-axis, then translated left
7
units, and up
2
units.
The new graph will have equation y=
Answer:
[tex]y=-3(x+7)+2[/tex]
Step-by-step explanation:
Alright, so the first mistake people make is to try to visualize this graph. For the sake of the problem, it does not matter in the slightest.
To start, we have y=f(x).
The first change is a vertical stretch. These are represented outside the parentheses. Meaning, the new stretched equation would be y=3(x). The three does not replace the "f", just no one would write the f into the equation as it is implied.
Next, the graph is reflected across the x-axis. This means that there is a negative outside of the parentheses. The new equation would be -3(x). As stretches are always greater than 1 and shrinks are between 0 and 1, it is clear the negative denotes a reflection.
Translations to the left are denoted as positives inside parentheses. In this case, left 7 would be -3(x+7).
Finally, upwards translations are positive numbers shown following the parentheses. Up two would make your final equation -3(x+7)+2.
Finish the other half of the graph if it was even and odd.
To solve this problem, first, let's remember the definitions of even and odd functions.
• A function f is ,even, if the graph of f is ,symmetric about the y-axis,.
,• A function f is ,odd, if the graph of f is ,symmetric about the origin.
a) To make the function even, we must complete the graph such the graph result is symmetric about the y-axis (the vertical axis). Doing that we get:
b) To make the function odd, we must complete the graph such the graph result is symmetric about the origin (the horizontal axis). Doing that we get:
0.4(2-) 0.2(9 + 7) A)-3 B - 1 C) 3 D) all real numbers
Let us solve the equation to arrange the steps
[tex]-3(4+3x)+5x=-16[/tex]In the first step, we must multiply the bracket by -3 (distributive property)
[tex](-3)(4)_{}+(-3)(3x)=-12-9x[/tex]Then the equation is
[tex]-12-9x+5x=-16[/tex]Now add the like terms on the left side
[tex]\begin{gathered} -12+(-9x+5x)=-16 \\ -12x+(-4x)=-16 \\ -12-4x=-16 \end{gathered}[/tex]Next step, add 12 to both sides
[tex]undefined[/tex]Base on table above is the scenario a proportional relationship
No
Explanations:A relationship is called a proportional relationship if it has two variables that are realated by the same ration. In this case there will be a proportionality constant.
In this table:
Let Height be represented as H
Let Time be represented as T
For the relationship to be a proportional relationship, it must obey the relation:
[tex]\begin{gathered} H\propto\text{ T} \\ H\text{ = kT} \\ \text{Where k is the proportionality constant} \end{gathered}[/tex]When T = 3, H = 15
Using H = kT
15 = 3k
k = 15 / 3
k = 5
When T = 6, H = 30
H = kT
30 = 6k
k = 30 / 6
k = 5
When T = 12, H = 45
H = kT
45 = 12k
k = 45 / 12
k = 3.75
Since the constant of proportionality is the the same for the three cases in the table, the scenario is not a proportional relationship
9b 9a) Use the slope formula to determine the rate of change eq y- and find the y-intercept "5" by substituting the x and y values into y=mx + b
A) We need to find the rate of change of the function first.
The rate of change or slope of the line is:
[tex]m=\frac{y_2-y_1}{x_2-x_1_{}}[/tex]Where x and y are the coordinates of a point in line.
In order to calculate the slope we can take the poinst:
x1 = -6, y1 = 4
x2 = -2, y2= 1
Using the formula of above we find that the slope is:
[tex]m=\frac{1-4}{-2-(-6)}=-\frac{3}{4}[/tex]Now, in order to find the value of y-intercept of the line we can use formula:
[tex]y=m\cdot x+b[/tex]Which is the function of the line. From the formula of above we don't know the value of b (the y-intercept).
But we know that the formula must be valid for a point in the line. We can find the value of b replacing the coordinates of a point in the line, let's choose: x = -6 and y = 4, so:
[tex]4=\text{ m}\cdot(-6)+b[/tex]Now we use the value of m of above:
[tex]4=(-\frac{3}{4})\cdot(-6)+b[/tex]And from the last equation we can see that:
[tex]b=4-\frac{3}{4}\cdot6=4-\frac{9}{2}=\frac{8}{2}-\frac{9}{2}=-\frac{1}{2}[/tex]So, the equation of the line is:
[tex]y\text{ = -}\frac{\text{3}}{4}\cdot x-\frac{1}{2}[/tex]And the y-intercept is obtain replacing x = 0, so the y-intercept is: y = -1/2
b) From the stepts of above we already know an equation that represents the function! It is:
[tex]y\text{ = -}\frac{\text{3}}{4}\cdot x-\frac{1}{2}[/tex]c) Now, we need to use the last equation to find y = n in the table. We know from the table that the value x for that value of y is x = 3, so we replace that value in the equation of the line:
[tex]y\text{ = -}\frac{\text{3}}{4}\cdot3-\frac{1}{2}=-\frac{9}{4}-\frac{1}{2}=-\frac{9}{4}-\frac{2}{4}=-\frac{11}{4}[/tex]So the value of n is:
[tex]n\text{ = -}\frac{\text{11}}{4}[/tex]If the price of bananas goes from $0.39 per pound to $1.06 per pound, what is the likely effect of quantity demanded?
When the price of bananas goes from $0.39 per pound to $1.06 per pound, the likely effect of quantity demanded is that it will reduce.
What is demand?The quantity of a commodity or service that consumers are willing and able to acquire at a particular price within a specific time period is referred to as demand. The quantity required is the amount of an item or service that customers will purchase at a certain price and period.
Quantity desired in economics refers to the total amount of an item or service that consumers demand over a given time period. It is decided by the market price of an item or service, regardless of whether or not the market is in equilibrium.
A price increase nearly invariably leads to an increase in the quantity supplied of that commodity or service, whereas a price decrease leads to a decrease in the quantity supplied. When the price of good rises, so does the quantity requested for that good. When the price of a thing declines, the demand for that good rises.
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In TUV, the measure of V=90°, the measure of U=58°, and TU = 38 feet. Find the length of VT to the nearest tenth of a foot.
Answer:
32.2 feet
Explanation:
The diagram given is a right angled triangle
Using the SOH CAH TOA identity
Given the following
Hypotenuse = 38
Opposite = x
Sin theta = opposite/hypotenuse
Sin 58 = x/38
x = 38sin58
x = 38(0.8480)
x = 32.23
Hence the length of VT to the nearest tenth of a foot. is 32.2feet
For the point P (-12,22) and Q (-7, 27), find the distance d(P,Q) and the coordinates of the midpoint M of the segment PQ. What is the distance?
The distance d(P,Q) is equal to 7.1 units and the coordinates of the midpoint M of the segment PQ are (-9.5, 24.5).
How to determine the distance between points P and Q?Mathematically, the distance between two (2) points that are located on a coordinate plane can be calculated by using this formula:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Substituting the given parameters into the formula, we have;
Distance, d(P, Q) = √[(-7 + 12)² + (27 - 22)²]
Distance, d(P, Q) = √[5² + 5²]
Distance, d(P, Q) = √[25 + 25]
Distance, d(P, Q) = √50
Distance, d(P, Q) = 7.1 units.
Midpoint on x-coordinate is given by:
xm = (x₁ + x₂)/2
xm = (-7 - 12)/2
xm = -19/2
xm = -9.5
Midpoint on y-coordinate is given by:
ym = (y₁ + y₂)/2
ym = (27 + 22)/2
ym = 49/2
ym = 24.5
Therefore, the coordinates of the midpoint M are equal to (-9.5, 24.5).
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We have a deck of 10 cards numbered from 1-10. Some are grey and some are white. The cards numbered are 1,2,3,5,6,8 and 9 are grey. The cards numbered 4,7, and 10 are white. A card is drawn at random. Let X be the event that the drawn card is grey, and let P(X) be the probability of X. Let not X be the event that the drawn card is not grey, and let P(not X) be the probability of not X.
Given:
The cards numbered are, 1,2,3,5,6,8, and 9 are grey.
The cards numbered 4,7 and 10 are white.
The total number of cards =10.
Let X be the event that the drawn card is grey.
P(X) be the probability of X.
Required:
We need to find P(X) and P(not X).
Explanation:
All possible outcomes = All cards.
[tex]n(S)=10[/tex]Click boxes that are numbered 1,2,3,5,6,8, and 9 for event X.
The favourable outcomes = 1,2,3,5,6,8, and 9
[tex]n(X)=7[/tex]Since X be the event that the drawn card is grey.
The probability of X is
[tex]P(X)=\frac{n(X)}{n(S)}=\frac{7}{10}[/tex]Let not X be the event that the drawn card is not grey,
All possible outcomes = All cards.
[tex]n(S)=10[/tex]Click boxes that are numbered 4,7, and 10 for event not X.
The favourable outcomes = 4,7, and 10
[tex]n(not\text{ }X)=3[/tex]Since not X be the event that the drawn card is whic is not grey.
The probability of not X is
[tex]P(not\text{ }X)=\frac{n(not\text{ }X)}{n(S)}=\frac{3}{10}[/tex]Consider the equation.
[tex]1-P(not\text{ X\rparen}[/tex][tex]Substitute\text{ }P(not\text{ }X)=\frac{3}{10}\text{ in the equation.}[/tex][tex]1-P(not\text{ X\rparen=1-}\frac{3}{10}[/tex][tex]1-P(not\text{ X\rparen=1}\times\frac{10}{10}\text{-}\frac{3}{10}=\frac{10-3}{10}=\frac{7}{10}[/tex][tex]1-P(not\text{ X\rparen is same as }P(X).[/tex]Final answer:
[tex]1-P(not\text{ X\rparen is same as }P(X).[/tex]
What is the slope of (-8, -3) and (-7, -6)
To find the slope, we use the following formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's replace the given points.
[tex]m=\frac{-6-(-3)}{-7-(-8)}=\frac{-6+3}{-7+8}=\frac{-3}{1}=-3[/tex]Hence, the slope is -3.A water tank holds 276 gallons but is leaking at a rate of 3 gallons per week. A second water tank holds414 gallons but is leaking at a rate of 5 gallons per week. After how many weeks will the amount of waterin the two tanks be the same?The amount of water in the two tanks will be the same inweeks.
In order to solve the problem we will first create equations to represent the volume of water on the gallons through the weeks. The output of the functions will be the volume of each and the entry will be the number of weeks passed.
For the first one:
[tex]\text{vol(week) = 276 -3}\cdot week[/tex]While on the second one:
[tex]\text{vol(week) = 414 -5}\cdot week[/tex]In order to calculate the number of weeks it'll take until they have the same volume of water we need to find the "week" which would make them equal. So we will equate both expressions and solve for that variable.
[tex]\begin{gathered} 276\text{ - 3}\cdot week\text{ = 414 - 5}\cdot week \\ 5\cdot\text{week - 3}\cdot week\text{ = 414 - 276} \\ 2\cdot\text{week = }138 \\ \text{week = }\frac{138}{2}\text{ = }69 \end{gathered}[/tex]It'll take 69 weeks for the tanks to have the same volume.
At noon a private plane left Austin for Los Angeles, 2100 km away, flying at 500 km/h. One hour later a jet left Los Angeles for Austin at 700 km/h. At what time did they pass each other?
Function g is defined as g(x)=f (1/2x) what is the graph of g?
Answer:
D.
Explanation
We know that g(x) = f(1/2x)
Additionally, the graph of f(x) passes through the point (-2, 0) and (2, 0).
It means that f(-2) = 0 and f(2) = 0
Then, g(-4) = 0 and g(4) = 0 because
[tex]\begin{gathered} g(x)=f(\frac{1}{2}x_{}) \\ g(-4)=f(\frac{1}{2}\cdot-4)=f(-2)=0 \\ g(4)=g(\frac{1}{2}\cdot4)=f(2)=0 \end{gathered}[/tex]Therefore, the graph of g(x) will pass through the points (-4, 0) and (4, 0). Since option D. satisfies this condition, the answer is graph D.
Using the image, identify the opposite rays (choose all that apply).
Solution
The answer is
A 14 m long ladder is placed against a tree. The top of the ladder reaches a point
13 m up the tree.
How far away is the base of the ladder from the base of the tree?
Give your answer in metres (m) to 1 d.p.
Answer:
Approximately 5.2 meters
Step-by-step explanation:
This formation will make a right triangle. The ground to the point in the tree is one of the legs. The base of the tree to the base of ladder is another leg and the length of the ladder is the hypotenuse. In this case, we already have the hypotenuse and one of the legs, so we need to find the value of another leg.
We can do so by using the Pythagorean Theorem which is [tex]a^2+b^2=c^2\\[/tex].
a and b represent the values of the two legs, and c is the hypotenuse. Since we already have the hypotenuse, we can change this equation a bit to find the other leg.
Let's assign the missing value, b in the theorem.
The new equation will be [tex]b^2=c^2-a^2[/tex].
We can insert the values for c and a and solve for b.
The new equation will be [tex]b^2 = 14^2-13^2[/tex].
[tex]b^2=196-169[/tex]
[tex]b^2=27[/tex]
[tex]\sqrt{b^2} =\sqrt{27}[/tex]
The square root of [tex]b^2[/tex] cancels out.
The approximate square root of 27 is 5.19 which we can round to 5.2.
The test results for 4 students are 96 83 78 and 83. If one more student's test score of 87 is added, what would increase?A. median B. meanC. modeD. range
Mean will increase because 87 is greater than 83 and 78, then the eman will be greater
Let p = x^2 + 6.Which equation is equivalent to (22 + 6)^2 – 21 = 4x^2 + 24 in terms of p?Choose 1 answer:А) p^2 + 4p - 21 = 0B) p^2 - 4p - 45 = 0C) p^2 - 4p - 21 = 0D) p^2 + 4p - 45 = 0
Given:
[tex](22+6)^2-21=4x^2+24[/tex][tex]\text{Let p = x}^2+6[/tex]Let's solve the equation in terms of p:
[tex]undefined[/tex]Without needing to graph determined the number of solutions for this system
Given the system of equations:
[tex]\text{ x + y = 6}[/tex][tex]\text{ y = -x + 6}[/tex]The two equations appear to be just the same, thus, we are only given one system of equations.
Therefore, the answer is letter B. It has infinite solutions because the two equations are just the same line.
Problem: A school has a student to teacher ratio of25:5. If there are 155 teachers at the school, howmany students are there?Mike's AnswerCarlos's Answer25 .5 1551552555x = 3875x=77525x = 775x=31There are 31 students at the school.There are 775 students at the scheel.Who is correct? Mike or Carlos? Explain the error thatwas made.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
ratio = 25:5 (students:teachers)
teachers = 155
students = ?
Step 02:
[tex]\begin{gathered} \text{students = 155 teachers }\cdot\text{ }\frac{25\text{ students }}{5\text{ teachers}} \\ \text{students = }775\text{ } \end{gathered}[/tex]Carlos is correct.
[tex]\frac{25}{5}=\frac{x}{155}[/tex]The answer is:
There are 775 students.
Carlos is correct.
Mike set the variables to find in the wrong way.
Mrs. algebra ordered some small and medium pizzas for her daughter‘s birthday party. The small pizzas cost $5.75 each and the medium pizzas cost $8.00 each. She bought three more medium pizzas than small pizzas and her total order came to $51.50 How many pizzas of each did Mrs. Algebra order? Write an equation and solve.
we have the following:
x is small pizzas
y is medium pizzas
[tex]\begin{gathered} 5.75\cdot x+8\cdot y=51.5 \\ y=x+3 \\ 5.75\cdot x+8\cdot(x+3)=51.5 \\ 5.75x+8x+24=51.5 \\ 13.75x=51.5-24 \\ x=\frac{27.5}{13.75} \\ x=2 \end{gathered}[/tex]therefore, the answer is:
2 small pizzas and 5 (2+3) medium pizzas
