The training wheel has an area approximately 286.34 square inches smaller than the regular wheel.
The area of a circle is given by the formula A = πr², where A is the area of the circle and r is the radius of the circle. Since we have the radii of both wheels, we can use this formula to find their respective areas.
The area of the training wheel is A₁ = π(3)² = 9π square inches.
The area of the regular wheel is A₂ = π(10)² = 100π square inches.
To find the difference in their areas, we can subtract A₁ from A₂:
A₂ - A₁ = 100π - 9π = 91π
So the difference in their areas is 91π square inches. To round to the nearest hundredth, we can use the approximation π ≈ 3.14:
91π ≈ 286.34 square inches
To know more about area here
https://brainly.com/question/14994710
#SPJ1
Match the equation or expression to the number of terms, the coefficients and the constants.
[tex]1.[/tex] The answers are given below
Equation: [tex]6xt +4yz -3 +10a = 1[/tex]
Number of terms: [tex]4[/tex]
Coefficients: [tex]6,4,10[/tex]
Constants: [tex]-3,1[/tex]
[tex]2.[/tex] Expression: [tex]25abc -2b +3ac -6bc +25[/tex]
Number of terms: [tex]5[/tex]
Coefficients: [tex]25,-2,3,-6[/tex]
Constants: [tex]25[/tex]
[tex]3.[/tex] Equation: [tex]25y -3xy+5x = 100[/tex]
Number of terms: [tex]3[/tex]
Coefficients: [tex]25,-3,5[/tex]
Constants: [tex]100[/tex]
How to break down mid point?To break down each equation or expression and identify the number of terms, coefficients, and constants.
[tex]1.[/tex] Equation: [tex]6xt +4yz -3 +10a = 1[/tex]
Number of terms: 4. There are four terms in this equation separated by addition and subtraction operators.
Coefficients: [tex]6,4,10[/tex]. These are the coefficients, which are the numerical values multiplied by the variables (xt, yz, a) in each term.
Constants: [tex]-3,1[/tex]. These are the constants, which are the numerical values without any variables that are added or subtracted in the equation.
[tex]2.[/tex] Expression:[tex]25abc -2b +3ac -6bc +25[/tex]
Number of terms: [tex]5[/tex] There are five terms in this expression separated by addition and subtraction operators.
Coefficients: [tex]25,-2,3,-6[/tex]. These are the coefficients, which are the numerical values multiplied by the variables (abc, b, ac, bc) in each term.
Constants: [tex]25[/tex]. This is the constant, which is the numerical value without any variables that is added in the expression.
[tex]3.[/tex] Equation: [tex]25y -3xy+5x = 100[/tex]
Number of terms:[tex]3[/tex]. There are three terms in this equation separated by addition and subtraction operators.
Coefficients: [tex]25,-3,5[/tex]. These are the coefficients, which are the numerical values multiplied by the variables (y, xy, x) in each term.
Constants: [tex]100[/tex]. This is the constant, which is the numerical value without any variables on the right-hand side of the equation.
Therefore, [tex]1.[/tex] The answers are given below
Equation: [tex]6xt +4yz -3 +10a = 1[/tex]
Number of terms: [tex]4[/tex]
Coefficients: [tex]6,4,10[/tex]
Constants: [tex]-3,1[/tex]
[tex]2.[/tex] Expression: [tex]25abc -2b +3ac -6bc +25[/tex]
Number of terms: [tex]5[/tex]
Coefficients: [tex]25,-2,3,-6[/tex]
Constants: [tex]25[/tex]
[tex]3.[/tex] Equation: [tex]25y -3xy+5x = 100[/tex]
Number of terms: [tex]3[/tex]
Coefficients: [tex]25,-3,5[/tex]
Constants: [tex]100[/tex]
Learn more about Coefficients
https://brainly.com/question/28975079
#SPJ1
What amount of a 80% acid solution must be mixed with a 55% solution to produce 600 mL of a 60% solution?
Answer:The amount of a 80% acid solution that must be mixed with a 55% solution to produce 600 mL of a 60% solution can be calculated using a simple algebraic equation. Let x represent the amount of the 80% acid solution in mL that needs to be mixed with the 55% solution.
The equation can be set up as follows:
0.80x + 0.55(600 - x) = 0.60(600)
Step-by-step explanation: The left-hand side of the equation represents the total amount of acid in the mixture. The first term, 0.80x, represents the amount of acid from the 80% solution, and the second term, 0.55(600 - x), represents the amount of acid from the 55% solution. The right-hand side of the equation represents the total amount of acid in the final 60% solution, which is 60% of 600 mL.
By solving this equation for x, we can determine the amount of the 80% acid solution that needs to be mixed with the 55% solution. Once we have the value of x, we can then calculate the amount of the 55% solution by subtracting x from 600 mL.
Internal Link: For a verified answer on a similar topic, check out this link: https://brainly.com/question/1234567 intext:Answer Expert Verified.
Let x=amount of 80% solution needed
Then 600-x=amount of 30% solution needed
Now we know that the pure acid in the 80% solution (0.80x) plus the amount of pure acid in the 30% solution ((0.30)(600-x)) has to equal the amount of pure acid in the final mixture(0.40*600), so our equation to solve is:
0.80x+0.30(600-x)=0.40*600 get rid of parens
0.80x+180-0.30x=240 subtract 180 from each side
0.80x+180-180-0.30x=240-180 collect like terms
0.50x=60 divide each side by 0.50
x=120 ml---------------------amount of 80% solution needed
600-x=600-120=480 ml---------------amount of 30% solution needed
CK
120*0.80+480*0.30=0.40*600
96+144=240
240=240
PLEASE HELP PLEASE ASAP I NEED THIS NOW
The slope-intercept form of the equation is y = 18x.
What is the function in slope-intercept formTo find the function in slope-intercept form, we have to write the general form below as;
y = mx + c
m = slope
c = y-intercept
To find the slope, we need to take two points from the table given;
slope (m) = y2 - y1 / x2 - x1
m = 720 - 450 / 40- 25
m = 18
The slope of the line is 18
we can use this with any point to find the y - intercept
y = mx + c
720 = 18(40) + c
720 = 720 + c
c = 720 - 720
c = 0
The equation of the line in slope-intercept form is y = 18x
b. To determine how far he travelled with 55 gallons of gas
y = 18x
y = 18(55)
y = 990 miles
c. How many gallons will be required to cover 630 miles
y = 18x
630 = 18x
x = 630 / 18
x = 35 gallons
Learn more on slope-intercept form here;
https://brainly.com/question/4074386
#SPJ1
Write the first four terms of each arithmetic sequence. first term 7 and common difference 15
Hence, 7, 22, 37, and 52 are the first four terms in the arithmetic series with initial term 7 and common difference 15.
what is arithmetic progression ?Algebraic progression is a series of numbers where each term following the first is derived by multiplying the previous president by a constant known as the common difference (d). An arithmetic progression often takes the form: A, A+D, A+2D, A+3D,... where "a" stands for the initial keyword and "d" for the common distinction.
given
The sequence's initial term is 7, and the shared discrepancy is 15. We can continuously add 15 to the preceding word to find the next terms.
As a result, the arithmetic sequence's first four terms are:
Initial term = 7
Term two: 7 plus 15 equals 22
Third term = 22 plus 15 equals 37
Fourth term: 37 plus 15 equals 52
Hence, 7, 22, 37, and 52 are the first four terms in the arithmetic series with initial term 7 and common difference 15.
To know more about arithmetic progression visit:
https://brainly.com/question/16947807
#SPJ1
3 divided by 5/3 i need help and i need longer
Answer: 1.8
Let's put our whole number and fraction side by side so we can visualize the problem we're trying to solve:
3 ÷
5
3
The trick to working out 3 divided by 5/3 is similar to the method we use to work out dividing a fraction by a whole number.
All we need to do here is multiply the whole number by the numerator and make that number the new numerator. The old numerator then becomes the new denominator. Let's write this down visually:
3 x 3
5
=
9
5
So, the answer to the question "what is 3 divided by 5/3?" is:
9
5
Sometimes, after calculating the answer we can simplify the resulting fraction down to lower terms. In this example though 9/5 is already in it's lowest possible form.
If you made it this far you must really love your fractions and dividing whole numbers by them. Hopefully this simple guide was easy for you to follow along and you can now go forth and divide more whole numbers by as many fractions as your heart desires.
Convert 3 divided by 5/3 to Decimal
One last little calculation before you go. It's common to want to express your result as a decimal and, to do that, all you need to do is divide your numerator by your denominator:
9
5
= 1.8
Which ordered pair is not included in a graph of y= 2 x + 5
Mimi chose A (0,0) how did she get that answer? and is she correct.
party opposed to expanding slavery (2 words, section 1)
Answer:
The party opposed to expanding slavery in the United States was the Republican Party. It was actually formed to go against slavery.
A motorboat travels 106 kilometers in 2 hours going upstream. It travels 142 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
Step-by-step explanation:
Rate UP stream = ( s - w) = 106 km / 2 hr
( where s = boat speed w = current speed )
(s-w) = 53 km/hr
Rate DOWNstream = ( s+w) = 142 / 2 = 71 kmhr
( s-w) + ( s+w) = 53 + 71 km/hr
2s = 124
s = 62 km /hr then s+w = 71 shows w = 9 km/hr
5000 people attend a match 50 people win a T-shirt whats the probability of winning a T-shirt
3/4 + x = 2. What is the value of x?
square root of 54 (simplified not 7.5)
Answer:
Step-by-step explanation:
7.3 is the anwser
Which equation best shows that 48 is a multiple of 3?
Choose 1 answer:
A
B
C
144= 3 x 48
3 = 48 ÷ 16
52 = 48 + 3
D3=48-45
The solid below is dilated by a scale factor of . Find the surface area of the solid
created upon dilation.
The surface area of the solid created upon dilation is equal to 36 units².
How to calculate surface area of a cylinder?In Mathematics and Geometry, the surface area (SA) of a cylinder can be calculated by using this mathematical equation (formula):
SA = 2πrh + 2πr²
Where:
h represents the height.r represents the radius.By substituting the given parameters into the formula for the surface area (SA) of a cylinder, we have the following;
Surface area = 2πrh + 2πr²
Surface area = 2(π)(9)(9) + 2(π)(9²)
Surface area = 324π units²
After applying a dilation with a scale factor of 1/3, the surface area of the cylinder is given by;
Surface area = 324π × (1/3)²
Surface area = 324π × 1/9
Surface area = 36 units²
Read more on surface area here: https://brainly.com/question/27118100
#SPJ1
1. Mason has a credit card debt of $15,600 that he would like to reduce by applying $8,500 of his inheritance money to the
balance.
In addition, he would like to modify his debt payment plan to pay off the remaining balance in 24 months rather than 60
months.
His credit card has an APR of 18%. How much will these changes save Mason in finance charges (interest)?
Hint: 1st, subtract 8500 from 15,600 to find the remaining balance he will pay in 24 months.
Use the formula
P=PV* (1/(1-(1+0)^n) where PV is the remaining balance, i-0.18/12, and n-24 months.
2nd, multiply your answer in step 2 by 24 months to find out the total amount you paid in 24 months.
3rd, find the interest you paid by subtracting 7100 from the amount you found in step 2.
4th, find out how much you would have paid had you not reduced the amount you owed by 8500 (in other words, 15,600).
Use the same monthly formula in step 1 where PV-15,600, i-0.18/12, and n-60 months.
5th, multiply the answer in step 4 by 60 months to find out how much you paid in total.
6th, to find the interest, subtract the amount in step 5 from 15,600 to find the interest.
Finally, find the difference between step 3 and step 6, and that is how much you saved.
a. $1,407.04
b. $3,302.59
c. $6,760.96
d. $8,168.40
a circle has a circumerence of 6 and an arc with a 60 degree central angle. what is the length of the arc
The length of the arc is 1 unit.
What is length of an arc?The distance that runs through the curved line of the circle making up the arc is known as the arc length.
length of an arc is expressed as;
l = tetha/360 ×2πr
the circumference of circle is expressed as ;
C = 2πr
6 = 2×3.14 × r
r = 6/6.28
r = 0.955 units
Therefore length of the arc
= 60/360 × 6
since 2πr is the circumference,
l = 360/360 = 1 unit
therefore the length of the arc is 1 unit.
learn more about length of an arc from
https://brainly.com/question/2005046
#SPJ1
The table shows several input and output values of a quadratic function f(x)
x f(x)
3.0 3.00
4.0 5.00
4.5 5.25
5.0 5.00
6.0 3.00
Which statements is tru about the function?
a) The maximum value of f(x) is 6
b) The maximum value of f(x) is 5.25
c) The zeroes of the function are 2 and 4
d) The zeroes of the function are 4 and 5
Answer:-by-step explanation:
the function has the x-intercept of (-2, 0)
the function has the y-intercept of (0, -8)
the function has the x-intercept of (4, 0)
A light source at a height of 8 metres is shining a laser beam onto the mirror on the ground. The light beam needs to be observed by a sensor at a height of 4 metres. If the total distance the laser beam travels is 15 metres, what is the distance between the bases of the light source and the sensor? Your answer should be a numerical value.
The lateral area of a cone is 587 pi symbol cm^2. The radius is 32cm. Finf the slant height to the nearest tenth.
Answer:
The lateral area of a cone is given by the formula:
L = πrs
Where r is the radius of the base, s is the slant height, and π is pi.
We are given that the lateral area L is 587π cm^2 and the radius r is 32 cm. Substituting these values into the formula, we get:
587π = π(32)s
Simplifying, we can cancel the π on both sides of the equation:
587 = 32s
Dividing both sides by 32, we get:
s = 18.34375
Rounding to the nearest tenth, we get:
s ≈ 18.3 cm
Therefore, the slant height is approximately 18.3 cm.
Step-by-step explanation:
Find the area
Round to nearest tenth
The area of the triangle is 87.6 cm².
How to find the area of a triangle?The area of the triangle can be found as follows:
Therefore,
area of a triangle = 1 / 2 bh
where
b = base of the triangleh = height of the triangleTherefore,
b = 17 cm
h = 10.3 cm
Hence,
area of a triangle = 1 / 2 × 17 × 10.3
area of a triangle = 1 / 2 × 175.1
area of a triangle = 87.55
area of a triangle = 87.6 cm²
learn more on area here: https://brainly.com/question/26179028
#SPJ1
The circle is divided into equal parts.
What fraction of the area of the circle is shaded?
+0
e
1
4
w|1
1
-
2
13% Complete
AZ
according to the given information we can say that the fraction of the area of the circle that is shaded is 1/4 or 0.25.
What is circle?Every point in a horizontal surface that is a certain distance above another point forms a circle (centre). It is a circle made out of point that are separated from each other in a horizontal direction as a result. At all angles, it is rotating symmetric about the centre. In the closed, two-dimensional plane of a circle, each pair of points is evenly separated from the "centre." A line that pierces the circle creates a specular symmetrical line. At all angles, it rotates symmetrically about the centre.
given,
If the circle is divided into two equal parts and one of them is shaded, then the shaded area is half of the total area of the circle. So the fraction of the area of the circle that is shaded is 1/2 or 0.5.
If the circle is divided into four equal parts and one of them is shaded, then the shaded area is one-fourth of the total area of the circle. So the fraction of the area of the circle that is shaded is 1/4 or 0.25.
Therefore, the answer depends on how many equal parts the circle is divided into and the number of shaded parts.
To know more about circle visit:
https://brainly.com/question/29142813
#SPJ1
Calcular el área de un triángulo equilátero si su base es de 8 m y una altura de 5 m
Answer:
[tex]tringle = \frac{1}{2} \times base \times hieght[/tex]
1/2 × 8×5
0.5×40
=20m
EACH STUDENT IN MR COOPERS CLASS GOT A APPLE ON THEIR FIELD TRIP TO THE APPLE ORCHAD THERE ARE 9 STUDENTS ON THE FIELD TRIP AND EACH APPLE HAS A MASS OF 70 G WHAT IS THE TOTAL MASS OF ALL THE APPLES
A student is graduating from college in 12 months but will need a loan in the amount of $10,720 for the last two semesters. The student may receive either an unsubsidized Stafford Loan or a PLUS Loan. The terms of each loan are: Unsubsidized Stafford Loan: annual interest rate of 5.95%, compounded monthly, and a payment grace period of six months from time of graduation PLUS loan: annual interest rate of 6.55%, compounded monthly, with a balance of $11,443.63 at graduation Which loan will have a lower balance, and by how much, at the time of repayment?
according to the question, the PLUS Loan will have a higher balance due at the time of repayment by $233.80 ($11,966.11 - $11,732.31).
what is interest ?Divide the principal times the interest rates, the length of time, and various other factors to arrive at simple interest. Simple return = principle + interest + hours is the marketing formula. The easiest way to compute interest is with this method. The most typical technique to figure out interest is to use a portion of the principal sum. He is only going to pay his share of the 100% interest, for example, if he loans $100 form a friend then agrees to pay it off with 5% interest. $100 (0.05) corresponds to $5. Interest must be paid as you borrow money and must be added to any loans you make. Interest is often determined as a yearly proportion of the loan total. The interest on the loan is this percentage.
given,
To compare the two loans, we need to calculate the total balance due for each loan at the time of repayment. We can start by calculating the balance due for the Unsubsidized Stafford Loan:
Principal: $10,720
Interest rate: 5.95% per year, compounded monthly
Time: 6 months grace period + 6 months repayment = 1 year
Number of periods: 12 months x 1/12 month per period = 12 periods
Using the formula for compound interest, the balance due on the Unsubsidized Stafford Loan after 1 year is:
B = P(1 + r/n)^(nt) + I [(1 + r/n)^(nt) - 1]/(r/n)
where B is the balance due, P is the principal, r is the annual interest rate, n is the number of times per year the interest is compounded, t is the time in years, and I is the monthly payment.
Plugging in the numbers, we get:
B = $10,720(1 + 0.0595/12)^(121) + $0 [(1 + 0.0595/12)^(121) - 1]/(0.0595/12)
B = $11,732.31
Now, let's calculate the balance due for the PLUS Loan:
Principal: $11,443.63
Interest rate: 6.55% per year, compounded monthly
Time: 6 months repayment
Number of periods: 6 periods
Using the same formula for compound interest, the balance due on the PLUS Loan after 6 months is:
B = $11,443.63(1 + 0.0655/12)^(120.5) + $0 [(1 + 0.0655/12)^(120.5) - 1]/(0.0655/12)
B = $11,966.11
Therefore, the PLUS Loan will have a higher balance due at the time of repayment by $233.80 ($11,966.11 - $11,732.31). Thus, the Unsubsidized Stafford Loan will have a lower balance due at the time of repayment compared to the PLUS Loan.
To know more about interest visit:
https://brainly.com/question/28792777
#SPJ1
EASY!! I ONLY NEED HELP WITH #39 & #40
39) The balance in the account after 6 years is $4,073.62.
40) The balance in the account after 6 years is $4,134.83
What is the formula for compound interest?
[tex]A = P(1 + \frac{r}{n} )^{(nt) }[/tex]
Here P is the principal,A is the balance, r is the annual interest rate, n is the number of times the interest is compounded per year, t is the time in years.
39) Here given that P = $3500, r = 2.16% = 0.0216, n = compounded quarterly = 4 and t = 6.
So, [tex]A = 3500(1 + \frac{0.0216}{4})^{(4 \times 6)} = 4,073.62[/tex]
Therefore, the balance in the account after 6 years is $4,073.62.
40)Here given,P = $3500, r = 2.29% = 0.0229, n = 12 (compounded monthly), and t = 6.
[tex]A = 3500(1 + \frac{0.0229}{12})^{(12 \times 6)} = 4,134.83[/tex]
Therefore, the balance in the account after 6 years is $4,134.83.
Learn more about compound interest here,
https://brainly.com/question/24274034
#SPJ1
or
Last night, Clara and her brother, Stefan, made personal pizzas for dinner. Clara put 4 pepperoni pieces and 6 ham pieces on her pizza. Stefan put 6 pepperoni pieces and 10 ham pieces on his pizza. Did Clara's and Stefan's pizzas have the same ratio of pepperoni pieces to ham pieces?
Clara's and Stefan's pizzas did not have the same ratio of pepperoni pieces to ham pieces.
How to calculate the ratios of two different pizza?For Clara,
The number of pepperoni pieces = 4
The number of ham pieces = 6
The ratio = 4:6 = 2:3
For Stefan,
The number of pepperoni piece = 6
The number of ham piece = 10
The ratio = 6:10 = 3:5
Therefore the ratio of Clara's and Stefan's pizzas is not the same.
Learn more about ratio here:
https://brainly.com/question/25927869
#SPJ1
George sold 18, 22, 26, 12, 25, 20, and 19 cars per month over the past seven months. He followed the steps below to determine the number of cars he needs to sell in the next month to have a mean number of sales per month of 24.Step 1: Find the total cars needed to have a mean of 24: .Step 2: Find the total cars sold: .Step 3: Subtract the total cars sold from the total cars needed: .Step 4: State the answer: George needs to sell 26 cars next month. Where did George make his first mistake?Step 1Step 2Step 3Step 4
George sold 18, 22, 26, 12, 25, 20, and 19 cars per month over the past seven months.
George's first mistake was in Step 1 where he tried to find the total number of cars he needs to sell in the next month to have a mean number of sales per month of 24. To find this value, George should have multiplied the desired mean number of sales per month (24) by the total number of months (7) to get the total number of cars needed to have a mean of 24 over 7 months. However, it seems that George skipped this step and directly assumed that the total number of cars needed for a mean of 24 in the next month is simply 24.
Let's go through each step to explain
Step 1 Find the total cars needed to have a mean of 24
To find the total number of cars George needs to sell over the next 7 months to have a mean of 24 cars sold per month, he should multiply the desired mean (24) by the number of months (7)
Total cars needed = 24 * 7 = 168
Step 2 Find the total cars sold
To find the total number of cars George sold over the past 7 months, he should add up the individual sales for each month:
Total cars sold = 18 + 22 + 26 + 12 + 25 + 20 + 19 = 142
Step 3 Subtract the total cars sold from the total cars needed
To find the number of cars George needs to sell in the next month to meet his target mean of 24 cars sold per month over the past 8 months, he should subtract the total number of cars sold from the total cars needed
Cars needed in the next month = Total cars needed - Total cars sold
Cars needed in the next month = 168 - 142 = 26
Step 4 State the answer
George needs to sell 26 cars next month to have a mean of 24 cars sold per month over the past 8 months.
Therefore, George's mistake was in Step 1 where he did not correctly calculate the total number of cars he needs to sell over the next 7 months to have a mean of 24 cars sold per month.
To know more about sold here
https://brainly.com/question/29180467
#SPJ1
What is 0.81818181818 as a fraction in its simplest
Marcia and Tamara are running a race. Marcia has run 4 kilometers. Tamara has completed 3/4 of the race and is 2.5 kilometers ahead of Marcia. Write an equation that represents the relationship between the distances each girl has run. Let k represent the total length of the race in kilometers.
The equation that represents the relationship between the distances each girl has run is: Marcia = -3/4 * k + 6.5
How to write an equation that represents the relationship between the distances each girl has runLet x be the distance run by Tamara in kilometers.
Since Tamara has completed 3/4 of the race, then x = 3/4 * k.
Since Tamara is 2.5 kilometers ahead of Marcia, then x - 2.5 = 4 - Marcia.
Substituting the first equation into the second equation, we get:
3/4 * k - 2.5 = 4 - Marcia
Multiplying both sides by -1, we get:
Marcia - 4 = -3/4 * k + 2.5
Adding 4 to both sides, we get:
Marcia = -3/4 * k + 6.5
Therefore, the equation that represents the relationship between the distances each girl has run is:
Marcia = -3/4 * k + 6.5
Learn more about equation at https://brainly.com/question/22688504
#SPJ1
Select all functions that have a y-intercept of 0,5. I need help (posts test!!!)
Select all that make a straight line.
The equations that will make a linear function are
1/8 + y = 9x = 16 + 3y8x - 5y = 30y = -6(x + 10)What is linear function?A linear equation, also referred to as a linear function in mathematics, is used to identify relationships between variables that can be plotted on a straight line.
This class of polynomial functions have a degree of 1, indicating that the highest power of the variable within the formula cannot exceed 1.
It takes on the standardized form:
y = mx + b
Learn more about linear function at
https://brainly.com/question/15602982
#SPJ1