The most appropriate choice for simple interest will be given by-'
Amount of money Josh have at the end of 5 years = $330
Fourth option is correct
What is simple interest?
Simple interest ( SI) is the interest earned on a certain principal at a certain rate over a certain period of time,
If P is the principal, rate is r %, time is t years,
SI = [tex]\frac{p \times r \times t}{100}[/tex]
Adding Principal and simple interest will give the amount
Here,
Principal deposited by Josh= $300
Rate of interest = 2%
Time = 5 years
Simple interest = [tex]\frac{300 \times 2 \times 5}{100}\\[/tex]
= $30
Amount of money Josh have at the end of 5 years = $(300 + 30)
= $330
Fourth option is correct
To learn more about simple interest, refer to the link:
https://brainly.com/question/25793394
#SPJ9
14. Mason has 2 quarters, and he needs 50 cents more to pay the turnpike toll. There are 5 dimes, 6 quarters, and 10 nickels in his glove compartment. If he reaches in and selects two coins at random without replacing the first one, find the probability of choosing two quarters. 99
we have in total of coins are
5+6+10=21
For the first coin, we have the probability of 6/21
Then we only left 5 quarters and 20 coins in total, the next probability will be 5/20
the total probability is
[tex]\frac{6}{21}\cdot\frac{5}{20}=\frac{30}{420}=\frac{1}{14}[/tex]the answer is 1/14
What is the solution to the equation below? 3* 3 O A. X= 12 OB. X= 18 C. X= 6 O D. x=9
Here, we want to solve the given equation
What we have to do here is to square both sides of the equation
We have this as follows;
[tex]\begin{gathered} \frac{\sqrt[]{3x}}{\sqrt[]{x-6}\text{ }}\text{ = 3} \\ \text{Squaring both sides will remove the roots on the left and we have;} \\ \frac{3x}{x-6}\text{ = }3^2 \\ \\ 3x\text{ = 9(x-6)} \\ 3x\text{ = }9x-54 \\ 9x-3x\text{ = 54} \\ 6x\text{ = 54} \\ \text{ x= }\frac{54}{6} \\ x\text{ = 9} \end{gathered}[/tex]Vectors and Complex numbers Part AYou drive 30 miles due east in a half hour. Then, you turn left and drive 30 miles north in 1 hour. What are your average speed andvelocity, and what are the rectangular and polar coordinates of your position?Part BYou have already travelled 30 miles east and then 30 miles north. To get back to the start, you travel 30 miles west in 1 hour and then 30 minutes south in a half hour. What are your average speed and average velocity for the whole rally?
Part A.
30 miles east in half hour next
turn left and drive 30 miles north in 1 hour
The average speed is given by
the total distance divided by the total amount of time.
In this case,
[tex]\begin{gathered} \text{average velocity=}\frac{30+30}{1.5+1} \\ \text{average velocity=}\frac{60}{2.5} \\ \text{average velocity=}24\text{ }\frac{miles}{hour} \end{gathered}[/tex]Now, the position in rectangular coordinates is (30,30)
In polar coordinates, we must find the angle theta and the lenght r.
This can be given as
[tex]\begin{gathered} r=\sqrt[]{x^2+y^2} \\ \end{gathered}[/tex]In our case x=30 and y=30, hence
[tex]\begin{gathered} r=\sqrt[]{30^2+30^2} \\ r=\sqrt[]{2\cdot30^2} \\ r=30\sqrt[]{2} \end{gathered}[/tex]On the other hand, angle theta is given by,
[tex]\theta=tan^{-1}\frac{y}{x}[/tex]hence,
[tex]\begin{gathered} \theta=tan^{-1}\frac{30}{30} \\ \theta=tan^{-1}1 \\ hence, \\ \theta=45\text{ degr}ees \end{gathered}[/tex]Therefore, in polar coordinates, point (30,30) is given by
[tex](r,\theta)=(30\sqrt[]{2},45)[/tex]Part B
Until now, we drove 30 miles east, next 30 miles north. Now, we must drive 30 miles west and 30 miles south.
Hence, we will drive 30+30+30+30=4*30=120 miles. Therefore, the average velocity is
[tex]\begin{gathered} \text{average velocity=}\frac{120}{1.5+1+1.5+1.5} \\ \text{average velocity=}\frac{120}{5.5} \\ \text{average velocity=}21.81\text{ }\frac{miles}{hour} \end{gathered}[/tex]Part A. Velocity.
Velocity is a vector. In this case, we must add to vectors:
vector V1 is given by
[tex]\begin{gathered} v_1=(\frac{30}{1.5},0) \\ \text{which is equal to } \\ v_1=(20,0) \end{gathered}[/tex]Vector V2 is given by
[tex]\begin{gathered} v_2=(0,\frac{30}{1}) \\ v_2=(0,30) \end{gathered}[/tex]then, resultant vector velocity is
[tex]\begin{gathered} v=v_1+v_2 \\ v=(20,0)+(0,30) \\ v=(20,30) \end{gathered}[/tex]find the x and the y intercept there should be 2 ordered pairs for the each solution
We have the line in standard form:
[tex]4x+5y=-20[/tex]We have to find the 2 intercepts.
The y-intercept correspond to the value of the line when x=0, so we can find the value of y that correspond to x=0 replacing x in the equation and solving for y:
[tex]\begin{gathered} 4x+5y=-20 \\ 4(0)+5y=-20 \\ 5y=-20 \\ y=-\frac{20}{5} \\ y=-4 \end{gathered}[/tex]Then, the ordered pair for the y-intercept is (0,-4).
In the case of the x-intercept the concept is equivalent but the coordinate that has a value of 0 is y. So we will replace y with 0 in the equation and solve for x:
[tex]\begin{gathered} 4x+5(0)=-20 \\ 4x=-20 \\ x=-\frac{20}{4} \\ x=-5 \end{gathered}[/tex]Then, the ordered pair for the x-intercept is (-5,0).
We can graph the line and its intercepts as:
Answer:
X-intercept: (-5, 0)
Y-intercept: (0,-4)
A coin is flipped 2,500 times. It lands on heads 1,223 times and tails 1,277 times. A die was rolled 60 times. It landed on one—11 times, two—9 times, four—12 times, five—12 times, and six—8 times. What is the empirical probability of flipping heads on the coin AND rolling a four on the die?
The empirical probability of flipping heads on the coin AND rolling a four on the die is 0.623.
What is probability?
When we do not really know how something will turn forth, we can talk about the probability of one outcome or the likelihood of several.
Given that,
the coin is flipped = 2,500 times.
heads =1,223 times and tails= 1,277 times.
and
A die was rolled = 60 times
one—11 times, two—9 times, four—12 times, five—12 times, and six—8 times.
The empirical probability of flipping heads on the coin AND rolling a four on the die = (1223/2500) + (8/60)
=0.623
The empirical probability of flipping heads on the coin AND rolling a four on the die is 0.623.
Learn more about probability here:
https://brainly.com/question/24756209
#SPJ1
You select a family with three children. If M represents a male child and F a female child, the set of equally likely outcomes for the children's genders is shown below. Find the probability of selecting a family with at least three male children.
{MMM, MMF, MFM, MFF,
The probability to select a family with atleast three male children is only 1/8.
What is Probability?A probability is a number that reflects the chance or likelihood that a particular event will occur.
First, you have the sample of the children.
We know that the family with 3 children, can have the sample space as given {MMM,MMF,MFM,FMM,FFM,FMF, FFF}
MMM: 3 Males
MMF: 2 males, 1 female
MFF: 1 male, 2 females
MFM: 2 males, 1 female (different order)
FMM: 1 female, 2 males
FFM: 2 females, 1 male
FMF: 2 females, 1 male
FFF: 3 females
If we count all of these possibilities, we have 8 possible cases of family with the childrens.
In only one of them, we have atleast three males , which is the first one
Therefore, the probability to select a family with atleast three male children is only 1/8.
To learn more on Probability click:
https://brainly.com/question/16722133
#SPJ1
Each day, Deshaun earns a fixed wage plus extra money for every hour of overtime he works. The graph shows his total pay (in dollars) versus the amount of overtime ( in hours) that he works.
Hello!
So, for question (a)
The point that represents Deshaun's salary without working overtime is that in which x=0, being x the overtime hours
In this case, when x=0, y=60, being y his total pay
Regarding question (b)
Notice that as the overtime hours increased so the total day does. Then, the function is increasing!
Moreover, this is a line, so we can look for its equation:
Notice that when he works 1 extra hour he receives 90 dollars as total pay, i.e., x=1 y=90
We already have 2 points! We can w
order from least to greatest 2/4, 25%, 0.2
To compare the three numbers we can pass to decimal form all of them:
[tex]\begin{gathered} \frac{2}{4}=\frac{1}{2}=0.5 \\ \text{25\%}=\frac{25}{100}=\frac{25}{4\cdot25}=\frac{1}{4}=0.25 \\ So,\text{ the order from }least\text{ to greatest is:} \\ 0.2,\text{ 25\%, }\frac{2}{4} \end{gathered}[/tex]thanks for the help!!!
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
cos x [tex]cos^{-1}[/tex] = 1
The value of [tex]cos(cos^{-1} \frac{5}{13} + cos^{-1}\frac{7}{25})[/tex] is 166/195.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
[tex]cos(cos^{-1} \frac{5}{13} + cos^{-1}\frac{7}{25})[/tex]
We will distribute cos with the expression.
[ cos x [tex]cos^{-1}[/tex] = 1 ]
So,
= cos x [tex]cos^{-1}[/tex] (5/13) + cos x [tex]cos^{-1}[/tex] (7/15)
= 5/13 + 7/15
= (75 + 91) / 195
= 166/195
Thus,
The value of [tex]cos(cos^{-1} \frac{5}{13} + cos^{-1}\frac{7}{25})[/tex] is 166/195.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
jean rents an electric sander for $2.50 per hour plus $6.00 for the sand paper. what is the cost of renting the sander for 10 hours ? use the function c = 2.5h + 6
Its a hard question i really don't know
Select the TABLE tab. What do all the points on this line have in common?
All the points in this line have the same value of y, as the slope is m=0 and y does not change with x.
The prism below has a base that is a regular pentagon whose perimeter is 25 feet and whose area is 43 squarefeet. The height of the prism is 11 feet. Which of the following is the volume of the prism?
The volume of a prism = Base area x Height
Base area = 43
Height = 11
Volume = 43 x 11
Volume = 473
Y=3/4x-5, C(12,-2) find perpendicular line
Owners of a recreation area are filling a small pond with water. Let y represent the total amount of water in the pond (in liters). Let x represent the total numberof minutes that water has been added. Suppose that x and y are related by the equation y = 700 +31x.Answer the questions below.Note that a change can be an increase or a decrease.For an increase, use a positive number. For a decrease, use a negative number.What was the starting amount of water in the pond?___ litersWhat is the change per minute in the amount of water in the pond?___ liters
Solution
Step 1:
y = 700 + 3x
y represents the total amount of water in the pond (in liters)
x represents the total number of minutes that water has been added
Step 2:
What was the starting amount of water in the pond?
Starting amount of water is when x = 0 minute
[tex]\begin{gathered} y\text{ = 700 + 31x} \\ y\text{ = 700 + 31}\times\text{ 0} \\ \text{y = 700 liters} \end{gathered}[/tex]Step 3:
What is the change per minute in the amount of water in the pond?
Change per minute in the amount of water in the pond = 31
Final answer
What was the starting amount of water in the pond?
700 liters
What is the change per minute in the amount of water in the pond?
31 liters
graph this line using slope
Graph this line using slope
Slope = (y2-y1)/ (x2-x1)
y = m x +b
the slope is m
The y-intercept is (0, b)
_____________________
y = 2x +4 (yellow line)
The slope = 2 = 2/1 = (y2-y1)/ (x2-x1)
The y-intercept is (0, 4)
x= 0
y = 4
First draw the point (0, 4)
x= 0
y = 4
- Since the slope is 2 = variation in y / variation in x
From (0,4) the next point could be 1 more in x and 2 more in y (1, 6)
To continue
From (1,6) the next point could be 1 more in x and 2 more in y (2, 8)
From (2,8) the next point could be 1 more in x and 2 more in y (3, 10)
From (3,10) the next point could be 1 more in x and 2 more in y (4, 12)
___________________________________________
You only have the positive part so you won't need this
From (0,4) the next point could be 1 less in x and 2 less in y (-1, 2)
To continue
From (-1, 2) the next point could be 1 less in x and 2 less in y (-2, 0)
Geometry help please
Question 13 to 15
(13) The angles are alternate interior angles .
(14) The angles are alternate exterior angles .
(15) The angles are vertically opposite angles.
What are the properties of parallel lines?In a plane, parallel lines are any lines that do not meet or intersect at any point. They are always parallel and equally spaced apart from one another. Lines that are parallel do not intersect. Infinity is where parallel lines meet, as well.
Additionally, pairs of angles, such as the ones below, are created when a transversal intersects two parallel lines.
Corresponding anglesAlternate interior anglesAlternate exterior anglesVertically opposite anglesLinear pairTwo lines are said to be intersecting if they cross at a single point in a plane. Perpendicular lines are those that cross one other at a 90-degree angle. In a plane, two lines are said to be parallel if they never cross at any point.
To know more about properties of parallels lines ,visit:
brainly.com/question/2437149
#SPJ13
A satellite is in orbit 600 km above Earth's surface. Earth's radius is about 6370 km. Using the Pythagorean Theorem, the distance (x) from the satellite to Earth's horizon is ______ km.What is the km? round the answer to the nearest whole number.
Answer:
2829.13 km.
Explanation:
If the radius of the Earth is 6370 km, the distance of the segment CD is also 6370 km.
Then, the sides of the rigth triangle are:
CB = 6370 km
AC = AD + DC
AC = 600 km + 6370 km
AC = 6970 km
AB = x
So, using the Pythagorean theorem we can calculate the value of x as follows:
[tex]\begin{gathered} AB=\sqrt[]{(AC)^2-(CB)^2} \\ x=\sqrt[\square]{6970^2-6370^2} \end{gathered}[/tex]Because AC is the hypotenuse and CB is on the legs of the triangle.
Therefore, solving for x, we get:
[tex]x=2829.13\text{ km}[/tex]Then, the answer is:
The distance (x) from the satellite to Earth's horizon is 2829.13 km.
845,000 rounded to the nearest thousand
it is already rounded
O FRACTIONSWriting unit fractions with a common denominator to add or...11Let's find312First, write the subtraction so the fractions have denominator 12.Then subtract.113121212?
Step 1
Given;
[tex]\frac{1}{3}-\frac{1}{12}[/tex]Required; To write the subtraction so that the denominators are all 12. Then subtract.
Step 2
Use equivalent fractions to make the denominator of 1/3 12
[tex]\begin{gathered} \frac{1}{3}=\frac{x}{12} \\ 12=3x \\ \frac{3x}{3}=\frac{12}{3} \\ x=4 \end{gathered}[/tex]Therefore, we will have;
[tex]\frac{1}{3}-\frac{1}{12}=\frac{4}{12}-\frac{1}{12}[/tex][tex]\frac{4}{12}-\frac{1}{12}=\frac{3}{12}=\frac{1}{4}[/tex]The answer will thus be;
[tex]\frac{1}{3}-\frac{1}{12}=\frac{4}{12}-\frac{1}{12}=\frac{3}{12\text{ }}\text{ which is =}\frac{1}{4}[/tex]Answer = 3/12 or 1/4 when reduced
Part C
Compare and contrast the relative frequency for the whole table in part B with the two-way frequency table given in the
activity introduction. What trends or generalizations can you identify from the data in the tables?
A frequency table is just a two-column "t-chart" or table that lists all of the potential outcomes and their corresponding frequencies as seen in a sample
What is a frequency table?A frequency table shows the values of a set together with how frequently they occur. The frequency of a certain data value in your dataset is how frequently it appears. You can learn which data values are typical and uncommon by using these tables.This refers to the representation of the frequency of an event in the form of a table.Therefore, when a two-way frequency table is employed, it illustrates the potential relationship between several sets of data visually.Please be aware that the answer to your query was given as a general overview because you did not supply the frequency table that was required or the patterns and generalizations that needed to be found.To learn more about frequency table refer to:
https://brainly.com/question/16148316
#SPJ9
Tony is registered for MAT-003, which meets from 8:00 AM – 9:15 AM, Monday – Thursday. How many total minutes does his class meet Monday – ThursdayTony is registered for MAT-003, which meets from 8:00 AM – 9:15 AM, Monday – Thursday How many hours does Tony’s class meet Monday – Thursday?
From 8:00AM to 9:15Am there are 1 hour (60 minutes) and 15 minutes.
Then, in a day the total minutes of class are 75. Multiply it by the number of days Monday-Thursday (4 days) to find the to tal minutes;
[tex]75\min \cdot4=300\min [/tex]Turn it into hours:
[tex]\begin{gathered} 1h=60\min \\ \\ 300\min \cdot\frac{1h}{60\min }=5h \end{gathered}[/tex]Then, Tony's class meet Monday-Thursday a total of 5 hoursThe points (-3,-6) and (9,4) are the endpoints of the diameter of a circle. Find the center, the length of the radius, and the equation of the circle. Keep values in exact form, no decimals.
Centre of the circle = (3, -1)
Length of the radius = 8
Equation of the circle = [tex](x-3)^{2} +(y+1)^{2} =61[/tex]
What is the centre of the circle?
Centre = Midpoint
[tex]\text{Midpoint}=(\frac{x_{1}+x_{2}}{2} ,\frac{y_{1}+y_{2}}{2} )\\\\=(\frac{-3+9}{2} ,\frac{-6+4}{2} )\\\\=(\frac{6}{2} ,\frac{-2}{2} )\\\\=(3,-1)[/tex]
Centre of the circle = (h, k) =(3, -1)
What is the length of the radius?
Length of the radius = [tex]\frac{\text{Length of the diameter}}{2}[/tex]
[tex]\text{Length of the diameter =}\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2}}\\\\=\sqrt{(9+3)^{2}+(4+6)^{2} } \\\\=\sqrt{(12)^{2}+(10)^{2} } \\\\=\sqrt{144+100 } \\\\=\sqrt{244} \\\\=15.62[/tex]
Length of the radius of the circle= [tex]\frac{15.62}{2} =7.81[/tex]
So, the length of the radius =7.81
= 8 (without decimal)
What is the equation of the circle?
A circle equation is given by,
[tex]{(x-h)^{2} +(y-k)^{2} } =r^{2} \\\\(x-3)^{2} +(y+1)^{2} =60.9\\\\(x-3)^{2} +(y+1)^{2} =61(\text{without decimal})[/tex]
To learn more about circles, refer:
https://brainly.com/question/25938130
#SPJ9
For the given piecewise function evaluate for the specific value of X
x = 4
4 > 3 , so , we use:
f(x)= x + 1
Replacing:
f(4) = 4 + 1 = 5
Answer:
f(4)= 5
Given the figure is a square, find x, y, and z.
Answer:
x=9
z=58 deg
y=37
Step-by-step explanation:
8x+50=12x+14
-8x from both sides
50=4x+14
-14 from both sides
36=4x
*1/4 to both sides
9=x
Because it is a square all the angles = 90
z+32=90
-32 from both sides
z=58
8*9+50=122
all sides are equal
y+85=122
-85 from both sides
y=37
Michael launched a new website to share news and photos of his town. The equation below estimates the number of followers, y, in x weeks after his launch. y = 82(1.045)^x Complete each of the 2 activities for this Task. Activity 1 of 2 What is the rate of growth for the number of followers each week? A 45% B. 1,045% C. 4.5% D. 82% Activity 2 of 2 How many followers should Michael expect in the 4th week? Round to the nearest whole number. Show your work please!
Consider the given expression,
[tex]y=82(1.045)^x[/tex]The first derivative gives the rate of growth for the number of followers.
Solve for the first derivative as,
[tex]\begin{gathered} \frac{dy}{dx}=82\times\frac{d \square}{dx}(1.045)^x \\ \frac{dy}{dx}=82\times(1.045)^x\ln (1.045) \\ \frac{dy}{dx}=y\times0.045 \\ \frac{dy}{dx}=4.5\text{ percent of y} \end{gathered}[/tex]Thus, the rate of growth of followers is approximately 4.5% each week.
Therefore, option C is the correct choice.
The number of followers corresponding to the 4th week is calculated as,
[tex]y=82\times(1.045)^4=82\times1.1925=97.7865\approx98[/tex]Thus, Michael should expect approximately 98 followers in 4th week.
The water park charges a $10 entry fee per person and a $3 parking fee per family vehicle. What is the total cost in tepeople ride in the same vehicle? what is the dependent variable
Which triangles are similar?17Triangle A12)151037g8Triangle BTriangle cA. Triangles A, B, and CB. Triangles A and CC. Triangles B and CD. Triangles A and B
The answer is C. triangles B and C are similar.
Similar triangles only differs between them by the size. All angles must be the same and all sides must be multiplied by the same factor of scale to transform from one triangle from another.
the only 2 triangles that share the same angle values are B and C. thus, the answer is option C
11 Type the correct answer in each box. x + 3x + 5+ 2= __ x + __4s-2s + 10= __ s + 10n + n + 7 + n + 4= __ n + __
SOLUTION
(1) We want to add
[tex]\begin{gathered} x+3x+5+2 \\ x\text{ means 1}x \\ \text{adding we have } \\ 4x+7 \end{gathered}[/tex]Hence, the answer is 4x + 7
(2)
[tex]\begin{gathered} 4s-2s+10 \\ =2s+10 \end{gathered}[/tex]Hence, the answer is 2s + 10
(3)
[tex]\begin{gathered} n+n+7+n+4 \\ we\text{ place the n's together and the numbers together, we have } \\ n+n+n+7+4 \\ \text{This also means } \\ 1n+1n+1n+7+4 \\ =3n+11 \end{gathered}[/tex]Hence, the answer is 3n + 11
A surveyor wants to find the height of a tower used to transmit cellular phone calls. he stands 120 ft away from the tower and measure the angle of evolution to be 40° . how tall is the Tower?
EXPLANATION
Let's represent the situation on a graph:
Let's call x to the height of the tower.
The height of the tower is given by the following trigonometric relationship:
[tex]\text{tangent 40}=\frac{opposite\text{ cathetus}}{\text{adjacent cathetus}}[/tex]Replacing terms:
[tex]\text{tangent 40 = }\frac{x}{120}[/tex]Multiplying 120 to both sides:
[tex]120\cdot tangent\text{ 40 = x}[/tex]Solving the argument:
[tex]120\cdot0.72=\text{ x}[/tex]Multiplying numbers:
[tex]120\cdot0.72=86.4\text{ ft}[/tex]The tower is 86.4 ft tall
On a 1200 foot stretch of highway through the mountains the road rises by a total of 40 feet find the slope of the road
Remember that
The formula to calculate the slope is
slope=rise/run
In this problem
rise=40 feet (vertical distance)
run=1,200 feet (horizontal distance)
so
slope=40/1,200
slope=4/120
simplify
slope=1/30