Solution
Given the savings account, and solve for the interest:
Principal = $6,367
Interest rate = 14%
time = 4years
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]First, convert R as a percent to r as a decimal
r = R/100
r = 14/100
r = 0.14 rate per year,
Then solve the equation for A
[tex]A=P(1+\frac{r}{n})^{nt}[/tex][tex]\begin{gathered} A=6367(1+\frac{0.14}{1})^{(1)(4)} \\ A=6367(1+0.14)^4 \\ A=10753.61 \end{gathered}[/tex]A = $10,753.61
Therefore the correct answer is $10,753.61 (nearest cent)
What is 6/24 in lowest terms(I’m reporting wrong answers)
The greatest common factor of 6 and 24 is 6.
Divide the numerator and denominator by 6.
6/24 = (6/6) / (24/6) = 1/4
Five students, Stella, Victoria, Alexander, Eva, and Hunter, line up one behind theother. How many different ways can they stand in line?
Permutations formula
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]where n things are chosen r at a time.
In this case, we need to find the number of permutations of n = 5 students chosen r = 5 at a time. That is,
[tex]\begin{gathered} _5P_5=\frac{5!}{(5-5)!} \\ _5P_5=\frac{5!}{0!} \\ _5P_5=\frac{5\cdot4\cdot3\cdot2\cdot1}{1} \\ _5P_5=120 \end{gathered}[/tex]They can stand in line in 120 different ways
How do I graph y = -4x + 6 thanks!
We have that the equation represents a line in slope-intercept form:
[tex]y=mx+b\Rightarrow y=-4x+6[/tex]We have that m is the slope, in this case, m = -4, and 6 is the y-intercept (0, 6). The y-intercept is the point where the line passes through the y-axis - at this point x = 0.
Therefore, we still need another point to do the graph of the line. This point can be the x-intercept: the point where the line passes through the x-axis, and, at this point, y = 0. Then, to find it, we can proceed as follows:
y = 0
[tex]y=0\Rightarrow0=-4x+6[/tex]Subtracting 6 from both sides of the equation, we have:
[tex]-6=-4x+6-6\Rightarrow-6=-4x[/tex]Now, we can divide both sides of the equation by -4:
[tex]-\frac{6}{-4}=-\frac{4}{-4}x\Rightarrow x=\frac{6}{4}\Rightarrow x=\frac{3}{2}=1.5[/tex]Now, we have the y-intercept (0, 6) and the x-intercept (1.5, 0), and with these two points, we can graph the line. We need to remember that a line can be defined by two points.
Which system of inequalities is shown? O Ayx у 2 в ух y2 с. у.х y2 р. уки
First, we need to find the equations of the two dotted lines.
One of the lines is parallel to the x-axis and passes through the point (0, 2), then its equation is:
y = 2
The other line has a slope of 1 and intercepts the y-axis at the point (0,0). Using the slope-intercept form with m = 1 and b = 0, its equation is:
y = mx + b
y = 1*x + 0
y = x
Given that the shaded region is below both lines and the lines are not included in the solution, then we need to use a "<" sign in the inequalities. Finally, the system of inequalities is:
y < x
y < 2
In ΔHIJ, the measure of ∠J=90°, the measure of ∠I=62°, and IJ = 86 feet. Find the length of HI to the nearest tenth of a foot.
To get the angle at H:
The total angle in a triangle = 180
< H = 180 - (90+ 62)
To get the length HI, the hypotenuse
[tex]\cos \text{ 62 = }\frac{86}{x}[/tex][tex]\begin{gathered} x\text{ = }\frac{86}{\cos \text{ 62}} \\ \\ x\text{ = }\frac{86}{0.4695} \\ x\text{ = 183.185 f}eet \end{gathered}[/tex]The length HI = x = 183. 2 Feet to the nearest tenth
Which of the functions below could possibly have created this graph?O A. F(x)=x²+x+3O B. F(x)=1.9x +15x² -6O C. F(x)=-x³ + 2x²-3xO D. F(x) = − 3x²¹ +7x² +15x
Solution
Now
Looking at the given graph, It has four values for x
And Option D has four has exponentswhich implies it has four values for x
The final answer
Option DOpa
Two more than the cube root of a number
two more means add 2 , +2
cube root of a number
A number is x
cube root of x :
∛x
Answer:
∛x + 2
What is the equation of the line that passes through the point (5, 3)and has a slope of -4/5
Given:
The slope of the line
[tex]m=-\frac{4}{5}[/tex]The line passes through from the point (5,3).
Required:
Find the equation of the line.
Explanation:
The equation of the line that passes through from the point and has slope m is given by the formula as:
[tex]y-y_1=m(x-x_1)[/tex]Consider
[tex](x_1,y_1)=(5,3)[/tex]Now the equation of the line:
[tex]\begin{gathered} y-3=\frac{-4}{5}(x-5) \\ 5(y-3)=-4(x-5) \\ 5y-15=-4x+20 \\ 4x+5y=35 \end{gathered}[/tex]Final Answer:
The equation of the line passes through from point (5,3) and has a slope -4/5 is 4x + 5y = 35
A student plays the following game. He tossed three coins. If he gets exactly two heads he wins $5. If he gets exactly one head he wins $3. Otherwise, he loses $2. On the average, how much should he win or lose per play of the game?
A student plays the following game. He tossed three coins. If he gets exactly two heads he wins $5. If he gets exactly one head he wins $3. Otherwise, he loses $2. On the average, how much should he win or lose per play of the game?
we have that
If he gets exactly two heads he wins $5.
the probability is
P=2/8
If he gets exactly one head he wins $3
the probability is
P=1/8
we have that
2/8+1/8=3/8
that means, that the probaility of any other result is 1-3/8=5/8
therefore
he win or lose per play
(2/8)*$5+(1/8)*$3-(5/8)*$2=(10/8)+(3/8)-(10/8)=3/8=$0.375
the answer is
He win $0.375 per game9+7x = -5Which is the following above Addition property of equality Subtraction property of equality Simplify Division property of equality Symmetric property of equality Distributive property
Given:
[tex]9+7x=-5[/tex]To find:
The properties.
Explanation:
Using the subtraction property of equality,
[tex]\begin{gathered} 9+7x-9=-5-9 \\ 7x=-14 \end{gathered}[/tex]Using the division property of equality,
[tex]\begin{gathered} \frac{7x}{7}=-\frac{14}{7} \\ x=-2 \end{gathered}[/tex]Final answer:
The properties used are,
• The subtraction property of equality
,• The division property of equality
On January 1, 2012 Hector put his life savings of $17,229 into a savings account at Barclays, which was pain 0.9 interest at the time. Over the next year, the inflation rate averaged 1.7%. Now consider the following propositions
Answer:
what propositions?
Step-by-step explanation:
A town’s population increases at a constant rate. In 2010 the population was 56,000 . By 2012 the population had increased to 81,000 . If this trend continues, predict the population in 2016. The population will be Number in 2016.
Given: A town's population increases at a constant rate. In 2010 the population was 56,000. By 2012 the population had increased to 81,000.
Required: To predict the population in 2016.
Explanation: The population is increasing at a constant rate. In 2 years, the increase in population is-
[tex]81000-56000=25000[/tex]Thus the slope (or rate of change of population per year) is-
[tex]\frac{25000}{2}=12500[/tex]Thus, in 2016 after 6 years, the increase in population will be-
[tex]12500\times6=75000[/tex]Hence, the population in 2016 will be-
[tex]56000+75000=131000[/tex]Final Answer: The population will be 131,000 in 2016.
6. Examine the two-way frequency table below.Gold Medals Silver Medals Bronze MedalsUSA 201842Spain 2511France 192726Based on the data in the two-way frequency table, what is the probability that a randomly selected player won a bronze medal given that the player represented Spain?22.4%24.4%13.995.5%PREVIOURPREVIOUS6 ofNEXTREVIEWSALSion outINTL
From the table, we can get the total number of players that took part in the games.
See the new table below;
From the table, we got the sum of players from each country, and also the sum of medals won by each player. This gave us a total of 201 when we calculate the total medals collected or the total from all the countries. Hence, the name two-way.
From the table, the number of Spain players that won bronze is 11, hence, the probability is;
[tex]\begin{gathered} \text{Probability = }\frac{n\text{umber of required outcome}}{n\text{ umber of total possible outcomes}} \\ P(\text{Spain player with bronze)= }\frac{n\text{ umber of Spain player that won bronze}}{\text{total n umber of players}} \\ =\text{ }\frac{11}{201} \\ =0.0547 \\ \text{Taking this to percentage, we have it to be 0.0547 x 100} \\ =5.47 \\ =5.5 \end{gathered}[/tex]Therefore, the probability of selecting a Spain player that won a bronze medal at random is 5.5%
6. Analyze Marc has one dollar, one quarter, one dime, one nickel, and
one penny. He spends 35 cents. How much money does he have left?
A $0.76
B $0.96
$1.06
D $1.16
What value for x makes the following statement true?
Answer:
2
Step-by-step explanation:
we can isolate the variable by subtracting 3x from both sides
3x + 12 = 5x + 8
-3x -3x
12 = 2x + 8
and then subtracting 8 from both sides
12 = 2x + 8
-8 -8
4 = 2x
then we divide by 2 on both sides
4 = 2x
÷2 ÷2
2 = x
flip the equation to get:
x=2
checking the solution by plugging in 2 in place of x:
(3 * 2) + 12 = (5 * 2) + 8
6 + 12 = 10 + 8
18 = 18
since the equation is true,
the solution x = 2 is correct.
divide decimals by decimals 033 divided by 688
The given numbers are 0.33 divided by 6.88
[tex]\frac{0.33}{6.88}=0.0479[/tex]Answer : 0.0479
AT&T is having a sale on all cell phones. They will give you a loan to pay for the phone. Your phone costs $899 How much will you pay for the phone if they charge you 4.5% interest, and it will take you 24 months to pay it off.
-How do you do this equation?
Answer:
Its a scam AT&T has no such sale going on right now.
Step-by-step explanation:
Name the rotation that maps the black triangle onto the red triangle. Explain how you know(See picture below)
We would compare the coordinates of corresponding vertices on the red and black triangles. The vertex at the top of the black triangle and the vertex at the bottom of the red triangle correspond to each other. We would compare them.
For black triangle, coordinate is (1, - 3)
For red triangle, coordinate is (- 1, 3)
If a vertex with coordinate, (x, y) is rotated 180 degrees counterclockwise about the origin, the new coordinate is (- x, - y). By rotating (1, - 3) 180 degrees counterclockwise, it becomes (- 1, - - 3) = (- 1, 3). This corresponds to the coordinate of the corresponding vertex of the red triangle. Thus, the rotation that maps the black triangle onto the red triangle is 180 degrees counterclockwise rotation about the origin
What is the inverse equation for h(x) = 2log(x-3) ?
Given the function:
[tex]h(x)=2log\left(x-3\right)[/tex]To find its inverse:
[tex]\begin{gathered} y=2log\left(x-3\right) \\ x=2log\left(y-3\right) \end{gathered}[/tex]solving for y:
[tex]\frac{x}{2}=log(y-3)[/tex][tex]\begin{gathered} 10^{\frac{x}{2}}=y-3 \\ \\ 10^{\frac{x}{2}}+3=y \end{gathered}[/tex]ANSWER
[tex]h^^{-1}(x)=10^{\frac{x}{2}}+3[/tex]Which definition best describes a perpendicular bisector?Required to answer. Single choice. A line segment from a vertex of the triangles to the opposite side that divides an angle into two congruent adjacent angles. A line segment from a vertex of the triangles to the midpoint of the opposite side.A line segment from any vertex perpendicular to the line containing the opposite side of a triangle.A line that is perpendicular to a side of the triangle and also bisects that side of the triangle (it goes through the midpoint).
Answer:
A line that is perpendicular to a side of the triangle and also bisects that side of the triangle (it goes through the midpoint)
Step-by-step explanation:
A perpendicular bisector is a line segment perpendicular to and passing through the midpoint, dividing it into two equal segments and creating right angles.
60 inches =___ feet please and thank you for your help
We know that:
[tex]1ft=12in\text{.}[/tex]Then:
[tex]1in=\frac{1}{12}ft\text{.}[/tex]Therefore:
[tex]60in=60\cdot(\frac{1}{12}ft)\text{.}[/tex]Simplifying the above result we get:
[tex]60\cdot(\frac{1}{12}ft)=\frac{60}{12}ft=5ft\text{.}[/tex]Answer:
[tex]60\text{ inches=5 feet.}[/tex]A line passes through the points (-21, -22) and (-14, -16). Find this line's equation in point-slope form. Using the point (-21, -22), this line's point-slope form equation is: Using the point (-14, -16), this line's point-slope form equation is:the point slope form has to be simplified
Answer:
Using point (-21, -22): y = (6/7)x - 4
Using point (-14, -16): y = (6/7)x - 4
Explanation:
The point-slope form of a line's equation is:
[tex]y-y_1=m(x-x_1)[/tex]Where (x₁, y₁) is a point in the line and m is the slope.
The slope of a line can be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x₁, y₁) and (x₂, y₂) are two points in the line. So, replacing (x₁, y₁) by (-21, -22) and (x₂, y₂) by (-14, -16), we get that the slope of the line is:
[tex]m=\frac{-16-(-22)}{-14-(-21)}=\frac{-16+22}{-14+21}=\frac{6}{7}[/tex]Now, using the point (-21, -22), we get that the equation of the line is:
[tex]\begin{gathered} y-(-22)=\frac{6}{7}(x-(-21)) \\ y+22=\frac{6}{7}(x+21) \end{gathered}[/tex]Then, we can simplify the equation as:
[tex]\begin{gathered} y+22=\frac{6}{7}(x)+\frac{6}{7}(21) \\ y+22=\frac{6}{7}x+18 \\ y+22-22=\frac{6}{7}x+18-22 \\ y=\frac{6}{7}x-4 \end{gathered}[/tex]On the other hand, using the point (-14, -16), the equation of the line is:
[tex]\begin{gathered} y-(-16)=\frac{6}{7}(x-(-14)) \\ y+16=\frac{6}{7}(x+14) \end{gathered}[/tex]Simplifying, we get:
[tex]\begin{gathered} y+16=\frac{6}{7}x+\frac{6}{7}(14) \\ y+16=\frac{6}{7}x+12 \\ y+16-16=\frac{6}{7}x+12-16 \\ y=\frac{6}{7}x-4 \end{gathered}[/tex]So, the answers are:
Using point (-21, -22): y = (6/7)x - 4
Using point (-14, -16): y = (6/7)x - 4
1 Decide whether the graph shown below is a function or not.
According to the vertical line test, a curve represents a function only if the vertical line drawn at any point intersects the curve atmost once.
Observe that the given curve fails to satisfy this condition.
This concludes that the given curve does not represent a function.
Jessica states -79 will make the inequality true.-80 > ? _> -89O FactO Fib
-80>-79>-89
To answer this we have to set a number line.
As we can see in the number line , if we move from left to right, -79 is higher than -80 (-79>-80)
So, the statement is false
Lily has 30 Marvel Funko Pops. The number of Marvel Funky Pops in her collection is only 60% of hes total Funko Pops. How many total Funko Pops are in her collection?
Lily has 30 Marvel Pops, they are 60% of the total Pops
How many in total ?
We can say that the realation between 30 an the total is the same relation between 60% and 100%, so we can write:
30/x = 60/100
[tex]\frac{30}{x}=\frac{60}{100}[/tex]Where x is the total number of Pops
Solving this for x:
x = 30(100)/60 = 3000/60 = 50
[tex]x\text{ = }\frac{\text{30(100)}}{60}=\frac{3000}{60}=50[/tex]Answer:
Number of total Funlo Pops in her collection: 50
hello I don't you can help me with this please
Approximately 10 hours
1) Gathering the data
Initial temperature: 79º F
0.8 each hour
84º
2) We can write an exponential function to find that out. So let's do it this way:
[tex]\begin{gathered} T_f=T_0(1+0.8)^h \\ 84=79(1.8)^h \\ \frac{84}{79}=\frac{79(1.8)^h}{79} \\ 1.06=1.8^h \\ \log _{10}1.06=\log _{10}1.8^h \\ h\log _{10}1.8=\log _{10}1.06 \\ h=10.087 \end{gathered}[/tex]Notice that since the temperature is rising, we have to add one to the factor, otherwise, it will decrease it.
Now let's convert that decimal number so that we may have a better approximation:
10 hours and 4 minutes
Solve the system of equations x + 2y = 0 Solve the equation for x.
Given the equation :
[tex]x+2y=0[/tex]Solve the equation for x:
[tex]x=-2y[/tex]Final Answer:
x = -2yIn-depth explanation:
Hi! The question is asking us to solve the equation x + 2y = 0 for x.
________________________
To Solve
Rearrange the equation for x.
________________________
All we need to do is subtract '2y' from both sides.
[tex]\implies\sf{x+2y=0}[/tex]
[tex]\implies\sf{x=0-2y}[/tex]
[tex]\implies\sf{x=-2y}[/tex]
∴ Equation: x = -2y
_______________________
A metallurgist has One alloy containing 49% copper and another containing 62% copper. How many pounds of each alloy must he used to make 51 pounds of a third alloy containing 56% copper?
Explanation
Step 1
a)
Let
x represents the pounds of the 49 % copper alloy
y represents the pounds of the 62 % copper alloy
then,
if we want to make a 51 pounds of a new alloy,
[tex]x+y=51\rightarrow equation(1)[/tex]b)this new allo contains 56% of copper , so
total of cooper = pounds of alloy * percentage
[tex]\begin{gathered} 0.49x+0.62y=51\cdot0.56 \\ 0.49x+0.62y=28.56\rightarrow equation\text{ (2)} \end{gathered}[/tex]Step 2
Solve the equations
a) isolate x in equation (1) and replace in equation(2)
[tex]\begin{gathered} x+y=51\rightarrow equation(1) \\ \text{subtract y on both sides} \\ x+y-y=51-y \\ x=51-y\rightarrow equation(3) \end{gathered}[/tex]Now, replace in equation (2)
[tex]\begin{gathered} 0.49x+0.62y=28.56\rightarrow equation\text{ (2)} \\ 0.49(51-y)+0.62y=28.56 \\ 24.99-0.49y+0.62y=28.56 \\ \text{add like terms } \\ 24.99+0.13y=28.56 \\ \text{subtract 24.99 on both sides} \\ 24.99+0.13y-24.99=28.56-24.99 \\ 0.13y=3.57 \\ \text{divide both sides by 0.13} \\ \frac{0.13y}{0.13}=\frac{3.57}{0.13} \\ y=27.46 \\ \end{gathered}[/tex]now, replace the y value into equation (3) to get x
[tex]\begin{gathered} x=51-y\rightarrow equation(3) \\ x=51-y \\ x=51-27.46 \\ x=23.54 \\ \end{gathered}[/tex]therefore, the answer is
23.54 lb of the 49% copper alloy
27.46 lb of the 62% copper alloy
If you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a 7 or 5? (Your answer must be in the form of a reduced fraction.)
In a deckk of 52 cards there are four 5 and four 7, so the probability to select randomly a 5 or a 7 is:
[tex]\begin{gathered} \text{prob}=\frac{success\text{ cases}}{total\text{ cases}} \\ \text{prob}=\frac{8}{52}=\frac{2}{13} \end{gathered}[/tex]The probability is 2/13
QUESTION IS IN IMAGE!! DONT SHOW WORK JUST THE ANSWER UNLESS YOU NEED TO
Given:
m∠SPQ = 113 degrees
Let's find the measure of angle RQS, m∠RQS.
By applying the angle-arc relationship, we have:
m∠SPQ = measure of arc SQ = 113 degrees.
Since RQ is the diameter, measure of arc RQ = 180 degrees.
Now, let's find the measure of arc RS:
measure of arc RS = 360 - arc SQ - arc RQ
measure of arc RS = 360 - 113 - 180 = 67 degrees.
To find the m∠RQS, apply angle-arc relationship:
[tex]\begin{gathered} m∠RQS=\frac{1}{2}arcRS \\ \\ m∠RQS=\frac{1}{2}*67 \\ \\ m∠RQS=33.5^o \end{gathered}[/tex]Therefore, the measure of angle RQS is 33.5 degrees.
ANSWER:
m∠RQS = 33.5°