The least amount of interest, if Pedro has a balance of $5810 on a credit card with an APR of 16.2%, is $78.345 for one month, so option A is correct.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given:
Pedro has a balance of $5810 on a credit card with an APR of 16.2%,
Calculate the simple interest for one month as shown below,
[tex]SI = P \times r \times t / 100[/tex]
SI = 5810 × 16. 2 × 1 / (12 ×100) [time in year = 1 / 12]
SI = $78.345
SI = 5810 × 16. 2 × 2 / (12 ×100) [For 2 months]
SI = $156.87
Therefore, the least amount of interest, if Pedro has a balance of $5810 on a credit card with an APR of 16.2%, is $78.345 for one month.
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The local bowling league had 48 bowlers during
the fall league. In the Spring there was a 25%
increase in the number of bowlers. How many
bowlers participated in the spring?
60 bowlers participated in the spring.
What is quotient?The local bowling league had 48 bowlers during the fall league. In the Spring there was a 25%increase in the number of bowlers.
The dividend is the number that is being divided (in this example, 15), and the divisor is the number that is being divided (in this case, 3). The Latin root of the term "quotient" is "quotiens," which means "how many times." The response to a division puzzle is a quotient. A division issue explains "how many times" one number may be divided by another.Formulate: based on the circumstances stated.
48 * ( 25% + 1 )
Determine the total or difference:
48 * 1.25
Determine the quotient or product:
60.
60 bowlers participated in the spring.
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What is the equation of a line passing through x1 y1 with slope?
The equation of a line passing through (x1, y1) is y - y1 = m(x - x1).
The equation of a line:
The equation of a line means an equation in x and y whose solution set is a line in the (x,y) plane. The most popular form in algebra is the "slope-intercept" form. y = mx + b. This in effect uses x as a parameter and writes y as a function of x: y = f(x) = mx+b.
Here we have to find the equation of a line passing through (x1, y1) and the slope.
Data given:
Point on the line = (x1, y1)
Slope = m
By this we get the equation of a line as:
y - y1 = m(x - x1)
Therefore the equation of a line is y - y1 = m(x-x1).
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6 deliveries in 2 hours = deliveries per hour
if you see this answer now please
The unit rate for the ratio 6 deliveries in 2 hours is 3 deliveries per hours
How to determine the unit rate for the ratio?From the question, we have the following parameters that can be used in our computation:
Ratio = 6 deliveries in 2 hours
The unit rate is simply the value of the above ratio
However, with a denominator of 1
This means that we evaluate the quotient in the above expression
So, we have the following representation
Ratio = 6 deliveries/2 hours
Express as unit rate
Unit rate = 3 deliveries per hours
Hence, the unit rate is 3 deliveries per hours
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If the exponential model f(x)=5(12)x is written with the base e, it will take the form a0ekx. What is a0 and what is k?.
The value of a₀ is 5 and value of k is 12 if the exponential model of 5 ˣ 12x is written with the base e.
Exponential models portray circumstances where the pace of progress of something is straightforwardly corresponding to the amount of that thing there is. In number related terms: dy dt = ky where dy dt is the pace of progress in a moment, y is how much what we're discussing right then and there, and k is the consistent of proportionality. We need to use logarithmic functions to evaluate the values.
We are given function in form of x which is f(x) = 5×12ˣ,it is equivalent to
=>f(x)=5 × expo(ln(12ˣ)
=>f(x) =5 ˣ [tex]e(^1^2)^x[/tex]
On comparing with the given equation - a₀[tex]e^(k)^x[/tex] ,we get
=>a₀=5 and k=12.
Hence, required values are 5 and 12,
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Lucinda has created a square pyramid mold for sand art. The sides of the base are each 11 inches, and the pyramid is 15 inches tall. Lucinda plans to full the pyramid three fourths full with colorful sand. How many cubic inches of the pyramid will contain sand?
Answer:
453.75
Step-by-step explanation:
To find the volume of a pyramid, we can use the formula V = (1/3)Bh, where V is the volume of the pyramid, B is the area of the base, and h is the height of the pyramid.
Since the base of the pyramid is a square, we can use the formula for the area of a square to find the area of the base. The formula for the area of a square is A = s^2, where A is the area of the square and s is the length of one side of the square. In this case, each side of the square base is 11 inches, so the area of the base is 11^2 = 121 square inches.
Now that we know the area of the base, we can use the volume formula to find the volume of the pyramid. The height of the pyramid is 15 inches, so the volume of the pyramid is V = (1/3) * 121 * 15 = 605 cubic inches.
Since Lucinda plans to fill the pyramid three fourths full with sand, the volume of the pyramid that will be filled with sand is 3/4 * 605 = <<3/4*605=453.75>>453.75 cubic inches.
Use the law of sines to solve for the variable
Answer:
y ≈ 60.6 units
Step-by-step explanation:
Given a triangle with angles 18° and 117°, and sides 21 opposite 18° and y opposite 117°, you want to know the value of y.
Law of sinesThe law of sines tells you the ratios of side length to the sine of the opposite angle are the same for all side/angle pairs in the triangle.
y/sin(117°) = 21/sin(18°)
y = 21·sin(117°)/sin(18°) ≈ 60.55
The value of y is about 60.6 units.
loser buys the pizza leona and fred are friendly competitors in high school. both are about to take the act college entrance examination. they agree that if one of them scores 5 or more points better than the other, the loser will buy the winner a pizza. suppose that in fact fred and leona have equal ability, so that each score varies normally with mean 24 and standard deviation 2. (the variation is due to luck in guessing and the accident of the specific questions being familiar to the student.) the two scores are independent. what is the probability that the scores differ by 5 or more points in either direction? follow the four-step process.
The probability that the scores differ by 5 or more points in either direction is 0.0764.
According to the Question,
the mean and standard deviation of are
μₓ = 24
σₓ = 2
We have to find the probability of the scores differ by or more points on either direction.
Considering the X₁ and X₂ as the random variable, the scores of Leon and Fred.
Define the variable:
D = X₁ - X₂
We have to find : P(IDI ≥ 5)
According to the Question, the two scores are independent
The mean of :
D : μₐ = 0
The standard deviation of :
D : σₐ = 2.828
Standardizing the mean and standard deviation:
D = -5
Z = X - μₐ / σₐ
= -5 -0 / 2.828
= -1.77
Now, we standardize
D = 5
Z = X - μₐ / σₐ
= 5 -0/ 2.828
= 1.77
Now,
Calculating the probability:
Using a table of typical normal probabilities as a guide,
P(D ≤ -5) or P(D ≥ 5)
= P ( z ≤ - 1.77) + P( z ≥ 1.77)
= P(z ≥ 1.77) + P(Z ≥ 1.77)
= 2P( z ≥ 1.77)
= 2[ 1 - p(z≤ 1.77)]
= 2[ 1 - 0.9618]
= 0.0764
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A batter hits a baseball with an initial horizontal speed of 74 mph and an initial rate of climb of 61 mph. how fast is the ball traveling when it leaves the bat? ____mph when the ball leaves the bat, what angle does it initially form with the horizon?___ ° in this context, gravity will change the ball's rate of climb over time but has no effect on the ball's horizontal speed. if the ball lands 2.851 seconds after it was hit, how many feet did the ball travel? (recall that there are 5,280 feet in one mile and 3600 seconds in one hour.) ______feet
The initial speed of the ball traveling when it leaves the bat is 95.9 mph and the angle at it initially forms with the horizon is 39.49°.
A parallelogram is a four-sided shape having two sets of parallel sides, with the opposite sides being equal in length and the angles opposite each other being equal. A triangle is a three-sided shape with three angles, the sum of which adds up to 180 degrees.
∠x + ∠y + ∠z = 180°
The baseball was hit by the batter with a starting speed of 74 miles per hour horizontally and a lift of 61 miles per hour. The initial speed
v = √(v(h)² + v(c)²)
v = √((74)² + (61)²)
v = 95.9 mph
The angle made will be -
Ф = tan⁻¹(61/74) = 39.49°
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5. The Nile River is 6,690.
kilometers long. This is 1,160
kilometers longer than the
Yangtze River. How long is the
Yangtze River?
The length of the Yangtze River is 5530 kilometers.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
Given that,
The length of the Nile river = 6,690 kilometers.
Also, The Nile river is 1,160 kilometers longer than the Yangtze River.
Let the length of Yangtze River is x kilometers,
Use equation format,
x + 1160 = 6690
x = 6690 - 1160
x = 5530
The length of the Yangtze River is 5530 kilometers.
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what is 3.944 rounded to the nearest hundreth?
the answer is 4
Step-by-step explanation:
how much cream that is 30% butterfat must be mixed with milk that is 3% butterfat to make 45 gallons of cream that is 12% butterfat?
15 gallons of 30% butterfat cream must be mixed with milk.
How to solve word problems?
It's actually fairly easy to solve word problems using a tried-and-true step-by-step approach.
Aloud to yourself, read the issue.Make a Drawing.Ask yourself, "What am I looking for?"List the items that have been provided.Locate the key phrases.Solve.Verify your work.If m is the gallons of 30% butterfat cream, and c is the gallons of 3% butterfat milk, then:
Let m be the milk and c be the cream:
m + c = 45 ⇒ (i)
0.03m + 0.3c = 0.12 * 45 ⇒ (ii)
Solve the system of equations with substitution or elimination. Using substitution:
0.30 m + 0.03 (45 − c) = 0.12 * 45
0.30 m + 1.35 − 0.03 c = 5.4
0.27 m = 4.05
m = 15
Hence, 15 gallons of 30% butterfat cream must be mixed with milk.
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What will happen to the object if the scale factor is greater than 1?
When the scale factor is greater than one, then the size of the object will enlarge
The scale factor is defined as the ratio of the new measurements of the object to the original measurements of the object
We can enlarge or shrink the size of the object by keeping the shape of the object same
The enlarge or shrink of he object can be determined by the value of scale factor
If the value of scale factor is between 0 and 1, then the object shirks and if the value of scale factor is greater than 1, then the object enlarge
Therefore, the size of the object will enlarge when the scale factor is greater than one
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a number of eggs,e ,divided 12
Answer: the answer is 1
Step-by-step explanation: if you divide 12 by 12
question 171 pts the annual salaries (in us dollars) of the registered nurses in two cities are given below. sample size sample mean sample sd city 1 12 66,000 1,100 city 2 12 68,000 2,200 test if the variances of the salary of the registered nurses in the two cities are the same. what is the value of the test statistic (write it up to second decimal place)? assume normal populations.
With a p-value of 0.000, the test statistic is 2.834.
what is test statistic?A statistical test's calculation of a number is known as a test statistic. It explains the distance between your observed data and the null hypothesis, which states that there is no correlation between the variables or difference between the sample groups,
given
sample size sample mean sample sd
City 1 12 66000 1100
City 2 12 68000 2200
mean is 71121 point ,41 standard deviation is sample size, the test hypothesis greater than 69110 point.
find dust statistics which are there , equation t, which equals x, bar minus mu, and sigma by rho type, is used to determine the test statistic.
The square root of 41 points equals minus 69110. Is it accurate that our test numbers come out to 1.719? Next, we need to determine the p value. P value is derived from x. Since our alpha in this instance is.05, our significance is more relevant than the p value.
Accordingly, there is little to no pay disparity between registered nurses in the two locations.
With a p-value of 0.000, the test statistic is 2.834.
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Is it true that f (0) = 0
Please help meeee !!!?!
Answer:
21
Step-by-step explanation:
For this problem, we basically want to find 2016/96.
2016=1920+96. So, 2016/96 = (1920+96)/96=20+1=21.
So, the hot air balloon travels 21 miles each hour.
''21'' because 2016 divided by 96 is 21
Solve for v.
3.8(v – 12.3) - 6.34 = 7.72
V =
Answer:
[tex]\boxed{\underline{\bf v=16}}[/tex]
Step-by-step explanation:
[tex]\tt 3.8\left(v-12.3\right)-6.34=7.72[/tex]
Simplify both sides of the equation:-
[tex]\tt 3.8(v-12.3)-6.34=7.72[/tex]
Distribute:-
[tex]\tt (3.8)(v)+(3.8)(-12.3)+-6.34=7.72[/tex]
[tex]\tt 3.8v+-46.74+-6.34=7.72[/tex]
Combine Like Terms:-
[tex]\tt (3.8v)+(-46.74+-6.34)=7.72[/tex]
[tex]\tt 3.8v+-53.08=7.72[/tex]
[tex]\tt 3.8v-53.08=7.72[/tex]
Add 53.08 to both sides:-
[tex]\tt 3.8v-53.08+53.08=7.72+53.08[/tex]
[tex]\tt 3.8v=60.8[/tex]
Divide both sides by 3.8:-
[tex]\tt \cfrac{3.8v}{3.8}=\cfrac{60.8}{3.8}[/tex]
[tex]\tt v=16[/tex]
______________________
Hope this helps!
Have a great day!
find the average speed of a world-class sprinter (to the nearest tenth) if he runs 100 yards in 10 sec
The Average speed of a world class sprinter, is he runs 100 yards in 10 sec is 36 km/h.
If an athlete can run 100 meters in 10 seconds, It is said that he cannot run 10 meters in one second. That may also apply to the physical world we live in. But you clearly state that you want to say mathematically whether he ran 10 meters in his 1 second.
If a sprinter runs 100 meters in 10 seconds, then, First, we need to convert meters to kilometers and seconds to hours. 1 meter = 1/1000 kilometers 100 meters = 100/1000 kilometers = 1/10 = 0.1 kilometers 1 second = 1/3600 hours 10 seconds = 10/3600 = 1/360 hours.
Now,
According to the question:
Given that,
Distance covered by sprinkler = 100m
Time taken by sprinkler = 10 seconds
Using the equation of velocity
Distance/ Time = velocity
Now, substituting the values -
= 100/10
= 10
Thus, the velocity is 10m/s
To convert it into m/s in to km/h -
= (10/1000) x 3600
= 36000/1000
= 36
Therefore, The average velocity of sprinkler is 36 km/h
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The ratio of Marta’s hourly pay to Khalid’s hourly pay is 6 : 5
Both Marta and Khalid get an increase of £1.50 in their hourly pay.
The ratio of Marta’s hourly pay to Khalid’s hourly pay after this increase is 13 : 11
Work out the hourly pay before the increase for Marta and for Khalid
The hourly pay before the increase for Marta and for Khalid is $18 and $15 respectively.
Given that, the ratio of Marta’s hourly pay to Khalid’s hourly pay is 6:5.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Now, Marta’s hourly pay is 6x and Khalid’s hourly pay is 5x
Both Marta and Khalid get an increase of £1.50 in their hourly pay.
So, Marta’s hourly pay will be 6x+1.50 and Khalid’s hourly pay will be 5x+1.50
The ratio of Marta’s hourly pay to Khalid’s hourly pay after this increase is 13:11
Here, (6x+1.50)/(5x+1.50) =13/11
11(6x+1.50)=13(5x+1.50)
⇒ 66x+16.5=65x+19.5
⇒ x=3
So, Marta’s hourly pay is $18 and Khalid’s hourly pay is $15
Therefore, the hourly pay before the increase for Marta and for Khalid is $18 and $15 respectively.
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May someone please help me out with this
Answer:
S=7
t=1
Step-by-step explanation:
Since we need to make these triangles congruent, s+36=43, and t+39=40. Solve for s by subtracting 36 from both sides of the equation (s+36-36=43-36 s=7), then solve for t by subtracting 39 from both sides (t+39-39=40-39 t=1)
-Hope this helped & Happy Holidays!
What value of n makes the equation true?
2/3n = -12
n=
Answer:
-18
Step-by-step explanation:
[tex]\frac{2}{3}n=-12 \\ \\ \frac{3}{2} \cdot \frac{2}{3}n=\frac{3}{2}(-12) \\ \\ n=-18[/tex]
Find the absolute value. What is 1/4
Answer:
0.25
Step-by-step explanation:
:)
Answer: the absolute value of 1/4 is 1
Step-by-step explanation:
jaci runs cross country for her high school. on average she runs 6 minutes per mile
The minutes that is used by Jaci to run 240 miles is 40 minutes.
How to calculate the number of minutes?Expression simply refers to the mathematical statements which have at least two terms that are related by an operator and contain either numbers, variables, or both. An average is one number chosen to represent a group of numbers; it is typically the sum of the numbers divided by the number of numbers in the group. By adding a group of numbers and then dividing by their count, the average, or arithmetic mean, is determined.
In this case, Jaci runs cross country for her high school. on average she runs 6 minutes per mile.
The minutes used to run 240 miles will be Total minutes divided by Speed:
= Total minutes / Speed
= 240 / 6
= 40 minutes
40 minutes is the amount of time Jaci spent running 240 miles.
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Complete question
jaci runs cross country for her high school. on average she runs 6 minutes per mile. What is the minutes used to ran 240 miles?
The drone rises 16 feet every 4 seconds. After 5 seconds, the drone is at a height of 26 feet.
Answer:the answer is 16 feet
Step-by-step explanation:
100 POINTS HELP ME Multinational businesses usually have a main office in their home location. What is this called?
A. home locale
B. subsidiary
C. headquarters
Answer:
C
Step-by-step explanation:
Everything else doesn't really make sense
Answer:
C. headquarters
Step-by-step explanation:
is the correct answer. A headquarters is the main office or center of operations for a business, particularly a large multinational corporation. A subsidiary, on the other hand, is a company that is owned or controlled by another company, often referred to as the parent company or holding company. A home locale is not a commonly used term in business, but it could refer to the location where a company is based or originated.
how does omega change over time?how does omega change over time?it increases proportionally with a.it decreases proportionally with a.it increases quadratically with time.it decreases as a increases.
As the time increases, the angular velocity i.e. omega also increases quadratically with time.
Given,
From the figure,
Radius of wheel = 0.2 m
Acceleration, a = 4t m/s^2
then the angular acceleration of wheel can be determined by formula,
[tex]a=\alpha * r[/tex]
Where, r=radius of wheel =0.2 m
[tex]4t=\alpha * 0.2\\20t=\alpha[/tex]
We know that the angular acceleration is the change in angular velocity over time.
[tex]\alpha=\frac{d\omega}{dt}\\\\20t=\frac{d\omega}{dt}\\\\d\omega=20tdt\\\\\omega=\int\limits^t_0 {20t} \, dt \\\\\omega=\frac{20t^2}{2}-0\\\\\omega=10t^2[/tex]
From the above equation it is clear that omega i.e. angular velocity is dependent of time
omega is directly proportional to square of time
For
t=1 then ω=10
t=2 then ω=10(4)=40
t=3 then ω=10(9)=90.....and so on.
It means as time increases, then angular velocity also increases quadratically with time.
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Your question is incomplete, here is the complete question.
When a body rotates about fixed axis , any point located in the body travels along the circular path. the angular acceleration α measures the rate of change of angular velocity. A cord is wrapped around a wheel, which is initially at rest when θ=0. The force F gives the cord an acceleration [tex]a= 4t\ m/s^2.[/tex]
How does omega change over time?
It increases proportionally with a. It decreases proportionally with a. It increases quadratically with time. It decreases as a increases.Consider the following expression and the simplified expression. Expression simplified expression 3 x squared + 5 y squared box + 3 box + 4 y squared + 6 9 x squared minus y squared + 9 which terms could be in the boxes to make the expressions equivalent?.
The simplified expression for the given problem will be :6x² and -10y²
Since the expression given to us is :
3 x² + 5 y²[] + 3 [] + 4 y²+ 6
= 3 x² + 5 y² + 4 y²[][]+6+3
=>3 x² + 9 y² [][]+9
The above equation is equal to 9 x²- y² + 9
=> 3 x² + 9 y² [][]+9 =9 x^2- y^2 + 9
now Equating the coefficients of x²and y² in LHS and RHS:
One box has = 9 x²- y²= +6x²
and the other will have = -y²- 9 = -10y²
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How to do product and quotient
1. To multiply two powers with the same base, we add their exponents.
2. An expression that you could simplify using the quotient of powers property is of: 3³/3² = 3.
The results of the expressions are given as follows:
3. 4^11.
4. 5^11.
5. 6^8.
6. 7^9.
What are the exponential rules for product and quotient?When two or more terms have the same base and different exponents and then are multiplied, the base is kept while the exponents are added.
When two terms have the same base and different exponents and then are divided, the base is kept while the exponents are subtracted.
The multiplication rule is used for each of the items from 3 to 6, as:
3. 4^11, as 2 + 9 = 11.
4. 5^11, as 3 + 8 = 11.
5. 6^8, as 7 + 1 = 8.
6. 7^9, as 3 + 4 + 2 = 9.
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Determine each feature of the graph of the given function.
f(x) = -5+10
2
Horizontal Asymptote: y =
Vertical Asymptote: x =
x-Intercept:
y-Intercept: (0,
Hole: (
,0)
No horizontal asymptote
No vertical asymptote
No x-intercept
No y-intercept
No hole
The features of the function are given as follows:
Horizontal asymptote: y = 5.Vertical asymptote: x = 2.x-intercept: No x-intercept.y-intercept: (0,-5).Hole: No holes.What are the features of the function?The horizontal asymptote is the limit of f(x) as x goes to infinity. To obtain this limit, we consider only the terms with the highest exponent of the numerator and of the denominator, hence:
g(x) = -5x/x -> y = 5 is the horizontal asymptote.
The vertical asymptote is the value of x for which the function is not defined, hence it is the zero of the denominator, thus:
x - 2 = 0 -> x = 2.
The x-intercept is the point (x,0), in which x is found when y = 0, hence:
-5x + 10 = 0
-5x = -10
5x = 10
x = 2.
However, the function is not defined at x = 2, meaning that it has no x-intercept.
The y-intercept is the value of y when x = 0, hence:
y = 10/-2 = -5.
The coordinates are (0,-5).
The entire function can be simplified as follows:
(-5x + 10)/(x - 2) = [-5(x - 2)]/(x - 2) = -5.
Meaning that the function has no holes.
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What is the equation of line passing through 3 4 and having slope 3 2?
The equation of the line passing through (3,4) and having slope m = 3/2 is y = 3/2x + 4.
Given points : (3,4)
The equation of a line with slope 3/2 and passing through point (3,4) is y = 3/2x + 4. This equation can be used to calculate the y-coordinate of any point on the line, given its x-coordinate. For example, if the x-coordinate of a point is 6, then its corresponding y-coordinate is 11. In general, for any x-coordinate, the corresponding y-coordinate is given by 3/2 times the x-coordinate plus 4.
Given slope : m = 3/2
We know that the equation of a line with slope m and passing through point (x1, y1)is given by :
y - y1 = m(x - x1)
Substituting the given values, we get
y - 4 = 3/2(x - 3)
Simplifying equation, we get
y = 3/2x + 4
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