Amount = P ( 1 + R ) ^n
= 37,500 ( 1 + 4.3% ) ^6
= 37, 500 ( 1. 043 ) ^6
= $ 48, 276. 65
What is the image of (-6, 5) after areflection over the line y = x?
SOLUTION
We want to find the image of (-6, 5) after a reflection over the line y = x
When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places.
So we have
[tex]\begin{gathered} y=x\rightarrow(y,x) \\ (-6,5)\rightarrow(5,-6) \end{gathered}[/tex]Hence the answer is (5, -6)
Otto spent 3/4 of the money he had saved on a new video game. If the video game cost $48, how much money did he have before he bought the game? (Just write the number)He spent $
Given:
Otto spent 3/4 of the money.
Cost of game $48.
So the money before he bought:
[tex]\begin{gathered} =\frac{3}{4}\times48 \\ =\frac{3\times48}{4} \\ =3\times12 \\ =36 \end{gathered}[/tex]The perimeter of a rectangle is 24 inches. The length is 2 inches. Use the numbers below to complete an equation to solve for the width, W. Numbers may be used more than once, just once, or not at all. Numbers ( 8, 24, 12, 4, 10, 2)
You have the following infornation about the dimensions of a rectangle:
- P: perimeter = 24 in
- l: length = 2 in
In order to determine the width of the rectangle, you take into account the formula for the perimeter of a rectangle, which is given by:
P = 2w + 2l
where w is the width of the retangle and l is the length. From the previous equation you can solve for w, just as follow:
P = 2w + 2l subtract 2l both sides
P - 2l = 2w divide between 2 both sides
(P - 2l)/2 = w
You replace the values of h and w into the previoues expression:
w = (24 - 2(2))/2 = 20/2 = 10
Hence, the width of the rectangle is w = 10 in
how do I find the correct answer.(put an in a small paragraph please.)
For the right traiangle, it is given that
[tex]undefined[/tex]Which of the following choices best describes the expression:(2x + 1) - (x + 3/2)A: equivalent to 1/2x - 1B: equivalent to x - 1/2 C: not equivalent to 1/2x - 1 or x - 1/2
In this case the answer is very simple. .
We need to apply algebraic rules to solve the expression.
(2x + 1) - (x + 3/2)
2x + 1 - x - 3/2
[tex]2x\text{ - x + 1 - }\frac{3}{2}\text{ = x + }\frac{2-3}{2}\text{ = x -}\frac{1}{2}[/tex]The solution is:
B: x - 1/2
solve the system of linear equations by graphing y= -x+7y=x+1
thus the answer is x=3, y=4
I need help now please the question is number 12??
12) This definition correspond to a conditional probability, where we express the probability of an event given another event.
Then, we can write:
A conditional probability contains a condition that may limit the sample space for an even.
2y=21 6x6y 12.) 3x 4x - 4y=0 O 13-7x+4y=24XE VERE 14 Hy2y = -19 X-212.8 Byty24 Y24. - y Solve each system by elimination. *** 15) 8x-6y=-20 14) AX- 2 -24-2y-10 3 0-6 2120) YaZ enho 23 16) 6x-129=242 -16x + y = 30 16x -1240 - 16X-1294 30 by=-TB * 8%=-20467 -x-by=4 == 끓 bylo 6*-12-24 -62-36=24 6x+1231-12 CM-1224 -42-7=21 6224-12 bts-12k-36)-243247 t-shay-246 18) -24 - 8x= 12 y 7. 5 18
The given sets of equations are,
[tex]\begin{gathered} 5y-4x-9=0\ldots\ldots(1) \\ 9y+11x+20=0\ldots\text{.}\mathrm{}(2) \end{gathered}[/tex]Multiplying equation (1) by 11 and equation (2) by 4 and adding both the equations,
[tex]\begin{gathered} 55y-44x-99+(36y+44x+80)=0 \\ 91y-19=0 \\ y=\frac{19}{91} \end{gathered}[/tex]Substituting the value of y in equation (1),
what is the slope x-5y=3
Explanation
Step 1
if you have an equation of a line isolate y to transform it into slope
Suppose that the weight in pounds of an airplane is a linear function of the amount of fuel in gallons and it’s tank. When carrying 16 gallons of fuel the airplane Waze 2188 pounds. When carrying 48 gallons of fuel it weighs 2364 pounds. How much does the airplane way if it is carrying 64 gallons of fuel.
Data:
• ( 16, 2188 )
,• ( 48, 2364 )
,• Linear function
[tex]y=mx+b[/tex]Procedure:
0. Building up the linear equation: finding the slope (,m,)
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2364-2188}{48-16}[/tex][tex]m=\frac{11}{2}[/tex]2. Finding the intersection with y-axis ( b ): choosing the first point given to replace the values in the linear function.
[tex]y=mx+b[/tex][tex]2188=\frac{11}{2}\cdot16+b[/tex][tex]2188=88+b[/tex][tex]88+b=2188[/tex][tex]b=2188-88[/tex][tex]b=2100[/tex]3. Obtaining the linear function of the given problem:
[tex]y=\frac{11}{2}x+2100[/tex]4. Finding the weight of the airplane when it is carrying 64 gallons of fuel.
[tex]y=\frac{11}{2}\cdot64+2100[/tex][tex]y=2452[/tex]Answer: 2452 pounds
The length of each leg of an isosceles triangle is 5 centimeters more than twice the length of the base. If the perimeter of this isosceles triangle is 95 centimeters, what is the length of the base?
Let's draw the situation to understand it better:
An isosceles triangle has two equal sides.
Let x be the length of the base
The perimeter is the add up of all sides:
Solve for x.
[tex]\begin{gathered} (5+2x)+(5+2x)+x=95 \\ 5x+10=95 \\ 5x=95-10 \\ 5x=85 \\ x=\frac{85}{5} \\ x=17 \end{gathered}[/tex]The length of the base is 17 centimeters.
Just want to make sure that my work is correct
The image below shows the information provided in the question:
Therefore, the triangle to be solved is drawn out to be:
Using the Tangent Trigonometric ratio, we have:
[tex]\tan \theta=\frac{\text{opp}}{\text{adj}}[/tex]Therefore, we have:
[tex]\begin{gathered} \tan \theta=\frac{2455}{700} \\ \theta=\tan ^{-1}(\frac{2455}{700}) \\ \theta=1.2930\text{ radians} \end{gathered}[/tex]The angle of elevation is 1.2930 radians.
Use the vertex formula to find the vertex of the quadratic function f(x) = – x² + 6x - 10.The vertex is(Type an ordered pair. Simplify your answer.)
We have the equation of the quadratic function:
[tex]-x^2+6x-10[/tex]We have to use the vertex formula to calculate the vertex. If h is the x-coordinate of the vertex, we can calculate it as:
[tex]h=\frac{-b}{2a}=\frac{-6}{2\cdot(-1)}=\frac{-6}{-2}=3[/tex]Then, we can calculate the y-coordinate replacing h in the equation:
[tex]\begin{gathered} y_v=-h^2+6h-10=-3^2+6(3)-10 \\ y_v=-9+18-10=-1 \end{gathered}[/tex]The vertex has coordinates (x,y) = (3,-1).
Question 27 (1 point)(01.05)What is the slope-intercept form equation of the line that passes through (5, 7) and (8, 22)? (1 point)Oay = -5x + 18Oby = 5x - 18cy = -5x - 18Ody = 5x + 18
The slope-intercept form of a line is expressed as follows;
[tex]y=mx+b[/tex]Where;
[tex]\begin{gathered} m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]To begin, we shall calculate the slope as shown below;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Using the two points given, we have;
[tex]\begin{gathered} (x_1,y_1)\Rightarrow(5,7) \\ (x_2,y_2)\Rightarrow(8,22) \end{gathered}[/tex]Therefore;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{22-7}{8-5} \\ m=\frac{15}{3} \\ m=5 \end{gathered}[/tex]To calculate the y-intercept, we shall insert the value of m into the equation, y = mx + b. We shall use the first point which is (5, 7).
Note that if we use the second point (that is 8, 22) the value of the y-intercept would be the same.
Hence we have;
[tex]\begin{gathered} x=5, \\ y=7 \\ m=5 \\ y=mx+b\text{ now becomes;} \\ 7=5(5)+b \\ 7=25+b \end{gathered}[/tex]Subtract 25 from both sides;
[tex]\begin{gathered} -18=b \\ b=-18 \end{gathered}[/tex]Now that we have the values of m and b, (the slope and the y-intercept), the equation becomes;
[tex]\begin{gathered} y=mx+b \\ y=5x+(-18) \\ y=5x-18 \end{gathered}[/tex]ANSWER:
The correct answer is option (b);
[tex]y=5x-18[/tex]what us the m or slope of this problem 9x-5y = 4
the slope = m = 9/5
Explanation:
equation: 9x-5y = 4
The above equation is a linear function.
It is in the form: y = mx + c
m =slope
c = intercept
Rewritting the given equation in the linear form:
9x = 4 + 5y
9x - 4 = 5y
5y = 9x - 4
divide through by 5:
y = (9x -4)/5
y = 9x/5 - 4/5
comparing the above equation wwith the linear form:
mx = x(9/5)
m = 9/5
c = -4/5
Hence, the slope = m = 9/5
It takes Andre 16 minutes to walk to school which is 80% as long as KarenHow long does it take Karen to walk to school?
0.8x=16
then x=16/0.8=20
therefore Karen takes 20 minutes to walk to school
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 105.2-cm and a standard deviation of 1.7-cm. For shipment, 26 steel rods are bundled together.Find the probability that the average length of a randomly selected bundle of steel rods is less than 104.3-cm. P(M < 104.3-cm) =
We know the population distribution for the length of the rods: normal distribution with mean 105.2 cm and a standard deviation 1.7 cm.
In this case, we have a sample of 26 units, so we have to adjust the standard error to this sample size.
We have to calculate the probability that the sample mean is less than 104.3 cm.
We start by calculating the z-score for this sample mean value:
[tex]\begin{gathered} z=\frac{X-\mu}{\frac{\sigma}{\sqrt{n}}} \\ \\ z=\frac{104.3-105.2}{\frac{1.7}{\sqrt{26}}}\approx\frac{-0.9}{0.3334}\approx-2.7 \end{gathered}[/tex]We can now calculate the probability by looking at the standard normal distribution:
[tex]P(M<104.3)=P(z<-2.7)=0.00347[/tex]Answer: P(M < 104.3 cm) = 0.00347
Rewrite the expression in terms of the given angle's reference angle; then evaluate the result. Write the exact answer. Do not round.sin1113
Rewrite the angle inside the expression as:
[tex]\frac{11\pi}{3}=4\pi-\frac{\pi}{3}[/tex]Apply sine function on both sides and use the identity sin(A-B) = sin A cos B - cos A sin B.
[tex]\begin{gathered} \sin (\frac{11\pi}{3})=\sin (4\pi-\frac{\pi}{3}) \\ =\sin 4\pi\cos \frac{\pi}{3}-\cos 4\pi\sin \frac{\pi}{3} \\ =0\cdot\cos \frac{\pi}{3}-1\cdot\frac{\sqrt[]{3}}{2} \\ =-\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]How many significant figures are present in the measurement 0.003m?
Given the measurement: 0.003 m
Following the rules:
• non-zero digits are always significant.
,• zeroes that come after the decimal point are only significant if the number is greater than 1 or if they are sandwiched between two non-zero digits for numbers that are smaller than 1.
,• if a zero is leading a number, before or after the decimal, it is not significant.
Hence:
ANSWER
number of significant figures = 1.
need help with this with all work shown and a summary because it helps me learn better
Answer: a = 7b
Explanation:
If a varies directly as b, the the equation representing this relationship is expressed as
a = kb
where
k is the constant of proportionality.
From the information given, when a = 49, b = 7
Substituting a = 49 and b = 7 into the equation, it becomes
49 = 7k
Dividing both sides by 7,
7k/7 = 49/7
k = 7
By substituting k = 7 into the equation, the equation relating a and b is
a = 7b
A store is selling pretzels for $1.35each. If the store sells 5 pretzels, howmuch money will they receive?
Given:
Pretzels for $1.35 each
Sell 5 pretzels
Find-:
How much money will they receive
Explanation-:
If one Pretzels for $1.35
So,
for 5 pretzel
[tex]\begin{gathered} =1.35\times5 \\ \\ =6.75 \end{gathered}[/tex]So, the store receives $6.75.
Find the value of r so that the line that passes through them has the given slope. (3,5)(-2,r) slope = -1
The slope is given by
[tex]-1=\frac{r-5}{-2-3}[/tex]then, we have to solve for r
[tex]\begin{gathered} -1=\frac{r-5}{-5} \\ 5=r-5 \\ r=10 \end{gathered}[/tex]Then r=10
Find the area of the smaller sector.Round to the nearest tenth.130°8.02 mArea = [? ]m?
First, find the area of the whole circle;
Area= π * radius^2 = π* (8.02)^2 = 202.07 m^2
Then, since the sector is 130° out of 360°
202.07 x (130/360) = 72.97 m^2
Solve for x. -0.3x + 7 = 0.2x + 3
Solve the equation for x, this way:
[tex]\begin{gathered} -0.3x+7=0.2x+3 \\ -0.3x-0.2x=3-7 \\ -0.5x=-4 \\ x=\frac{-4}{-0.5} \\ x=8 \end{gathered}[/tex]x has a value of 8.
Henry keeps track of the number of people inside a music hall to attend a concert by looking at the number of scanned tickets. He plotted the data on the graph below, where x=0x=0 represents the time at 6 p.m., then drew a line of best fit. If we extended the line, what would the value of yy tell us when x=4x=4?
Given that he uses the graph to keep track of the number of people inside the music hall by looking at the number of scanned tickets.
• Where:
x = 0 represents the time 6 pm
If the line is extended, let's determine what the value of y when x = 4 would tell us
Since when x = 0, the time is 6 pm.
When x = 4, the time will be:
6 pm + 4 = 10 pm
The line of best fit is always used for the prediction of data.
Therefore, if the line is extended, the value of y when x = 4 will tell us a prediction of how many people will be in the music hall at 10 o'clock.
ANSWER:
A. A prediction of how many people will be in the music hall at 10 o'clock.
Find the domain and range of this relation. is it a function?(0,0),(1,1),(2,4),(3,9),(4,-6)
Data: (x,y)
(0,0),(1,1),(2,4),(3,9),(4,-6)
Domain: All the x-values in the relation
Range: All the y-values in the relation
A function is a relation where each input (x-value) has only one output (y-value)
For the given relation:
Domain:
[tex]\lbrace0,1,2,3,4\rbrace[/tex]Range:
[tex]\lbrace0,1,4,9,-6\rbrace[/tex]As each values of x has one corresponding value of y, it is a functionIf a customer is sold an item for $225 and the item was marked up 80%, what was the original cost of the item?
The item was sold for $225 and the original cost of the item is unknown. The mark up of the item is 80%. The original cost can be solved below
let
cost price = x
[tex]\begin{gathered} \text{selling price=\$225} \\ \text{ cost price=?} \\ \text{ mark up=80\%}=\frac{80}{100} \\ profit=\frac{80}{100}\times x=0.8x \\ 225=0.8x+x \\ 225=1.8x \\ x=\frac{225}{1.8} \\ x=\text{ \$125} \end{gathered}[/tex]Use the graph of f(x)=x^2 to write an equation for the function represented by the graph.
The graph of y=x² is plotted and attached below.
We observe that the given graph is shifted horizontally downwards in 3 Units as shown below:
Therefore, the function represented by the graph is:
[tex]y=x^2-3[/tex]iss compoundd interestt greaterr thann simplee interestt
Answer
If the period for the calculation of interest is 1 year, then compound interest and simple interest are same, otherwise compound interest is greater once the period of calculation is more than one.
Explanation
We can prove this using an example below.
Given principal =$2000, interest rate =5% , time = 2 years, we would have
[tex]S.I=\frac{PRT}{100}=\frac{2000\times5\times2}{100}=\text{ \$}200[/tex]If we find the compound interest for two years, we would have;
[tex]\begin{gathered} A=P\left(1+\frac{r}{n}\right)^{nt} \\ A=2,000.00\left(1+\frac{0.05}{1}\right)^{1\times2} \\ A=2,000.00\left(1+0.05\right)^2 \\ A=$ 2,205.00 $ \end{gathered}[/tex]The interest becomes
[tex]C.I=A-P=2205-2000=205[/tex]By comparison, we can see that compound interest is greater than simple interest.
You and your classmates create 16 paintings to sell at the PTA auction to raise money for your school. In order to pay for the materials you bought to make the paintings, you need to sell each of the paintings for $1.75. When transporting the paintings to the auction, one of your parents accidentally drops two of the paintings in the street and they are run over by a garbage truck. What is the new minimum price you need to set for the remaining paintings in order to pay for the materials?
Given that there are 16 paintings to sell at a PTA auction.
In order to pay for the materials, he needs to sell each of the paintings for $1.75 each. So, the cost of material is
[tex]1.75\times16=28[/tex]The total cost of the material is $28.
Two of the paintings are damaged during transportation. So he needs to sell only 14 paintings to get $28.
So, he needs to sell each of the paintings at:
[tex]\frac{28}{14}=2[/tex]Thus, the new minimum price he needs to set for the remaining paintings in order top