a cell phone company offers two different monthly plans.plan a charges $41 for unlimited cell phone minutes plus $0.10 per text message.Plan b charges $31 for unlimited cell phone minutes plus $0.15 per text message.How many text messages must a customer send in order for the cost of plan a to be equal to cost of plan b
41+0.10x = 31+0.15x
10 +0.10x=0.15x
10=0.05x
x=10/.05
x= 200 text messages
check 200*0.10 = 20 +41 =61
200*0.15 = 30+31 = 61
they equal each other so number of texts is 200
A customer must send 200 text messages for the cost of Plan A ($41 plus $0.10 per text) to be equal to the cost of Plan B ($31 plus $0.15 per text).
To find out how many text messages a customer must send for the cost of Plan A to be equal to the cost of Plan B, we can set up an equation based on the cost structures given. Let x be the number of text messages sent.
Cost of Plan A: $41 + $0.10x
Cost of Plan B: $31 + $0.15x
To find the point where both plans cost the same, we set the costs equal to each other:
41 + 0.10x = 31 + 0.15x
Solving the equation:
0.05x = 10
x = 10 / 0.05
x = 200
The customer must send 200 text messages for the costs of Plan A and Plan B to be equal.
An isosceles triangle has a base with length 15 inches and two congruent sides with lengths of 15 inches each. Find the height of the triangle. (Round your answer to the nearest tenth of an inch.)
Final answer:
By using the Pythagorean theorem on one of the right triangles formed by dividing the isosceles triangle, we find the height to be approximately 13.0 inches when rounded to the nearest tenth.
Explanation:
To find the height of an isosceles triangle with a base of 15 inches and congruent sides each 15 inches, we can use the Pythagorean theorem or note that the triangle can be split into two right triangles by a height dropping from the vertex opposite the base to the midpoint of the base.
The midpoint will divide the 15-inch base into two segments, each 7.5 inches. The height of the isosceles triangle is the same as the height of the right triangle.
Using the Pythagorean theorem (a² + b² = c²), we can find the height (h) knowing that the hypotenuse (c) is one of the congruent sides (15 inches) and one leg (a, half of the base) is 7.5 inches:
h² + (7.5 inches)² = (15 inches)²
h² + 56.25 inches sup>2 = 225 inches²
h² = 225 inches² - 56.25 inches²
h² = 168.75 inches²
h = sqrt{168.75 inches²}
h approx 12.99 inches, which rounds to 13.0 inches to the nearest tenth.
Therefore, the height of the isosceles triangle rounds to 13.0 inches.
6/5 × 25/24 multiple
$765.13 is deposited at the end of each month for 2 years in an account paying 12% interest compounded monthly. Find the amount of the account. Round your answer to the nearest cent.
The final amount is = $ 959.779
What is compound interest?
Compound interest is when you earn a hobby on both the cash we've got stored and the hobby we earn.
calculation:-
principal amount = $765.13
rate if interest = 12%
for 1st year:-
interest amount= $765.13*12/100
= $ 91.8156
final amount = $765.13 + $ 91.8156
= $ 856.9456
for 2nd year:-
principal amount = $ 856.9456
12% interest on $ 856.9456 = $ 102.833472
final amount = $ 856.9456+$ 102.833472
= $ 959.779 answer
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If point A lies on the line of reflection, where does the reflected image, point A', lie?
Jane is one of 50 students to take a standardized math test that includes 100 multiple choice questions. If she has the highest score of any student with a raw score of 87, what is her percentile score?
Inez waters her plants every two days. She trims them every 15 days. She did both today. When will she do them both again?
The answer is 30 days.
The solution for this is to find the least common multiple. By getting the multiple of both numbers.
Multiples of 2: 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40…..
Multiples of 15: 15,30,45,60,75……..
The Least Common Multiples of 2 and 15 is 30. So, Inez will do them both again in 30 days.
The least common multiple (LCM) of two numbers is the smallest number that is multiple by the both number.
What is the simplified form of the expression? (2 – 9c)(–8)
What percent of 645 is 187.05?
To find what percent 187.05 is of 645, one can use the following formula:
[tex]\[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \][/tex]
In this case, the Part is 187.05 and the Whole is 645. Plugging these values into the formula gives:
[tex]\[ \text{Percentage} = \left( \frac{187.05}{645} \right) \times 100 \][/tex]
Now, calculate the fraction:
[tex]\[ \text{Percentage} = \left( \frac{187.05}{645} \right) \times 100 = \left( 0.29155 \right) \times 100 \][/tex]
[tex]\[ \text{Percentage} = 29.155 \][/tex]
Therefore, 187.05 is approximately 29.155% of 645. To express this as a fraction, one can write:
[tex]\[ \text{Percentage} = \frac{187.05}{645} \times 100 = \frac{18705}{645} \approx 29.155\% \][/tex]
To get the exact fraction, we can simplify:
[tex]\[ \text{Percentage} = \frac{187.05}{645} \times 100 = \frac{18705}{645} \times \frac{20}{20} = \frac{374100}{12900} \][/tex]
Simplifying the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 300, we get:
[tex]\[ \text{Percentage} = \frac{374100 \div 300}{12900 \div 300} = \frac{1247}{430} \][/tex]
So, the exact fraction representing the percentage is:
[tex]\[ \text{Percentage} = \frac{1247}{430} \times 100 \][/tex]
[tex]\[ \text{Percentage} = \frac{1247}{4.3} \][/tex]
[tex]\[ \text{Percentage} = 29.00 \% \][/tex]
Thus, 187.05 is exactly 29% of 645.
In a set of integers between 18 and 95, inclusive, how many are divisible by 6 but not 12?
"let v = r 2 with the usual addition and scalar multiplication defined by k(u1, u2) = (ku1, 0). determine which of the five axioms of vector spaces involving scalar multiplication v satisfies and which fail. for the ones it satisfies, prove that it satisfies the axiom. for those that fail, show that it fails with a counterexample."
EASY 5 POINTS!! Which expression gives the correct volume of the figure?
Answer : The correct option is, [(10 × 4 × 5) + (5 × 5 × 5)] cubic inches.
Step-by-step explanation :
As we know that,
Formula used for volume of cube is:
[tex]V=(a)^3[/tex]
or,
[tex]V=a\times a\times a[/tex]
where,
V = volume of cube
a = side of cube
Formula used for volume of cuboid is:
[tex]V=l\times b\times h[/tex]
where,
V = volume of cuboid
l = length of cuboid
b = breadth of cuboid
h = height of cuboid
The given figure is formed by the combination of two figure that is cube and cuboid.
Volume of cube = [tex](a)^3[/tex]
Given :
a = side of cube = 5 inch
Volume of cube = [tex]5\times 5\times 5[/tex] cubic inches
and,
Volume of cuboid = [tex]l\times b\times h[/tex]
Given :
l = length of cuboid = 10 inch
b = breadth of cuboid =5 inch
h = height of cuboid = 4 inch
Volume of cuboid = [tex]10\times 5\times 4[/tex] cubic inches
Total volume of figure = Volume of cuboid + Volume of cube
[tex](10\times 5\times 4)+(5\times 5\times 5)[/tex] cubic inches
Thus, the correct volume of the figure will be,
[tex](10\times 5\times 4)+(5\times 5\times 5)[/tex] cubic inches
Which of the following types of data are likely to be normally distributed? Check all that apply.
A. The time it takes for an airliner to fly from Los Angeles to New York
B. The distance of an archer's shots from the center of a target
C. The driving distances of American commuters
D. The outcomes of flipping a coin fifty times
E. The amount of popcorn that pops per bag
The answer is A. the time it takes for an airliner to fly from Los Angeles to New York city and B. the distance of an archer's shot from the centre of a target.
What is a normal distribution?A normal distribution is a symmetrical continuous probability distribution in which values are usually clustered around the mean.
A & B should each have a range of values that cover most occurrences with outlying values that decrease in number as they move further away from the dominant value range, which is the definition of a normal distribution.
Therefore, The answer is A the time it takes for an airliner to fly from Los Angeles to New York City and B the distance of an archer's shot from the centre of a target.
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Two cars that are 150 miles apart start driving toward each other on parallel roads. The average speed of the first car is 60 miles per hour. The average speed of the second car is 55 miles per hour. Which equation can be used to determine t, the time it takes for the two cars to pass each other?
60t – 55t = 0
60t + 55t = 1
60t + 55t = 150
60t – 55t = 150
The equation that can be used to determine t, the time it takes for the two cars to pass each other is:
60t + 55t = 150
Option C is the correct answer.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
The equation that can be used to determine t, the time it takes for the two cars to pass each other is:
60t + 55t = 150
Here,
60t represents the distance covered by the first car in time t, and 55t represents the distance covered by the second car in time t.
When they meet, the sum of their distances would be equal to the total distance between them, which is 150 miles.
Therefore,
We can add their distances and set them equal to 150 miles to solve for t.
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2.8 meters linen divided into 45 cm pieces = # of pieces and waste
If f(x)=-4x^2+15,then f(-3)=??
The value of f(-3) for the given function f(x) = -4x² + 15 will be -21.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
As per the given function,
f(x) = -4x² + 15
Put x = -3
f(-3) = -4(-3)² + 15
⇒ -4 x 9 + 15
⇒ -36 + 15 = -21
Hence "The value of f(-3) for the given function f(x) = -4x² + 15 will be -21".
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Jack was 11 years older than Pricilla. Together their ages totaled 151 years.what are their ages?
The amount of carbon-14 present in animal bones t years after the animal's death is given by P(t)= -0.00012097t. How old is an ivory tusk that has lost 34% of its carbon-14?
I believe the equation you gave is wrong because the standard form of equation for C-14 decay is in the form of:
A = Ao e^-kt
So I think the right form of equation is (correct me if I’m wrong):
P(t) = Po e^(-0.00012097t)
Where,
Po = initial value of C-14 at t = 0
t = time elapsed
Since it is given that:
P = (1 – 0.34) Po
P = 0.66 Po
Therefore, t is:
0.66 Po = Po e^(-0.00012097 t)
0.66 = e^(-0.00012097 t)
taking ln of both side:
ln 0. 66 = -0.00012097 t
t = - ln 0. 66 / 0.00012097
t = 3,434.86 years
Therefore the ivory tusk is about 3,435 years old.
the following data values represents a population. What is the variance of the values? 6, 10, 14, 2
Answer:20 !
Step-by-step explanation:
What is the next number in the series? 83 79 75 71 67
83-79 =4
79-75 = 4
the numbers are decreasing by 4
so the next number would be 67-4 = 63
what is e/4 + 2f-3 when e =12 andf =1/2
-7=7d-8
help me with the equation for that problem
eliminate the parameter. x = 5 cos t, y = 5 sin t help please!
Final answer:
To eliminate the parameter 't' from the equations x = 5 cos t and y = 5 sin t, use the Pythagorean identity which leads to the non-parametric equation of a circle: x^2 + y^2 = 25.
Explanation:
To eliminate the parameter 't' from the parametric equations x = 5 cos t, y = 5 sin t, we can use the Pythagorean identity sin^2(t) + cos^2(t) = 1. Plugging in the given expressions for x and y:
(x/5) = cos(t)
(y/5) = sin(t)
We can square both sides of these equations and then add them together:
(x/5)^2 + (y/5)^2 = cos^2(t) + sin^2(t)
As cos^2(t) + sin^2(t) equals 1, the equation simplifies to:
(x/5)^2 + (y/5)^2 = 1
Thus, the eliminated parameter equation representing the same curve without the parameter 't' is:
x^2 + y^2 = 25
This is the equation of a circle with a radius of 5, centered at the origin.
(6) (Bonus question: worth 10 points. Total points for assignment not to exceed 100.) Use an iterated integral to compute the volume of the ellipsoid x^2/a^2 + y^2/b^2 + z^2/c^2 = 1. The a, b, and c are positive constants.
find cosx if tanx cscx=2
A)2
B)square root 2
C)square root 2/2
D)1/2
The value of cosx if "tanx cscx = 2" is 1/2. The correct option is D)1/2
What is Trigonometry?From the question, we are to determine the value of cosx
From the given information,
tanx cscx=2
Recall that,
[tex]tan(x )= \frac{sin (x)}{cos(x)}[/tex]
and
[tex]csc(x) = \frac{1}{sin(x)}[/tex]
Then,
Substitute these values into the given equation
tanx cscx = 2 becomes
[tex]\frac{sin (x)}{cos(x)} \times \frac{1}{sin(x)} = 2[/tex]
[tex]\frac{1}{cos(x)} = 2[/tex]
∴ [tex]cos(x) = \frac{1}{2}[/tex]
Hence, the value of cosx if "tanx cscx = 2" is 1/2. The correct option is D)1/2
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Round 1.136 to the nearest hundredth
What is the greatest number of triangular sections, each with a base of 5 inches and a height of 8 inches, that can be cut from a rectangular piece of paper measuring 30 inches by 40 inches?
Question part points submissions used give two sets of five numbers that have the same mean but different standard deviations. set 1: 2, 3, 7, 11, 12 set 2: 5, 6, 7, 8, 9 set 1: 2, 4, 6, 8, 10 set 2: 3, 4, 5, 7, 11 set 1: 4, 5, 7, 8, 11 set 2: 3, 6, 7, 9, 10 set 1: 3, 4, 6, 9, 13 set 2: 2, 5, 7, 8, 13 set 1: 4, 6, 7, 8, 15 set 2: 3, 6, 7, 10, 14 give two sets of five numbers that have the same standard deviation but different means.
Which question is not a good survey question?
a) Don’t you agree that the financial crisis is essentially over?
b) On average, how many hours do you sleep per day?
c) What is your opinion of educational funding this year?
d) Are you happy with the availability of electronic products in your state?
Answer:
See image
Step-by-step explanation:
Plato
A psychologist claims that less than 5.8 percent of the population suffers from professional problems due to extreme shyness. Express the null hypothesis and the alternative hypothesis in symbolic form. Use p, the true percentage of the population that suffers from extreme shyness. Select one: a. H0: p = 5.8% H1: p < 5.8% b. H0: p > 5.8% H1: p ≤ 5.8% c. H0: p < 5.8% H1: p ≥ 5.8% d. H0: p = 5.8% H1: p > 5.8%
Answer:
Step-by-step explanation: