Data:
Loan=$278 at 10%
A simple interest is calculated for payments on the initial capital.
If the total interest was $174.12.
If the interest is on a year. You calculated the interes of one year. The 10% of $278:
[tex]278\cdot\frac{10}{100}=27.8[/tex]In a year the interest is $27.8.
Then, $174.12 divided into $27.8 is the number of years of the loan:
[tex]\frac{174.12}{27.8}=6.26\approx6[/tex]Then, the loan was for 6 yearsHere is a graph representing the relationship in question 3. Interpret the set of coordinates (30, 7).
children's tickets sold
60
55
50
45
40
30
25
20
5
(30, 7)
10 15 20 25 30 35 40
adult tickets sold
O 7 children's tickets and 30 adult tickets were sold
O 30 children's tickets and 7 adult tickets were sold
O When 7 tickets are sold, $30 is collected
O (30, 7) is not a possible solution
The correct option 2 that is 30 children's tickets and 7 adult tickets were sold.
Given : A graph which has adult tickets in the x - axis
and children tickets in the y - axis
The marked point is ( 30, 7 )
this means that the value of x axis 30 and y axis is 7
thus from the above information it is clear that there are 30 children's tickets and 7 adult tickets were sold.
So the correct option is Option 2
To know more about interpretation of information from graphs you may visit the link which is mentioned below;
https://brainly.com/question/28418462
#SPJ1
Kayle is playing a game. She starts the game with 500 points. Her first 5 turns and the change in points are shown in the table.
How many points does Kayle have after her 5th turn?
Responses
−550 points
negative 550 points
−150 points
negative 150 points
350 points
350 points
1,150 points
Kayle have 1300 points after her 5th turn as the final score is sum of all score in the 5 rounds that come up to 1300.
What is addition?One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division. The total amount or sum of the two whole numbers is obtained by adding them. Combining things and counting them as one big group is done through addition. In math, addition is the process of adding two or more numbers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation. When you add two or more numbers together, you get the sum of the numbers. The sum is the outcome of adding two or more numbers.
Here,
The final score will be the sum of all scores after 5th turn.
initial score=500
first round=−550 points
second round=−150 points
third round=350 points
fourth round=1,150 points
500+-550+-150+350+1150
=500-550-150+350+1150
=1300 points
After her fifth turn, Kayle had 1300 points because the total of her five rounds' scores added up to 1300.
To know more about addition,
https://brainly.com/question/25450012?referrer=searchResults
#SPJ1
What single transformation was applied to
quadrilateral A to get quadrilateral B?
A.translation
B.rotation
C. Reflection
D.dilation
The transformation that is applied to the quadrilateral A to get quadrilateral B is translation.
We can see that the quadrialteral A and B look exactly the same.
It is just that they are being moved from one place to another.
So. it cannot be a rotation or a reflection.
Also, the size of both the quadrilaterals are same.
So, it can also not be a dilation.
So, the transformation that is applied is:
Translation.
Therefore, the transformation that is applied to the quadrilateral A to get quadrilateral B is translation.
Learn more about translation here:
https://brainly.com/question/900753
#SPJ9
Find the parallel line for (2,0) y=-5x+3
The linear equation parallel to y=-5x+3 is:
y = -5*x + 10
How to find the parallel line?Two lines are parallel if and only if both lines have the same slope.
Remember that the general line is:
y = m*x + b
Where m is the slope and b is the y-intercept.
So a line parallel to:
y = -5x + 3
Must have a slope equal to -5, so our line is:
y = -5*x + b
To find the value of b we use the fact that the line passes through (2, 0), then:
0 = -5*2 + b
0 = -10 + b
10 = b
Then the line is:
y = -5*x + 10
Learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
Stan's cookie recipe makes 242424 cookies and calls for exactly 384384384 sprinkles. he is wondering how many sprinkles (p)(p)left parenthesis, p, right parenthesis he will need to make 606060 cookies. he assumes each cookie will have the same number of sprinkles.
Using tha basic multiplication and division, Stan will need 960 sprinkles to make 60 cookies.
What is algebra?In the branch of mathematics known as algebra, a situation is described using mathematical symbols, variables, and arithmetic operations like addition, subtraction, multiplication, and division that produce meaningful mathematical expressions.
The sprinkles needed for 1 cookie are given by
24 cookies need sprinkles = 384
1 cookie will need sprinkles = 384 ÷ 24
= 16 sprinkles
Now, sprinkles needed for 60 cookies are given by
1 cookie needs sprinkles = 16
60 cookies will need sprinkles = 16 × 60
= 960 sprinkles
To know more about multiplication, visit:
https://brainly.com/question/4686237
#SPJ4
The correct question is:
"Stan's cookie recipe makes 24 cookies and calls for exactly 384 sprinkles. He is wondering how many sprinkles (p) he will need to make 60 cookies. He assumes each cookie will have the same number of sprinkles. How many sprinkles does Stan need to make 60 cookies?"
PLEASE HELP PLEASE HELP!!!!
You run m miles on Monday, the same amount on Tuesday, and 3 miles on Wednesday. Write an expression in the simplest form that represents the total amount in each situation.
(please show work)
The mean, or average, is equal to the sum of all the miles divided by the number of terms you added together. We have 4 terms that will be added, but are missing one term. We will solve for the missing term by setting up an equation for the average and solving for x, the number of miles you must run on Thursday.
3 = (2 + 3 + 4 + x) / 4
12 = 2 + 3 + 4 + x
12 = 9 + x
x = 3 miles
Two angles are supplementary.
The measure of the larger angle is four more than three times the measure of the smaller angle. Find the measures of both angles.
Answer:
44° and 136°
Step-by-step explanation:
let x represent the smaller angle then larger angle is 3x + 4
supplementary angles sum to 180° , so
x + 3x + 4 = 180
4x + 4 = 180 ( subtract 4 from both sides )
4x = 176 ( divide both sides by 4 )
x = 44
3x + 4 = 3(44) + 4 = 132 + 4 = 136
then
smaller angle = 44° and larger angle = 136°
Square root of 4n^2+4n^2
PLEASE HELP
Giving brainliest
Answer: 8n^2
Step-by-step explanation:
I did test and got 100
Given the polynomial f(x) = x4 + 3x3 − 3x2 − x, which of the following is true? (1 point)
(x + 1) is a factor since f(−1) = 0.
(x − 1) is a factor since f(−1) = 0.
(x + 1) is a factor since f(1) = 0.
(x − 1) is a factor since f(1) = 0.
The factor of the polynomial is (x-1)
f(x)=x4 + 3x3 − 3x2 − x
At x=1 the value of the polynomial is 0
so this is factor of the polynomial (x-1)
To learn more about factor visit: https://brainly.com/question/14209188
#SPJ1
Trees in the backyard need soil around their roots. ?Chris buys 4 pounds of soil. How many ounces of soil does he have for the trees?
Answer:
64 ounces.
Step-by-step explanation:
You multiply the mass amount by 16 since there are 16 ounces in 1 pound. 16*4=64.
Find all solutions of the following equation in the interval [0, 2pi).2cos^2 x = 2- sin
Step 1: problem
[tex]2\cos ^2x\text{ = 2 - sinx}[/tex]Step 2: Concept
[tex]\text{cos}^2x=1-sin^2x[/tex]Step 3: Method
[tex]\begin{gathered} 2\cos ^2x\text{ = 2 - sinx} \\ 2(1-sin^2x)\text{ = 2 - sinx} \\ 2-2sin^2x\text{ = 2 - sinx} \\ 2-2=2sin^2x\text{ - sinx} \\ 2\sin ^2x\text{ - sinx = 0} \\ \sin x\text{ (2sinx - 1 ) = 0} \end{gathered}[/tex][tex]\begin{gathered} \sin x\text{ = 0 or 2sinx - 1 = 0} \\ x\text{ = }\sin ^{-1}0\text{ or 2sinx = 1} \\ \text{ x = 0 or sinx = }\frac{1}{2} \\ \text{ x = }\sin ^{-1}(\frac{1}{2})\text{ = 30} \end{gathered}[/tex][tex]x\text{ = 0, }\pi,\text{ }\frac{\pi}{6},\text{ }\frac{5\pi}{6}[/tex]Final answer
If a television screen is 20 inches wide
and 15 inches high, what is the size of the
TV?
Diagonal problems
25 is the diagonal of tv with the given dimensions .
What is diagonal ?In geometry, a diagonal is a line segment connecting two vertices of a polygon or polyhedron that are not on the same edge. A diagonal is an informal term for any sloping line.
CalculationThe length of diagonal is the length of the hypotenuse of a right angled triangle for which the lengths of the sides making right angle are 20" and 15", hence is
=
√20^2 + 15^2
=√400 + 225
= √625
= 25
learn more about diagonal here :
brainly.com/question/12274248
#SPJ13
how do you multiply 120 by 1/6
The expression is,
[tex]\frac{1}{6}\times120[/tex]On solving, we have,
[tex]\begin{gathered} 120\times\frac{1}{6}\Rightarrow\frac{120\times1}{6}=20 \\ \end{gathered}[/tex]Thus, the required answer is 20.
can someone please help me with this?
Answer:
3=3x+3
4=2x+8
Step-by-step explanation:
the diameter of a circle is 14 centimeters what is the radius? give the exact answer in simplest form
The radius is half the diameter, that is:
[tex]r=\frac{D}{2}[/tex]In this case D=14 cm, hence:
[tex]r=\frac{14}{2}=7[/tex]therefore the radius is 7 cm.
What is an equation of the line that passes through the points (3, -4) and (-4, 3)
The equation of a line passing through the point (3, -4)and (-4, 3) is y = -x - 1
How to find equation of a line?The equation of a line passing through a point can be represented as follows;
In slope intercept form,
y = mx + b
where
m = slopeb = y-interceptThe line is passing through the point (3, -4) and (-4, 3).
Therefore,
slope = m = 3 + 4 /-4 - 3
m = 7 / -7
m = -1
Let's find the y-intercept using (3, -4)
-4 = -(3) + b
b = -4 + 3
b = -1
Therefore, the equation of the line is y = -x - 1
learn more on equation of a line here: brainly.com/question/23558787
#SPJ1
When attacked by a giant hornet, Japanese honeybees cluster together to form a ball around the hornet and then generate heat by buzzing. The honeybees can endure temperatures of up to 48C, which is 3C greater than the hornet can tolerate. Find the maximum temperature tolerated by a Japanese giant hornet.
_______ degrees Celsius
The required temperature that can be tolerated by Japanese hornets is 45°C.
Given that,
The honeybees can endure temperatures of up to 48C, which is 3C greater than the hornet can tolerate.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
honeybees temperature = 48
According to the question temperature endure by hornet,
= honeybees temperature - 3
= 48 - 3
= 45°C
Thus, the required temperature that can be tolerated by Japanese hornets is 45°C.
Learn more about arithmetic here:
https://brainly.com/question/11424589
#SPJ1
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 10.8 seconds
Step-by-step explanation:
[tex]-16t^2 +170t+40=10\\\\16t^2 -170t-30=0\\ \\ t=\frac{-(-170) \pm \sqrt{(-170)^2 -4(16)(-30)}}{2(16)}\\\\t \approx 10.8 \text{ } (t > 0)[/tex]
Solve the following equation for A
4 = gA
Read the following sentence.We will go to the park tomorrow if you finish your homework.What is the connecting word in the sentence and what logical symbol represents it?
The connecting word in the sentence is If.
The logical symbol is
[tex]\rightarrow[/tex]Therefore, the correct option is Option 2.
Which of the pictures below shows the graph of the inequality y
Firstly, less than and greater than signs are represented with a chained line on the graph. Therefore,
[tex]\begin{gathered} yThe graph is B. Picture Dhow to solve this problem? Result from step 1: Expected value is -$3.23.
The expected value was already calculated as:
[tex]E=-3.23[/tex]The expected value is the mean value you would get per try.
Since we played 623, the expected value is 623 times the expected valu for a single play, so:
[tex]E_{623}=623\cdot E=623\cdot(-3.23)=-2012.29[/tex]So, the expected value after playing 623 times is to -$2012.29, that is, lose $2012.29.
Tonio works for a website that sells theater tickets and receives a base salary of $18,200 per year. He earns a commission of 2.3% for all ticket sales, which average $15,500 per week. He also gets a "viewed” fee of 3 cents each time someone comes to the website, whether or not any tickets are purchased. The number of visitors to the website averages 12,400 per month a) what is the total commission Tonio will earn this year. b) What is the total amount Tonio earns from visits to the website?c) What are Tonio’s total earnings for the year?
Tonio's salary is composed by:
- A base value of $18,200.
- A commission of 2.3% for all ticket sales, which average $15,500 per week. Hence 52 x 15,500 per year, as a year has 52 weeks.
- Another commission of $0.03 per visitor to the website, which averages 12,400 per month, hence 12 x 12,400 per year, as a year has 12 months.
Then, the total commissions are given by:
T = 0.023x52x15500 + 0.03x12x12400 = 23002
Tonio will earn a total of $23,002 in commissions this year.
Total amount Tonio earns from visits to the website: 0.03x12x12400 = $4464
Tonio’s total earnings: $18,200 + $23,002 = $41202
Review Josh’s steps for solving the equation :
[tex]x^2-6x-7=0\\ \\ x^2-6x=7\\\\x^2-6x+9=7+9\\\\(x-3)^2=16\\\\x-3=6\\x=19\\\\x-3=-16\\x=-13[/tex]
a) State what method he was using to solve the equation.
b) Explain where in his work he had a mistake.
c) Show how to fix his mistake and what the correct answer should be.
The method Josh was using to solve the equation is completing the square method.
Josh made mistake where he was supposed to find the square root of both sides.Josh should fix his mistake by finding the the square root of both sides and the correct answer should be x = 1 or -7How to solve quadratic equation?x² - 6x -7 = 0
a = 1
b = -6
c = -7
x² - 6x = 7
Find the half of b and square it, then add to both sides
x² - 6x + 9 = 7 + 9
factorize the expression on the right
(x - 3)² = 16
Find the square root of both sides(x - 3) = √16
x - 3 = ± 4
x = 4 - 3 or x = -4 - 3
x = 1 or -7
Therefore, the correct answer to the quadratic equation using completing the square method is x = 1 or -7
Read more on quadratic equation:
https://brainly.com/question/10449635
#SPJ1
a car travels 100 miles at a speed of 40 mph
calculate how long the journey lasts give answers in hours and minutes
Answer:
2 Hours and 20 Minutes
Step-by-step explanation:
100/40 = 2.5
2 Hours and 20 Minutes
Jermaine bought a pickleball paddle that cost $65.90. he also bought four pickle balls. he spent $79.90. part a: which equation can you use to find p, the cost of each pickle ball? part b: what was the cost of each pickle ball?
Answer:
a. 65.90 + 4p = 79.90
4p = 14.00
b. p = 3.50
the treasures location has an absolute value between 1 1/2 and 9 show on the number line where the treasure could be
The location is between values of 1 1/2 and 9.
The values being absolute it means that they have no sign, i.e. they can be either positive or negative.
Since the values are both positive, you have to draw a positive number line.
The purple line indicates the possible locations over the number line.
Find the number that makes the ratio equivalent to 1:2 5:_
Answer:
10
Step-by-step explanation:
1x5=5
2x5=10
which function is the inverse of f(x)= arccsc x
Let's begin by identifying key information given to us:
[tex]\begin{gathered} f(x)=arccsc(x)_{} \\ f\mleft(x\mright)=y \\ \Rightarrow y=arccsc(x) \\ We\text{ will proceed to i}nterchange\text{ }the\text{ }variables,\text{ we have:} \\ x=arccsc(y) \\ We\text{ will make ''y'' the subject of the formula, we have:} \\ y=\frac{x}{arccsc}\Rightarrow y=csc(x) \\ y=csc(x) \\ y=f^{-1}\mleft(x\mright) \\ \Rightarrow f^{-1}(x)=csc(x) \\ \\ \therefore f^{-1}(x)=csc(x) \end{gathered}[/tex]a bag of 13 marbles contains 5 marbles with red on them, 6 with blue on them, 7 with green on them and 5 red and green on them....... I'll take a picture of the rest of the question
We have to calculate the probability that we choose a marble that has either red or green on it.
We have a total of 13 marbles.
We can draw a Venn diagram to look at the green and red marbles:
We can see in the diagram that is expected to all the marbles that have red on it to have also green, because they are not mutually exclusive.
Then, we can calculate the probabilities as:
[tex]\begin{gathered} P(G\cup R)=P(G)+P(R)-P(G\cap R) \\ P(G\cup R)=\frac{7}{13}+\frac{5}{13}-\frac{5}{13}=\frac{7}{13} \end{gathered}[/tex]NOTE: If we write the exact color of each marble we will get:
1) 6 blue marbles
2) 2 only green marbles, as 5 of the 7 marbles that have green are "red and green" marbles.
3) 0 only red marbles: all 5 of the marbles that have red are "red and green"marbles.
4) 5 red and green marbles.
Then, if we add, we get 6 + 2 + 5 = 13 marbles.
The marbles that have red or green are: 2 green and 5 red and green, so there are 7 marbles that have red or green.
Then, the probability is equal to number of successful events / total events = 7/13.
It is the same result as the previous calculation.
Answer: the probability is 7/13.