The simple interest is given by:
[tex]SI=Prt[/tex]where P is the principal (the amount we invest in the account), r is the interest rate and t is the time of investment.
Let P be the interest Larry made in the 2% account, the simple interest in this case is given by:
[tex]0.02P[/tex]Now for the second account we would have an envestment of (17000-P), then the simple interest have to be:
[tex]0.05(17000-P)[/tex]and we know that both investments have to be equal to 610, then we have:
[tex]\begin{gathered} 0.02P+0.05(17000-P)=610 \\ 0.02P+850-0.05P=610 \\ -0.03P=610-850 \\ -0.03P=-240 \\ P=\frac{-240}{-0.03} \\ P=8000 \end{gathered}[/tex]Therefore Larry invested $8000 in the 2% account and $9000 in the 5% account.
Solve the system of two equations in two variables.6x - 7y = 282x + 4y = -16
Answer:
Explanation:
Given the system of equations
[tex]\begin{gathered} 6x-7y=28 \\ 2x+4y=-16 \end{gathered}[/tex]We intend to use the elimination method to solve it.
• Multiply the first equation by 2
,• Multiply the second equation by 6
This gives us:
[tex]\begin{gathered} 12x-14y=56 \\ 12x+24y=-96 \end{gathered}[/tex]We eliminate x by subtracting.
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Answer:
followed
Step-by-step explanation:
now gimmie
Need Help Asaaaappp look at scrrenshot
PR = 32
Equation:
Perimeter = PR + RQ + QP
67 units = (4x) + (x + 2) + (3x + 1)
67 = 8x + 3
64 = 8x
x = 8 units
Substitute x:
PR = (4x) = 4 * 8 = 32 units
RQ = (x + 2) = 8 + 2 = 10 units
QP = (3x + 1) = 3 * 8 + 1 = 25 units
PR = 32
Equation:
Perimeter = PR + RQ + QP
67 units = (4x) + (x + 2) + (3x + 1)
67 = 8x + 3
64 = 8x
x = 8 units
Substitute x:
PR = (4x) = 4 * 8 = 32 units
RQ = (x + 2) = 8 + 2 = 10 units
QP = (3x + 1) = 3 * 8 + 1 = 25 units
Identify the domain and range of the relation. Is the relation a function? Why or why not?
{(-3, 1), (0, 2), (1, 5), (2, 4), (2, 1)}
Domain={-3, 0, 1, 2}, Range={1,2,5,4} and the relation is not a function.
What is a function?A relation is a function if it has only one y-value for each x-value.
The given relation is {(-3, 1), (0, 2), (1, 5), (2, 4), (2, 1)}
The domain is the set of all the first numbers of the ordered pairs.
In other words, the domain is all of the x-values.
Domain={-3, 0, 1, 2}
The Range is the set of all the second numbers of the ordered pairs.
In other words, the range is all of the y-values.
Range={1,2,5,4}
The given relation is not a function because there are two values of y for one value of x. It means 4 and 1 are values of 2.
Hence Domain={-3, 0, 1, 2}, Range={1,2,5,4} and the relation is not a function.
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Persevere with Problems Analyze how the circumference of a circle would change if the diameter was doubled. Provide an example to support your explanation.
Circumference of a circle . Girth
Circumference C= π•D
Then if D'=2D
New Circumference C'= π•2D = 2•π•D
Circumference is doubled, if diameter is doubled
EXAMPLE
Suppose D= 5 cm
Then C= π•5 = 15.70
If D'= 2•5=10 cm
Then C'= π•10= 31.415
Now divide C'/C = 31.415/15.70 = 2.00
Find the distance between the two points. Write your answer as a decimal rounded to the hundredths place if needed.
We need to find the distance between the two points given. Use the distance formula:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Replace using P1(3,-9) and P2(-2,4):
[tex]d=\sqrt[]{((-2)_{}-3_{})^2+(4_{}-(-9)_{})^2}[/tex][tex]d=\sqrt[]{(-5)^2+(13)^2}[/tex][tex]d=13.9283[/tex]Rounded to the hundredths:
[tex]d=13.93[/tex]Which of the following ordered pairs is a solution to the equation 2x+y=2? Select all that apply.(11,0)(−4,10)(−13,4)(−11,−1)(0,2)
You have the following equation:
2x + y = 2
In order to determine which of the given pairs is a solution, replace the values of x and y of such pairs and verify the equation, as follow:
(11,0)
2(11) + 0 = 22 ≠ 2 it's not a solution
(-4,10)
2(-4) + 10 = -8 + 10 = 2 it's a solution
(-13,4)
2(-13) + 4 = -26 + 4 ≠ 2 it's not a solution
(-11,-1)
2(-11) + (-1) = -22 - 1 ≠ 2 it's not a solution
(0,2)
2(0) + 2 = 2 it's a solution
If z = 30, use the following proportions to find the value of x. x : y = 3:9 and y : z = 6 : 20.
We are given the following proportions:
[tex]\begin{gathered} x:y=3:9 \\ y:z=6:20 \end{gathered}[/tex]The second proportion is equivalent to:
[tex]\frac{y}{z}=\frac{6}{20}[/tex]Now, we substitute the value of "z":
[tex]\frac{y}{30}=\frac{6}{20}[/tex]Now, we multiply both sides by 30:
[tex]y=30\times\frac{6}{20}[/tex]Solving the operation we get:
[tex]y=9[/tex]Now, since we have the value of "y" we can use the first proportion to get the value of "x":
[tex]x_:y=3:9[/tex]This is equivalent to:
[tex]\frac{x}{y}=\frac{3}{9}[/tex]Now, we substitute the value of "y":
[tex]\frac{x}{9}=\frac{3}{9}[/tex]Now, we multiply both sides by 9:
[tex]x=9\times\frac{3}{9}[/tex]Solving the operations:
[tex]x=3[/tex]Therefore, the value of "x" is 3.
Y = X - 8. y = -x +6* Parallel Perpendicular Neither
The equation of a line given in slope-intercept form is written as
[tex]\begin{gathered} y=mx+b \\ \text{Where m is the slope. This means the coeeficient of x is the slope} \end{gathered}[/tex]For two lines to be parallel, their slopes must equal to each other. Also for the two lines to be perpendicular, their slopes must be a negative inverse of each other. An example of negative inverse is given as;
[tex]\begin{gathered} -\frac{1}{4}\text{ is a negative inverse of 4} \\ \text{Likewise, -4 is a negative inverse of }\frac{1}{4}\text{ } \end{gathered}[/tex]The slope of the first line is 1, since the line is given as,
y = x - 8
(The coefficient of x is 1)
The slope of the second line is -1, since the line is given as,
y = -x + 8
(The coefficient of x is -1)
Therefore, since both slopes are not equal and not negative inverses of each other, then the correct answer is NEITHER.
hi help I've been trying to solve this for an hour and I just really need the correct answer please help
First we can se the points that each line passes, and those are:
(-1, 5) & (0, 2)
(-5, -2) & (0, -4)
From this, we calculate each function, that is:
*Line 1:
[tex]m_1=\frac{2-5}{0-(-1)}\Rightarrow m_1=-3[/tex]And we calculate the first function:
[tex]y-2=-3(x-0)\Rightarrow y=-3x+2[/tex]*Line 2:
[tex]m_2=\frac{-4-(-2)}{0-(-5)}\Rightarrow m_2=-\frac{2}{5}[/tex]And we calculate the second function:
[tex]y+4=-\frac{2}{5}(x-0)\Rightarrow y=-\frac{2}{5}x-4[/tex]So the system is:
Area of a rectangle: A Solve for) Find l when A= 24 ft and u
The area of the rectangle is 24 ft^2
the width of the rectangle is w = 8 ft
The expression for the area of the rectangle is given as follows.
A = l * w
[tex]\begin{gathered} 24=l\times8 \\ l=\frac{24}{8}=3 \end{gathered}[/tex]The length is l = 3 ft.
[tex]l=\text{ 3 ft}[/tex]Rafael is buying ice cream for a family reunion. The table shows the prices for different sizes of two brands of ice cream.
the correct answer is that the small size of the brand Cone dreams, because the price of each pint in it will be $2.125 =4.25/2, and if we calculate the price per pint with the other options it would be the minimum of all of them.
In the triangle below, suppose that mZH= (6x-4)°, mZ1 = (2x-5)°, and m
Find the degree measure of each angle in the triangle.
(2x - 5) ⁰
H (6x-4)
x
mZH =
m 41 =
mZJ =
1
X
Answer: H = 122, I = 37, J = 21
Step-by-step explanation:
All the angles of a triangle add up to 180 degrees.
(6x - 4) + (2x - 5) + x = 180
Combine like terms
9x - 9 = 180
Solve for x
9x = 189
x = 21
m<H = (6*21 - 4) = 122
m<I = (2*21-5) = 37
m<J = 21
Graph the function and state the domain and range.g(x)=x^2-2x-15Domain-Range-Graphed function-
The domain: -∞ < x < ∞
The range: g(x) ≥ -16
Explanation:The given function is:
[tex]g(x)\text{ = x}^2\text{-2x-15}[/tex]The domain is a set of all the valid inputs that can make the function real
All real values of x will make the function g(x) to be valid
The domain: -∞ < x < ∞
The range is the set of all valid outputs
From the function g(x):
a = 1, b = -2
[tex]\begin{gathered} \frac{b}{2a}=\frac{-2}{2(1)}=-1 \\ g(-1)=(-1)^2-2(-1)-15 \\ g(-1)=1-2-15 \\ g(-1)=-16 \end{gathered}[/tex]Since a is positive, the graph will open upwards
Therefore, the range of the function g(x) is: g(x) ≥ -16
The graph of the function g(x) = x^2 - 2x - 15 is plotted below
which point lies on the line with the slope of m=7 that passes through the point (2,3)
Answer:
B. Monkey Man
Step-by-step explanation:
M+o+n+k+e+y
The Max or Min can be found by using the line of symmetry. That line of symmetry can be found by finding the midpoint of the two x-intercepts.Since the line of symmetry is x =-1 Write the function rule to find the coordinate to the minimum of this parabola.[tex]f (x) = (x - 2)(x + 4)[/tex]your answer should be in the form (_,_)
We know that, for a parabola, the minimum, or the maximum, is given by the vertex of the parabola. The formula for the vertex of the parabola is given by:
[tex]x_v=-\frac{b}{2a},y_v=c-\frac{b^2}{4a}[/tex]And we have the coordinates for x and y for the vertex.
We can see that the line of symmetry is x = -1, and this is the same value for the value of the vertex for x-coordinate, that is, the x-coordinate is equal to x = -1.
With this value for x, we can find the y-coordinate using the given equation of the parabola:
[tex]f(x)=(x-2)\cdot(x+4)\Rightarrow f(-1)=(-1-2)\cdot(-1+4)\Rightarrow f(-1)=(-3)\cdot(3)[/tex]We can also expand these two factors, and we will get the same result:
[tex]f(x)=(x-2)\cdot(x+4)=x^2+2x-8=(-1)^2+2\cdot(-1)-8=1-2-8=-1-8=-9[/tex]Therefore, the value for the y-coordinate (the value for the y-coordinate of the parabola, which is, at the same time, the minimum point for y of the parabola) is:
[tex]f(-1)=(-3)\cdot(3)\Rightarrow f(-1)=-9[/tex]The minimum point of the parabola is (-1, -9) (answer), and we used the given function (rule) to find the value of the y-coordinate.
We can check these two values using the formula for the vertex of the parabola as follows:
[tex]f(x)=(x-2)\cdot(x+4)=x^2+2x-8[/tex]Then, a = 1 (it is positive so the parabola has a minimum), b = 2, and c = -8.
Hence, we have (for the value of the x-coordinate, which is, at the same time, the value for the axis of symmetry in this case):
[tex]x_v=-\frac{2}{2\cdot1}\Rightarrow x_v=-1[/tex]And for the value of the y-coordinate, we have:
[tex]y_v=c-\frac{b^2}{4a}\Rightarrow y_v=-8-\frac{2^2}{4\cdot1}=-8-\frac{4}{4}=-8-1\Rightarrow y_v=-9[/tex]
A triangular pryamid is shown in the diagram. What is the volume of the triangular pyramid?
Given the following question:
[tex]\begin{gathered} V=\frac{1}{3}BH \\ B=\text{ Base Area} \\ A=\frac{1}{2}BH \\ B=7.8 \\ H=4 \\ A=\frac{1}{2}7.8(4) \\ 7.8\times4=31.2 \\ 31.2\div2=15.6 \\ A=15.6 \\ V=\frac{1}{3}BH \\ B=15.6 \\ H=4 \\ \frac{1}{3}15.6(4) \\ 15.6(4)=62.4 \\ 62.4\div3=20.8 \\ V=20.8 \end{gathered}[/tex]Volume is equal to 20.8 cubic centimeters.
Make the following conversions. Round to 2 decimal places, where necessary.8 feet 9 inches toa. Inches: in.b. Feet: ft
Given the measurement
[tex]8feet\text{ 9inches}[/tex]a) To convert to inches,
Where
[tex]1ft=12in[/tex][tex]8ft\text{ to inches}=8\times12=96[/tex]8 feet 9 inches in inches is
[tex]\begin{gathered} 8ft\text{ 9in}=8ft+9in=96+9=105in \\ 8ft\text{ 9in}=105in \end{gathered}[/tex]Hence, 8 feet 9 inches in inches is 105in
b) To convert to feet,
Where
[tex]1in=\frac{1}{12}ft[/tex][tex]9in\text{ to f}eet=9\times\frac{1}{12}=\frac{9}{12}=0.75ft[/tex]8 feet 9 inches in feet is
[tex]8ft\text{ 9in}=8ft+9in=8+0.75=8.75ft[/tex]Hence, 8 feet 9 inches in feet is 8.75ft
A chef is going to use a mixture of two brands of italian dressing. the first brand contains 7% vinegar and the second brand contains 12% vinegar. the chef wants to make 280 milliliters of a dressing that is 9% vinegar. how much of each brand should she use
We know that
• The first brand contains 7% vinegar.
,• The second brand contains 12% vinegar.
,• The chef wants 280 milliliters with 9% vinegar.
Using the given information, we can express the following equation.
[tex]0.07x+0.12(280-x)=0.09(280)[/tex]Notice that 0.07x represents the first brand, 0.12(280-x) represents the second brand, and 0.08(280) represents the final product the chef wants to make.
Let's solve for x.
[tex]\begin{gathered} 0.07x+33.6-0.12x=25.2 \\ -0.05x=25.2-33.6 \\ -0.05x=-8.4 \\ x=\frac{-8.4}{-0.05} \\ x=168 \end{gathered}[/tex]Therefore, the chef needs 168 of the first brand and 112 of the second brand.Notice that 280-168 = 112.
Consider the graph of g(x) shown below. Determine which statements about the graph are true. Select all that apply.
SOLUTION
From the graph, the root of the equation is the point where the graph touches the x-axis
[tex]x=-4,x=0[/tex]Hence the equation that models the graph becomes
[tex]\begin{gathered} x+4=0,x-0=0 \\ x(x+4)=0 \\ x^2+4x=0 \\ \text{Hence } \\ g(x)=x^2+4x \end{gathered}[/tex]Since the solution to the equation are x=-4 and x=0
Hence the equation has two real zeros
The minimum of g(x) is at the point
[tex]\begin{gathered} (-2,-4) \\ \text{Hence minimum is at x=-2} \end{gathered}[/tex]The minimum of g(x) is at x=-2
The vertex of g(x) is given by
[tex]\begin{gathered} x_v=-\frac{b}{2a} \\ \text{and substistitute into the equation to get } \\ y_v \end{gathered}[/tex][tex]\begin{gathered} a=1,\: b=4,\: c=0 \\ x_v=-\frac{b}{2a}=-\frac{4}{2\times1}=-\frac{4}{2}=-2 \\ y_v=x^2+4x=(-2)^2+4(-2)=4-8=-4 \\ \text{vertex (-2,-4)} \end{gathered}[/tex]Hence the vertex of g(x) is (-2,-4)
The domain of the function g(x) is the set of input values for which the function g(x) is real or define
Since there is no domain constrain for g(x), the domain of g(x) is
[tex](-\infty,\infty)[/tex]hence the domain of g(x) is (-∞,∞)
The decreasing function the y-value decreases as the x-value increases: For a function y=f(x): when x1 < x2 then f(x1) ≥ f(x2)
Hence g(x) decreasing over the interval (-∞,-2)
Therefore for the graph above the following apply
g(x) has two real zeros (option 2)
The minimum of g(x) is at x= - 2(option 3)
the domain of g(x) is (-∞,∞) (option 4)
g(x) decreasing over the interval (-∞,-2)(option 4)
the value of square root (8/64)³
The expression is
[tex]\begin{gathered} (\sqrt[]{\frac{8}{64}})^3 \\ By\text{ simplifying, we have} \\ (\sqrt[]{\frac{1}{8}})^3 \\ =\text{ (}\frac{1}{8})^{\frac{3}{2}} \\ 0.0442 \end{gathered}[/tex]Find the value of x that makes ADEF ~AXYZ..yE1052x – 114D11FX5x + 2Zх=
Given that the triangles are similar, we can express a proportion between their sides. DE and XY are corresponding sides. EF and YZ are corresponding sides. Let's define the following proportion.
[tex]\begin{gathered} \frac{XY}{DE}=\frac{YZ}{EF} \\ \frac{10}{5}=\frac{14}{2x-1} \end{gathered}[/tex]Now, we solve for x
[tex]\begin{gathered} 2=\frac{14}{2x-1} \\ 2x-1=\frac{14}{2} \\ 2x=7+1 \\ x=\frac{8}{2} \\ x=4 \end{gathered}[/tex]Hence, the answer is x = 4.It takes a hose 3 minutes to fill a rectangular aquarium 8 inches long, 10 inches wide, and 14 inchestall. How long will it take the same hose to fill an aquarium measuring 23 inches by 25 inches by 26inches?minutesEnter an integer or decimal number [more..]Round your answer to the nearest minuteSubmit
Answer:
[tex]40\text{ minutes}[/tex]Explanation:
Firstly, we have to calculate the rate at which the hose works
We can get that by dividing the volume of the first aquarium by the time taken to fill it
The volume of the first aquarium can be calculated using the formula:
[tex]V\text{ = L}\times B\times H[/tex]Where:
L is the length of the aquarium
B is its width
H is its height
The volume of the first aquarium is thus:
[tex]V\text{ = 8}\times10\times14\text{ = 1120 in}^3[/tex]We have the filling rate as:
[tex]\frac{1120}{3}\text{ in}^3\text{ per minute}[/tex]Now, let us get the volume of the second aquarium
We use the same formula as the first
We have the volume as:
[tex]23\times25\times26\text{ = 14,950 in}^3[/tex]Now, to get the time taken, we divide the volume of the second aquarium by the rate of the first
Mathematically, we have that as:
[tex]14950\text{ }\times\frac{3}{1120}\text{ = 40 minutes approximately}[/tex]When you start your career, you decide to set aside $500 every quarter to deposit into an investment account. The investment firm claims that historically their accounts have earned an annual interest rate of 10.0% compounded quarterly. Assuming this to be true, how much money will your account be worth after 25 years of depositing and investing? Round your answer to the nearest cent. Do not include labels or units. Just enter the numerical value.
Given:
The principal amount = $500
Interest rate = 10% quarterly
Required:
Find the deposing amount after 25 years.
Explanation:
The amount formula when the interest is compounded quarterly is given as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where r = interest rate
t = time period
n = The number of compounded times
The amount after 25 years is:
[tex]\begin{gathered} A=500(1+\frac{0.1}{4})^{4\times25} \\ A=500(1+.025)^{100} \\ A=500(1.025)^{100} \end{gathered}[/tex][tex]\begin{gathered} A=500\times11.81371 \\ A=5906.8581 \end{gathered}[/tex]Final Answer:
The amount after 25 years will be &5906.85
There are two boxes containing only red and purple pens.Box A has 12 purple pens and 3 red pens.Box B has 14 purple pens and 6 red pens.A pen is randomly chosen from each box.List these events from least likely to most likely.Event 1: choosing a purple or red pen from Box A.Event 2: choosing a green pen from Box B.Event 3: choosing a purple pen from Box B.Event 4: choosing a purple pen from Box A.Least likelyMost likelyEventEventEventEvent
Event 1: choosing a purple or red pen from Box A
All pens are purple or red so the probability is:
[tex]P=\frac{12+3}{15}=\frac{15}{15}=1[/tex]Event 2: choosing a green pen from Box B
We don't have green pens, so the probability is 0.
Event 3: choosing a purple pen from Box B
We have 14 purple pens and 20 total pens, so:
[tex]P=\frac{14}{20}=\frac{7}{10}=0.7[/tex]Event 4: choosing a purple pen from Box A
We have 12 purple pens and 15 total pens, therefore:
[tex]P=\frac{12}{15}=\frac{4}{5}=0.8[/tex]Listing from least likely to most likely, we have:
event 2 < event 3 < event 4 < event 1
Answer:
Event 2, Event 3, Event 4, Event 1
Simplify the following expression.2(0.5x - 3)2-[?]x2 – [ ]x + [ ]-
1st blank = 0.25
2nd blank = 3
3rd blank = 9
Explanation:[tex]\begin{gathered} \text{Given: (0.5x - 3)}^2 \\ \\ To\text{ simplify the expression we expand} \end{gathered}[/tex]Using distributive property:
[tex]\begin{gathered} (0.5x-3)^2\text{ = (0.5x - 3)(0.5x - 3)} \\ =\text{ 0.5x (0.5x - 3) - 3(0.5x - 3)} \\ =\text{ 0.5x(0.5x) -3(0.5x) -3(0.5x) - 3(-3)} \end{gathered}[/tex][tex]\begin{gathered} =0.25x^2\text{ - 1.5x - }1.5x\text{ + 9} \\ =0.25x^2\text{ - 3.0}x\text{ + 9} \\ =0.25x^2\text{ - 3x + 9} \\ \\ \text{first balnk = 0.25} \\ \text{second blank =3} \\ \text{third blank = 9} \end{gathered}[/tex]-1.5(x - 2) = 6. What is X equaled to
Answer:
x-2=6÷(-1.5)
x-2=-4
x=-4-2
x=-6
The composition of rigid motions T (-20,-6) •T (19,23 describes the route of a limousine in a city from its starting position. Describe the route in words. Assume that the positive y-axis points north. First the limousine drives (Type whole numbers.) block(s) east and block(s) north, and then it drives block(s) east and block(s) south.
You have the following rigid motion:
[tex]T_{<-20,-6>}T_{<19,23>}[/tex]The previous transformation means that the limousine was translated 20 units to the west and 6 units downward (south), next, the limousine was translated 19 units to the east and 23 units upward (north).
Hence, the limousine drives 20 blocks to the east and 6 blocks to south, and then it drives 19 block to the east and 23 blocks to north.
What is a solution of a system of linear equations in three variables?
Hello!
When we have a system with the same number of variables and equations, we can obtain the value for all variables.
Knowing it, the right alternative will be:
Alternative B.
In statistics, how do I find the p-value? I understand how to get the z-value. Please help! I am so confused. Thank you in advance!
SOLUTION:
Step 1:
In this question, we are meant to discuss the p-value.
1. The p-value is calculated using the sampling distribution of the test statistic under the null hypothesis, the sample data, and the type of test being done (lower-tailed test, upper-tailed test, or two-sided test).
2.
3. What is the p-value in statistics?
The p-value is a number, calculated from a statistical test, that describes how likely you are to have found a particular set of observations if the null hypothesis were true. P-values are used in hypothesis testing to help decide whether to reject the null hypothesis.
4. How do I know when the test is left-tailed, right-tailed, or two-tailed?
Left-tailed test: The critical region is in the extreme left region (tail) under the curve.
Right-tailed test: The critical region is in the extreme right region (tail) under the curve.
5. How do you know when to use a one - tailed or two - tailed test?
This is because a two-tailed test uses both the positive and negative tails of the distribution.
In other words, it tests for the possibility of positive or negative differences. A one-tailed test is appropriate if you only want to determine if there is a difference between groups in a specific direction.
6. The formulae that involves z-score:
7. The formulae that involves p -value and standard deviation: