Answer:
B 40 yards for $45 is the best deal at $1.13 per yard
Step-by-step explanation:
Break it down by finding the unit price per yard (divide cost by yardage)
A. 30/20 = $1.50 per yard
B. 45/40 = $1.125 per yard
C. 70/50 = $1.40 per yard
D. 85/65 = $1.30 per yard
Answer:a
Step-by-step explanation:
A small box of raspberries costs $2. A large box of raspberries costs $6. Use this information to complete the sentence below.
What sentence below
Tom walks 1/3 of a mile in 1/4 of an hour. At this rate, how many miles will tom walk in 1 hour ?
Tom walks at a rate of 4/3 miles per hour, which means he will walk 1.333 miles in one hour at this rate.
To find out how many miles Tom will walk in 1 hour, we need to determine the distance he covers in 1/4 of an hour and then calculate how much he would walk in 1 hour at that rate.
Given Tom walks 1/3 of a mile in 1/4 of an hour, first find how much he walks in 1 hour:
1/3 mile ÷ (1/4 hour) = 1/3 mile * 4/1 hour = 4/3 miles in 1 hour
Therefore, Tom will walk 4/3 miles in 1 hour at that pace.
Tom would walk 4/3 miles or 1 and 1/3 miles in 1 hour given that he walks 1/3 of a mile in 1/4 of an hour based on the unit rate calculation.
The question deals with finding out how many miles Tom will walk in 1 hour if he walks 1/3 of a mile in 1/4 of an hour. To calculate this, we use the concept of a unit rate, which is finding how much of something is done in one unit of something else, in this case, miles per hour. Since Tom walks 1/3 of a mile in 1/4 of an hour, we can set up a proportion to find out how many miles he would walk in 1 full hour.
The proportion is: (1/3) miles / (1/4) hour = x miles / 1 hour. To solve for x, we multiply both sides of the equation by 1 hour so x would equal (1/3) miles \/ (1/4) hour. To simplify the right side, we invert the fraction in the denominator and multiply:
x = (1/3) miles \/ (1/4). When we multiply by the reciprocal of 1/4, which is 4, we get x = (1/3) \/ 1 \/ 4 = 4/3 miles.
Therefore, at this rate, Tom would walk 4/3 miles or 1 and 1/3 miles in 1 hour.
What are the different measurements for angles and how do we convert between them? Explain with examples of your own.
Angles are usually given in degrees or in radians.
A circle is 360 degrees.
To convert degrees to radians, multiply the known degree by π/180.
Example 45 degrees = 45 x π/180 = 0.7854 radians.
To convert radians to degrees, multiply the known radian by 180/π.
5 radian = 5 x 180/π = 286.48 degrees.
The correlation between the measurements is written below.
What is an Angle ?An angle is a combination of two rays with a common endpoint.
The endpoint is called as the vertex of the angle,the rays are called the sides.
The various units in which angle is measure are Degree, radians and revolutions
A revolution is the measure of an angle formed when the initial side rotates all the way around its vertex until it reaches its initial position
One radian (1 rad) is the measure of the central angle (an angle whose vertex is the center of a circle) that intercepts an arc whose length is equal to the radius of the circle.
A degree is equal to 360 revolutions.
The correlation between the measurements can be written as
[tex]\rm 1 \;radian =(\dfrac{180}{\pi })^o = \dfrac{1}{2\pi } revolution[/tex]
For example 30° = π/6 radian = 1/12 revolutions
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1. C = 2(pi)r and C = d(pi) are the formulas for finding the _____________ of a circle.
Answer:
Circumference
Step-by-step explanation:
The circumference is the distance around the circle. It relates the number of times the diameter will encircle the circumference as 3.14 or π. As a result, the formulas for the circumference of a circle are C = 2πr and C = πd.
Please help me out with this question, THANKS!
Answer:
line B.)
Step-by-step explanation:
2x+5y=10
5y=-2x+20
(5y/5) (2x+10/5)
y= (-2/5)x +2
Andrew plays 1/4 of a song in 1/8 of a minute. How much time, in minutes, does it take him to play an entire song?
1/4 = 1/8
times by 4 to find the whole song as 1/4 × 4 is 1
1 = 4/8
4/8 = 1/2 of a minute
PLEASE HELP What is the radical form of the expression 423 ? 43−−√ 34−−√ 42−−√3 24−−√3
For this case we must express the number "423" in a radical way.
We have to, we can rewrite it as:
[tex]423 = 9 * 47 = 3 ^ 2 * 47[/tex]
So, we have to:
[tex]423 = \sqrt {3 ^ 2 * 47}[/tex]
By definition of properties of powers and roots we have:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So:
[tex]423 = \sqrt {3 ^ 2 * 47} = 3 \sqrt {47}[/tex]
Answer:
[tex]3 \sqrt {47}[/tex]
Answer:
3^√4^2
Step-by-step explanation:
Solve each equation (Isolating first)
[tex]3[/tex] · [tex](\frac{1}{8})^{2x} = 12[/tex]
[tex]2[/tex] ·[tex](\sqrt[3]{5})^{4x} = 50[/tex]
[tex]3 \times {( \frac{1}{8} )}^{2x} = 12 \\ \Leftrightarrow {( \frac{1}{8} )}^{2x} = 4 \\ \Leftrightarrow {( {2}^{ - 3}) }^{2x} = {2}^{2} \\ \Leftrightarrow {2}^{ - 6x} = {2}^{2} \\ \Leftrightarrow - 6x = 2 \\ \Leftrightarrow x = - \frac{1}{3} \\ \\ 2 {\sqrt[3]{5}}^{4x} = 50 \\ \Leftrightarrow { \sqrt[3]{5} }^{4x} = 25 \\ \Leftrightarrow {5}^{ \frac{4x}{3} } = {5}^{2} \\ \Leftrightarrow \frac{4x}{3} = 2 \\ \Leftrightarrow 4x = 6 \\ \Leftrightarrow x = \frac{3}{2} [/tex]
Answer to Q1:
x= -1/3
Step-by-step explanation:
We have given the equations.
We have to solve these equations.
The first equation is :
[tex]3.(\frac{1}{8})^{2x}[/tex]
[tex](\frac{1}{8})^{2x}=4[/tex]
[tex](2^{-3x})^{2x}=4[/tex]
[tex]2^{-6x}=4[/tex]
[tex]2^{-6x}=2^{2}[/tex]
As we know that bases are same then exponents are equal.
-6x = 2
x = 2/-6
x=-1/3
Answer to Q2:
x = 3/2
Step-by-step explanation:
The given equation is :
[tex]2.\sqrt[3]{5}^{4x}=50[/tex]
We have to find the value of x.
First,we multiply both sides of equation by 1/2 we get,
[tex]5^{4x/3}=25[/tex]
[tex]5^{4x/3}=5^{2}[/tex]
4x/3=2
4x = 6
x = 3/2
about what point on parabola y=x^2 is 5 units away from the origin along the curve
the distance from the origin is 5, so
sqrt(x²+y²)=5
x²+y²=25
substitue y=x²
y+y²=25
y²+y-25=0
solve using calculator or the formula
to get
y =( -1+sqrt(1+4*25))/2
or y = (-1-sqrt(1+4*25))/2
the second solution is rejected because a square cannot be negative
the value of x is the positive or negative (sqrt... or -sqrt...) or y
Two less than 3 times a number is the same as the number plus 10. What is the number?
This should help
3 * a - 2 = a + 10
HELP PLEASE!!!!!!!!!!!!!!MATH IS HARDDDDDDDDDDDDDD
Answer:
92
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
140 = x+2 + 2x
Combine like terms
140 = 3x +2
Subtract 2 from each side
140-2 = 3x+2-2
138 = 3x
Divide by 3
138/3 = 3x/3
46=x
We want to find angle B
B = 2x
B = 2(46)
B = 92
PLEASE HELP!!!
Is investing $4,000 at an interest rate of 5% (compounded annually) and $4,000 at an interest rate of 7% (compounded annually) always, sometimes, or never the same as investing $8,000 (the total of the two principals) at an interest rate of 6% (compounded annually)? Why or why not? Does it matter how long you leave it in the account?
Explain using words and examples, and justify your answer.
No, it is not the same because in option 1, the interest is calculated based on two different principal amounts and then added together. The principal amounts will be different every year because of the varying interest rates. Since one of the interest rates in option 1 is 7%, the principal will grow at a faster rate because the interest rate is applied to a greater and greater principal amount over time. In option 2, the interest is being calculated only on one principal
Answer:
Step-by-step explanation:
No, they are not always the same - the only time that they will be the same is after the first year:
$4000*1.05 + $4000*1.07 = $8480 = $8000*1.06
From there on, they will diverge. For example after the second year:
$4000*1.05^2 + $4000*1.07^2 = $8989.6
$8000*1.06^2 = $8988.8
After the third year:
$4000*1.05^3 + $4000*1.07^3 = $9530.672
$8000*1.06^3 = $9528.128
After the nth year:
The first option gives $4000*(1.05^n + 1.07^n)
The second option gives $8000*(1.06^n)
= $4000*(2)*(1.06^n)
= $4000*(1.06^n + 1.06^n)
Because 1.07^n - 1.06^n > 1.06^n - 1.05^n for n>1, the first option will be a better investment.
The Homerun Hitter's Academy charges thirty-five dollars per hour for batting lessons, with a registration fee of fifteen dollars per year. Janice's parents paid $155 in the month of August.
Answer:
Step-by-step explanation:
If you are asking how many hours she spent on the batting lessons, we can use an equation to solve this type of problem.
Lets represent the hours she spent batting in august with h.
$35h+15=$155
Since each hour costs 35 dollars, its reasonable that $35 times the number of hours she spent practicing would be the correct way to represent that.
Now, lets solve.
Subtract 15 on both sides.
$35h=$140
Divide both sides by 35 to isolate h.
h=4
She spent four hours on batting lessons that month.
Hope this helps!
The number of hours will be 4 hours.
Let the number of hours used be represented by h.
Based on the question, the equation that will be used in solving the question will be:
15 + (35 × h) = 155
15 + 35h = 155
Collect like terms.
35h = 155 - 15
35h = 140
Divide both side by 35
35h/35 = 140/35.
h = 4.
The number of hours is 4 hours.
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Determine the values. The value of x is . The measure of is degrees. The measure of is degrees.
Answer:
X= 5
EF= 58 degrees
GH= 55 degrees
Step-by-step explanation:
Answers on edg.
Answer:
14
Step-by-step explanation:
Need help ASAP
What is the area of this triangle
Enter your answer as a decimal in the box
[tex]\boxed{A=43.54cm^2}[/tex]
Step-by-step explanation:To find this area we will use the law of cosine and the Heron's formula. First of all, let't find the unknown side using the law of cosine:
[tex]x^2=12^2+8^2-2(12)(8)cos(65^{\circ}) \\ \\ x^2=144+64-192(0.42) \\ \\ x^2=208-80.64 \\ \\ x^2=127.36 \\ \\ x=\sqrt{127.36} \\ \\ \therefore \boxed{x=11.28cm}[/tex]
Heron's formula (also called hero's formula) is used to find the area of a triangle using the triangle's side lengths and the semiperimeter. A polygon's semiperimeter s is half its perimeter. So the area of a triangle can be found by:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex] being [tex]a,\:b\:and\:c[/tex] the corresponding sides of the triangle.
So the semiperimeter is:
[tex]s=\frac{12+8+11.28}{2} \\ \\ s=15.64cm[/tex]
So the area is:
[tex]A=\sqrt{15.64(15.64-12)(15.64-8)(15.64-11.28)} \\ \\ \therefore \boxed{A=43.54cm^2}[/tex]
To fill a planting bed, Mr.Carver uses 5 buckets of soil to 4 buckets peat moss. He needs to use 324 buckets in all to fill the bed. How many buckets of soil and peat moss will he use?
please help bc i am kristinas little sister :(
Buckets of Soil : Buckets of Peat Moss = 5 : 4
Since Mr Carver needs to use 324 buckets in all,
He needs to use 324 * 5/9 = 180 buckets of Soil and 324 * 4/9 = 144 buckets of Peat Moss.
Mr. Carver will use 180 buckets of soil and 144 buckets of peat moss to fill the planting bed, based on the given ratio of 5 buckets of soil to 4 buckets of peat moss.
The problem at hand revolves around ratios and proportions where Mr. Carver is using a mix of soil and peat moss in a specific ratio to fill a planting bed. Given the ratio of 5 buckets of soil to 4 buckets of peat moss, we need to find the total number of buckets for each that will sum up to 324 buckets. First, we'll find the total number of parts in the ratio by adding 5 (for soil) and 4 (for peat moss), which gives us 9 parts. Since we have the total amount of 324 buckets, we can find the value of one part by dividing 324 by 9, which gives us 36.
Once we have the value of one part, we multiply it by the number of parts for soil and peat moss to find their respective quantities:
Soil: 5 parts x 36 buckets per part = 180 bucketsPeat moss: 4 parts x 36 buckets per part = 144 bucketsTherefore, Mr. Carver will use 180 buckets of soil and 144 buckets of peat moss to fill the planting bed.
Please help me with this :)
Answer:
It is the answer C
Step-by-step explanation:
Sphere A is similar to sphere B. If the radius of sphere A is 3 times the radius of sphere B, then the volume of sphere A is times the volume of sphere B.
Answer:
27 times
Step-by-step explanation:
Given that sphere A is similar to sphere B
Let radius of sphere B be x. Then the radius of
sphere A be 3 times radius of sphere B = 3x
Volume of sphere A = [tex]V_A=\frac{4}{3} \pi (3x)^3\\V_A=36 \pi x^3[/tex]
Volume of sphere B = [tex]V_B = \frac{4}{3} \pi x^3[/tex]
Ratio would be
[tex]\frac{V_A}{V_B} =\frac{36 \pi x^3}{\frac{4}{3}\pi x^3 } \\=27[/tex]
i.e. volume of sphere is 27 times volume of sphere B.
Answer: 27
Step-by-step explanation: ANSWER ON EDMENTUM/PLUTO
What is the slope-intercept form of the function that contains the points (6, 2) and (4, 8)?
Answer:
y = -3x + 20
Step-by-step explanation:
See attached photo for explanation
(0.0196N) x (0.016m) =
Answer: [tex]0.0003136\ J[/tex] or [tex]3.136*10^{-4}J[/tex]
Step-by-step explanation:
By definiition, when you multiply 1 Newton (N) by 1 meter (m), the unit obtained is an unit called "Joule", whose symbol is J.
Joule (J) is an unit of energy, work or heat.
Then to solve the exercise, you must multiply 0.0196 N by 0.016 m. Therefore, you obtain that the product is:
[tex](0.0196N)(0.016m)=0.0003136J[/tex] or [tex]3.136*10^{-4}J[/tex]
Answer: 0.000314mn
Step-by-step explanation:
(0.0196N)*(0.016M)
0.000314mn
Find the circumference of the circle in terms of pi? [30]
Answer:
60π
Step-by-step explanation:
If the circle has radius of 30 units, substitute r=30 into the formula C = 2πr.
C = 2π(30)
C = 60π
To find the circumference of the circle shown here, let's start with writing the formula down.
Circumference = 2[tex]\pi[/tex]r
We have to divide 60 by 2 because the radius is always half the diameter. Now, we can plug in 30 for r in the formula.
Now we have
circumference = 2[tex]\pi[/tex]30.
This equals 60[tex]\pi[/tex].
Please answer this question, will give brainliest!
Answer:
MN = 9.1 cmStep-by-step explanation:
If MN is tangent of a circle then the angle M is a right angle.
We have a dimeter of acircle d = 8 cm.
Therefore the radius CM = 8 cm : 2 = 4cm.
In a right triangle CMN use the Pythagorean theorem:
[tex]CM^2+MN^2=CN^2[/tex]
Substitute CM = 4cm and CN = 9.9 cm:
[tex]4^2+MN^2=9.9^2[/tex]
[tex]16+MN^2=98.01[/tex] subtract 16 from both sides
[tex]MN^2=82.01\to MN=\sqrt{82.1}\\\\MN\approx9.1[/tex]
At t=0, a rock is dropped from rest from the top of a building 256 ft high. With what velocity will it strike the ground? What is it acceleration
Answer:
128 ft / second.
Step-by-step explanation:
It's acceleration is due to gravity and is 32 ft s^-2.
To find the velocity when it hits the ground we use the equation of motion
v^2 = u^2 + 2gs where u = initial velocity, g = acceleration , s = distance.
v^2 = 0^2 + 2 * 32 * 256
v^2 = 16384
v = 128 ft s^-1.
The rock will strike the ground with a velocity of 128 ft/s and will experience an acceleration of 32 ft/s^2.
Explanation:First, we need to calculate the time it takes for the rock to fall to the ground. We can use the equation h = (1/2)gt^2, where h is the height of the building (256 ft) and g is the acceleration due to gravity (32 ft/s^2). Solving for t, we find t = sqrt(2h/g) = sqrt(2(256)/32) = 4 seconds.
Next, we can calculate the velocity of the rock just before it hits the ground. We can use the equation v = gt, where g is the acceleration due to gravity and t is the time it takes to fall (4 seconds). Plugging in the values, we find v = (32 ft/s^2)(4s) = 128 ft/s.
Lastly, the acceleration of the rock is equal to the acceleration due to gravity, which is 32 ft/s^2.
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Petra wants to buy a skateboard. The skateboard deck usually costs $37.50, but it is on sale for 20% off. If the sales tax rate is 5.2%, how much will Petra pay for the skateboard deck in all?
A. $30.00
B. $31.56
C. $31.95
D. $39.45
Answer:31.56
Step-by-step explanation:
take 37.50 and divide it by 100
then multiply that by 80
you should get 30,
30 is 80% of 37.50 which is 20% off of the original price
then you divide 30 by 100 and multiply it by 5.2
this will get you 1.56
add that to 30 and you get 31.56
Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph.
y= -7 sec x
Answer:
Option c. Reflection across the x-axis and vertical stretch by a factor of 7
Step-by-step explanation:
If the graph of the function [tex]y = cf(x)[/tex] represents the transformations made to the graph of [tex]y = f(x)[/tex] then, by definition:
If [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor a.
If [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor a.
If [tex]c <0[/tex] then the graph is reflected on the x axis.
In this problem we have the function [tex]y = -7secx[/tex] and our paretn function is [tex]y = secx[/tex]
therefore it is true that
[tex]c = -7\\\\|-7|> 1\\\\-7 <0[/tex].
Therefore the graph of [tex]y = secx[/tex] is stretched vertically by a factor of 7 and is reflected on the x-axis
Finally the answer is Option c
Determine all numbers at which the function is continuous.
If the graph of any function is an unbroken curve, then the function is continuous. Let's study the function at the the point [/tex]x=5[/tex]:
At this point the function has the following value:
[tex]f(5)=-\frac{3}{4}[/tex], so the function in fact exists here, but let's find the limit here using:
[tex]f(x)=\frac{x^2-7x+10}{x^2-14x+45}[/tex]
So:
[tex]\underset{x\rightarrow5}{lim}\frac{x^2-7x+10}{x^2-14x+45}[/tex]
By factoring out this function we have:
[tex]\underset{x\rightarrow5}{lim}\frac{(x-2)(x-5)}{(x-5)(x-9)} \\ \\ \therefore \underset{x\rightarrow5}{lim}\frac{(x-2)}{(x-9)} \\ \\ \therefore \frac{(5-2)}{(5-9)}=-\frac{3}{4}[/tex]
Since [tex]\underset{x\rightarrow5}{lim}f(x)=f(5)[/tex] then the function is continuous here.
Let's come back to our function:
[tex]f(x)=\frac{x^2-7x+10}{x^2-14x+45}[/tex]
If we factor out this function we get:
[tex]f(x)=\frac{(x-2)}{(x-9)}[/tex]
Notice that at x = 9 the denominator becomes 0 implying that at this x-value there is a vertical asymptote. The graph of this function is shown below and you can see that at x = 9 the function is not continous
Therefore, the answer is:
b. continous at every point exept [tex]x=9[/tex]
Answer:
B: continuous at every real number except x = 9
Step-by-step explanation: EDGE 2020
Given F= {(0,1), (2,4), (4,6), (6,8)} and G= {(2,5), (4,7), (5,8), (6,9), (7,5)}(F-G) (6)
Answer:
(F-G)(x) = -1
Step-by-step explanation:
The notation (F - G)(x) means to subtract each function when x = 6. According to the sets when x = 6 then F is (6,8) and G is (6,9). To subtract the functions, subtract their output values. (F-G)(x) = 8 - 9 = -1.
Solve the differential equation by variation of parameters, subject to the initial conditions y(0) = 1, y'(0) = 0. 36y'' − y = xex/6
The homogeneous ODE
[tex]36y''-y=0[/tex]
has characteristic equation
[tex]36r^2-1=0[/tex]
with roots at [tex]r=\pm\dfrac16[/tex], and admits two linearly independent solutions,
[tex]y_1=e^{x/6}[/tex]
[tex]y_2=e^{-x/6}[/tex]
as the Wronskian is
[tex]W(y_1,y_2)=\begin{vmatrix}e^{x/6}&e^{-x/6}\\\\\dfrac16e^{x/6}&-\dfrac16e^{-x/6}\end{vmatrix}=-\dfrac13\neq0[/tex]
Variation of parameters has us looking for solutions of the form
[tex]y_p=u_1y_1+u_2y_2[/tex]
such that
[tex]u_1=-\displaystyle\int\frac{y_2xe^{x/6}}{W(y_1,y_2)}\,\mathrm dx[/tex]
[tex]u_2=\displaystyle\int\frac{y_1xe^{x/6}}{W(y_1,y_2)}\,\mathrm dx[/tex]
We have
[tex]u_1=\displaystyle3\int x\,\mathrm dx=\dfrac{3x^2}2[/tex]
[tex]u_2=\displaystyle-3\int xe^{x/3}\,\mathrm dx=-9e^{x/3}(x-3)[/tex]
and we get
[tex]y_p=\dfrac{3x^2e^{x/6}}2-9e^{x/6}(x-3)[/tex]
The general solution is
[tex]y=y_c+y_p[/tex]
[tex]y=C_1e^{x/6}+C_2e^{-x/6}+\dfrac{3x^2e^{x/6}}2-9e^{x/6}(x-3)[/tex]
The initial conditions tell us
[tex]\begin{cases}1=C_1+C_2+27\\\\0=\dfrac{C_1}6-\dfrac{C_2}6-\dfrac92\end{cases}\implies C_1=\dfrac12,C_2=-\dfrac{53}2[/tex]
so that the particular solution is
[tex]y=\dfrac12e^{x/6}-\dfrac{53}2e^{-x/6}+\dfrac32x^2e^{x/6}-9e^{x/6}(x-3)[/tex]
Maria did the work to see if 8 is a solution to the equation s-3=11.
s-3=11
8-3=11
5=11
Does her work show that 8 a solution to the equation?
A.)Yes, because the last line of the work is true.
B.)Yes, because 11 minus 8 equals 3.
C.)No, because 8 is even and the other numbers in the equation are odd.
D.)No, because the last line of the work is not true. 5 and 11 are not equal.
Answer: Option D.
Step-by-step explanation:
The expressions of boths sides of the equation must have the same value Or, in other words, if we call the expresion on the left side of the equation A, and the expression on the right side of the equation B, then:
[tex]A=B[/tex]
Keeping the above on mind, you can see that 5 and 11 are not equal, then:
5≠11
The correct value of s is:
[tex]s-3=11\\s=11+3\\s=14[/tex]
Substituting:
[tex]14-3=11\\11=11[/tex]
Answer:
No, because the last line of the work is not true. 5 and 11 are not equal.
Step-by-step explanation:
The discriminant of the function is_