Answer:
12.7
Step-by-step explanation:
If this is a right triangle then you just have to use pythagorean theorem. If fifteen is the hypotenuse then fifteen squared minus eight squared will give you x squared. Fifteen squared is 225 and eight squared is 64 so you subtract 64 from 225 to acquire the number 161. The square root of 161 is not exact but when rounded it is 12.7
Divide the school into classes and then randomly select students from each class is an example of:
Answer:
Stratified sampling
Step-by-step explanation:
Members of the population are divided into two or more subgroups called strata, that share similar characteristics like age, gender, or ethnicity. A random sample from each stratum is then drawn. For instance, if we divide the population of college students into strata based on the number of years in school, then our strata would be freshmen, sophomores, juniors, and seniors. We would then select our sample by choosing a random sample of freshmen, a random sample of sophomores, and so on.
This technique is used when it is necessary to ensure that particular subsets of a population are represented in the sample. Since a random sample cannot guarantee that sophomores would be chosen, we would used a stratified sample if it were important that sophomores be included in our sample. Furthermore, my using stratified sampling you can preserve certain characteristics of the population. For example, if freshmen make up 40% of our population, then we can choose 40% of our sample from the freshmen stratum. Stratified sampling is one of the best ways to enforce "representativeness" on a sample.
In 2 days, 48,000 gallons of oil
Answer:
Deepwater Horizon
good movie too btw
-Hops
Answer:
48 000 gallons / 2 days = 24 000 gallons per day
24 000 gallons / 24 hours = 1 000 gallons per hour
1 000 gallons / 60 minutes = 16.(6) gallons per minute
I had the same question on a quizz, the question was:In two days, 48,000 gallons of oil gushed out of a well. At what rate did the oil flow from the well?
Hope that was helpful.Thank you!!!
35. In a simple random sample of 25 high school students, the sample mean of the SAT scores was 1450, and the sample variance was 900. Assume that the data come from a normal distribution , a 95.4 % Confidence interval for the population mean is a. 1450 +/- 180 b. 1450 +/- 18 c. 1450 +/- 12 d. 1450 +/- 360
Answer:
[tex]1450-2.0\frac{30}{\sqrt{25}}=1450-12[/tex]
[tex]1450+2.0\frac{30}{\sqrt{25}}=1450+12[/tex]
And the best option would be:
c. 1450 +/- 12
Step-by-step explanation:
Information provided
[tex]\bar X=1450[/tex] represent the sample mean for the SAT scores
[tex]\mu[/tex] population mean (variable of interest)
[tex]s^2 = 900[/tex] represent the sample variance given
n=25 represent the sample size
Solution
The confidence interval for the true mean is given by :
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
The sample deviation would be [tex]s=\sqrt{900}= 30[/tex]
The degrees of freedom are given by:
[tex]df=n-1=2-25=24[/tex]
The Confidence is 0.954 or 95.4%, the value of [tex]\alpha=0.046[/tex] and [tex]\alpha/2 =0.023[/tex], assuming that we can use the normal distribution in order to find the quantile the critical value would be [tex]z_{\alpha/2} \approx 2.0[/tex]
The confidence interval would be
[tex]1450-2.0\frac{30}{\sqrt{25}}=1450-12[/tex]
[tex]1450+2.0\frac{30}{\sqrt{25}}=1450+12[/tex]
And the best option would be:
c. 1450 +/- 12
A group of 52 people attended a ball game. There were three times as many children as adults in the group.
Set up a system of equations that represents the numbers of adults and children who attended the game and solve the system to find the number of children who were in the group.
Answer:
39 children and 13 adults
Step-by-step explanation:
3children = 1 adult
52 = x * (3children + 1adult)
52= x * 4
13 = x
x = 13
total children = 3x
3x = 39
The problem poses a system of linear equations where the number of attendees 'a + c = 52' and 'c = 3a'. Resolving these equations gives 'a = 13' adults and 'c = 39' children.
Explanation:This is a problem about creating and solving a system of linear equations. Let's denote the number of adults who attended the ball game as 'a' and the children who attended the game as 'c'. According to the problem, we have two parts of information that can be written as equations:
The total number of individuals who attended the game, or 'a + c = 52'. The number of children in attendance were three times the number of adults, or 'c = 3a'.You can substitute the equation for 'c' in the first equation: a + (3a) = 52. Solving this, you find that 'a' equates to 13. Substitute 'a = 13' into the second equation, you will find that 'c = 39'. This indicates that there were 13 adults and 39 children who attended the game.
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Think about the properties of a square. Is a square also a rhombus? Is it also a rectangle? Answer each question and explain your answers. Write two to four sentences.
Yes, a square can be considered as a rhombus and a rectangle both.
What is a square?The square is a quadrilateral with all sides equal and all angles equals to 90° and having equal diagonals.
Square being a rhombus and a rectangle :-
Rhombus :-
It has it's all sides equal having their diagonals equal and intersect at right angle rhombus is a parallelogram so a square, all the properties that a rhombus holds are also the properties of a square, so we can say a square can be considered as a rhombus.
Rectangle :-
A square is always a rectangle because, it has all the properties of a rectangle, such as parallel and equal opposite sides, vertex angles being a right angle, diagonals being equal.
Hence, a square can be considered as a rhombus and a rectangle both.
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Final answer:
A square is both a rhombus and a rectangle because it has four equal sides and four right angles, fulfilling the criteria for both shapes.
Explanation:
A square indeed has all the properties of a rhombus, which is a parallelogram with four equal sides, and it also has the properties of a rectangle, which is a quadrilateral with four right angles. Since a square has four equal sides and four right angles, it satisfies the criteria to be called both a rhombus and a rectangle. Therefore, the answer is yes; a square is both a rhombus and a rectangle.
Which one of the properties described below DOES NOT apply to the perpendicular bisector of a segment?
A) It must be longer than the original segment.
B) It is perpendicular to (makes a 90 angle with) the original segment.
C) It divides the original segment into two equal pieces.
D) Every point on the perpendicular bisector is the same distance from both endpoints of the segment.
Answer: C
Step-by-step explanation: It divides the original segment into two equal pieces
The properties that do not apply for the perpendicular bisector should be option c. that it divides the original segment to two equal pieces.
Properties that applied to the perpendicular bisector of a segment:It should be more than the original segment. It should be perpendicular for making 90 angles along with the original segment. Also, each and every point on the perpendicular bisector should contain a similar distance that lies from the segment endpoints.Learn more about segment here: https://brainly.com/question/2818266
VERY URGENT.
You will get Brainliest.
Here are three math questions:
1.) A rectangular prism has a volume of 2,592 cubic yards. The height of the prism is 32 yards.
What is the area of the base of the prism?
2.) A rectangular prism has a volume of 432 cubic feet and a height of 9 feet.
Which dimensions could be the length and width of the prism?
Select each correct answer.
28 ft long and 20 ft wide
3 ft long and 16 ft wide
6 ft long and 8 ft wide
13 ft long and 4 ft wide
24 ft long and 2 ft wide
3.) A rectangular prism has a volume of 960 cubic units. The area of the base is 80 square units.
What is the height of the prism?
_____ units
Answer:
(1)Base Area= 81 square yards.
(2)
3 ft long and 16 ft wide 6 ft long and 8 ft wide 24 ft long and 2 ft wide(3)Height=12 Units
Step-by-step explanation:
Question 1
Volume of the rectangular prism=2,592 cubic yards.
Height of the rectangular prism=32 yards
Volume of a rectangular prism =lbh (where lb is the Base Area)
Therefore:
lbh=2592
32lb=2592
lb=2592/32=81
Base Area= 81 square yards.
Question 2
Volume of the rectangular prism=432 cubic feet.
Height of the rectangular prism=9 feet
Volume of a rectangular prism =lbh (where lb is the Base Area)
Therefore:
lbh=432
9lb=432
lb=432/9=48
Base Area= 48 square yards.
Any dimension whose product is 48 is a possible choice.
They are:
3 ft long and 16 ft wide 6 ft long and 8 ft wide 24 ft long and 2 ft wideQuestion 3
Volume of the rectangular prism=960 cubic units.
Base Area of the rectangular prism, lb=80 Square Units
Volume of a rectangular prism =lbh (where lb is the Base Area)
Therefore:
lbh=960
80h=960
h=960/80=12
Height= 12 units.
Answer:
81 square yards.
Step-by-step explanation:
what the other guy said just less words
when oxygen reacts with hydrogen it has the capacity to release 29 kilojoules of energy. Inside a fuel cell, oxygen reacts with hydrogen to produce 23 kilojoules of useful energy. The rest of the energy is lost as heat. Whats the efficiency percent of the fuel cell?
Answer:
79
Step-by-step explanation:
Insurance company records indicate that 14% of its policyholders file claims involving theft or robbery of personal property from their homes. Suppose a random sample of 500 policyholders is selected. What is the standard deviation of the sampling distribution of the sample proportion of policyholders filing claims involving theft or robbery from their homes?
Answer:
Standard deviation = 7.76
Step-by-step explanation:
The formula for determining standard deviation when dealing with population proportion is expressed as
Standard deviation = √npq
Where
n represents the number of samples from the population.
p represents the probability of success.
q represents the probability of failure.
From the information given,
n = 500 policyholders
p = 14% = 14/100 = 0.14
q = 1 - 0.14 = 0.86
Standard deviation = √500 × 0.14 × 0.86 = 7.76
Answer: std dev = 0.01552
Step-by-step explanation:
we will solve this by taking a step by step analysis of the problem.
i hope at the end of this section, you will feel confident to try out other questions.
given that the size of the sample (n) = 500
The Insurance company records indicate that 14% of its policyholders file claims involving theft or robbery of personal property from their homes.
hence sample proportion of policyholders filing claims involving theft or robbery from their homes (p) = 14% =0.14
let Z be the number of policyholders files involving theft or robbery of personal property from their homes.
so Z~Bin(500,0.14) and p=Z/500
we know from basic mathematics that standard deviation = √(variance)
so variance is given thus;
V[Z] = 500*0.14*(1-0.14)
or V[p] = V[Z/500] = 500*0.14*0.86/500² = 0.14*0.86/500
so standard deviation is;
sqrt[V[p]]=sqrt(0.14*0.86/500) = sqrt(0.0002408) = 0.01552
∴ the standard deviation = 0.01552
cheers i hope this helps!!!!
25.2 + 800 - 427..43 × 2.4 ÷ 13
Step-by-step explanation:
25.2 + 800 - 427.43 x 2.4 ÷ 13
825.2 - 1025.832 ÷ 13
200.632 ÷ 13
= 15.44
HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing. Check all that apply.
Answer:
D
Step-by-step explanation:
The absolute value parent function is [tex]\mid x \mid[/tex], or answer choice D. Hope this helps!
Trigonometry: Question 2
In triangle ABC with right angle C, the measure of angle A is 37
degrees, and the length of the hypotenuse is 10. What is the length of
AC?
Select one:
12,5
7.9
Answer:
b = 7.9
Step-by-step explanation:
A = 37 a =
B = 53 b =
C = 90 c = 10
B = 180 - 90 -37 = 53
[tex]\frac{sinB}{b} = \frac{sinC}{c}\\ \frac{sin(53)}{b} = \frac{sin(90)}{10}\\ b = \frac{10 sin(53)}{sin(90)} \\b = 7.9[/tex]
To find the length of side AC in a right-angled triangle ABC with angle A of 37 degrees and hypotenuse 10, we use the cosine function. AC equals the hypotenuse multiplied by the cosine of angle A, resulting in AC being approximately 7.9 units long.
Explanation:The student wants to know the length of side AC in a right-angled triangle ABC, where angle C is a right angle, angle A is 37 degrees, and the hypotenuse (side BC) is 10. To find the length of side AC, we will use trigonometric functions. Specifically, we will use the cosine function, which relates the adjacent side to the hypotenuse in a right-angled triangle. The cosine of angle A (cos 37°) is equal to the adjacent side (AC) divided by the hypotenuse (BC).
The formula is: Cosine of angle A = AC / BC
This can be rewritten as: AC = BC * Cosine of angle A
By substituting the given values (BC = 10 and angle A = 37°), we get:
AC = 10 * cos(37°)
To find cos(37°), we can use a calculator set to degree mode. The calculation gives us:
AC = 10 * 0.7986 (approximately)
Therefore, AC ≈ 10 * 0.7986 = 7.986
AC is approximately 7.9 units long.
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f(x)=x^2 what is g(x)
Answer:
D. g(x)=4x^2
Step-by-step explanation:
Answer: g(x)=4x^2
check picture below
. The time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal probability distribution with average time 10 minutes and a standard deviation of 2 minutes. If five individuals fill out the form on Day 1 and six individuals fill out the form on Day 2, what is the probability that the sample average time taken is less than 11 minutes for BOTH days?
Answer:
Probability that the sample average time taken is less than 11 minutes for Day 1 is 0.86864.
Probability that the sample average time taken is less than 11 minutes for Day 2 is 0.88877.
Step-by-step explanation:
We are given that the time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal probability distribution with average time 10 minutes and a standard deviation of 2 minutes.
Also, five individuals fill out the form on Day 1 and six individuals fill out the form on Day 2.
(a) Let [tex]\bar X[/tex] = sample average time taken
The z score probability distribution for sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean time = 10 minutes
[tex]\sigma[/tex] = standard deviation = 2 minutes
n = sample of individuals fill out form on Day 1 = 5
Now, the probability that the sample average time taken is less than 11 minutes for Day 1 is given by = P([tex]\bar X[/tex] < 11 minutes)
P([tex]\bar X[/tex] < 11 minutes) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{11-10}{\frac{2}{\sqrt{5} } }[/tex] ) = P(Z < 1.12) = 0.86864
The above probability is calculated by looking at the value of x = 1.12 in the z table which has an area of 0.86864.
(b) Let [tex]\bar X[/tex] = sample average time taken
The z score probability distribution for sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean time = 10 minutes
[tex]\sigma[/tex] = standard deviation = 2 minutes
n = sample of individuals fill out form on Day 2 = 6
Now, the probability that the sample average time taken is less than 11 minutes for Day 2 is given by = P([tex]\bar X[/tex] < 11 minutes)
P([tex]\bar X[/tex] < 11 minutes) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{11-10}{\frac{2}{\sqrt{6} } }[/tex] ) = P(Z < 1.22) = 0.88877
The above probability is calculated by looking at the value of x = 1.22 in the z table which has an area of 0.88877.
If u = <-7, 6> and v = <-4, 17>, which vector can be added to u + 3v to get the unit vector <1, 0> as the resultant vector?
With u = <-7, 6> and v = <-4, 17>, we have
u + 3v = <-7, 6> + 3 <-4, 17> = <-7, 6> + <-12, 51> = <-19, 57>
We want to find a vector w such that
u + 3v + w = <1, 0>
Subtract u + 3v from both sides to get
w = <1, 0> - (u + 3v) = <1, 0> - <-19, 57>
w = <20, -57>
To get the required vector, subtract u + 3v from the unit vector <1, 0>. The required vector is <20, -57>.
Explanation:To find the vector that can be added to u + 3v to get the unit vector <1, 0>, we need to subtract u + 3v from the unit vector. This will give us the required vector. Let's calculate:
Unit vector: <1, 0>
u + 3v: <-7, 6> + 3<-4, 17> = <-7, 6> + <-12, 51> = <-19, 57>
Required vector = Unit vector - (u + 3v) = <1, 0> - <-19, 57> = <1 + 19, 0 - 57> = <20, -57>
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What are the solution(s) to the quadratic equation 50 - x2 = 0?
x = +2/5
x = +63
x = 15/2
no real solution
Answer:
±5sqrt(2) = x
Step-by-step explanation:
50 - x^2 = 0
Add x^2 to each side
50 - x^2 +x^2= 0+x^2
50 = x^2
Take the square root of each side
±sqrt(50) = sqrt(x^2)
±sqrt(25*2)) = x
±sqrt(25) sqrt(2) = x
±5sqrt(2) = x
Samantha measured 40 1/2 inches. Over the 5 1/2 years, she grew to a height of 57 inches. During the 5 1/2 years, what was the average yearly change in samanthas height?
Answer:
The average yearly change in samanthas height was of 3.3 inches.
Step-by-step explanation:
She mesured 40 1/2 = 40.5 inches.
In 5 1/2 years = 5.5 years, she grew to 57 inches.
During the 5 1/2 years, what was the average yearly change in samanthas height?
The total change was of 57-40.5 = 16.5 inches
16.5/5 = 3.3
The average yearly change in samanthas height was of 3.3 inches.
An ice cream cone has a radius of 2 in. How much melted ice cream will the cone hold if it has a height of 6 inches?
Answer:
it will hold 25.13 cubic inches of melted ice cream
Step-by-step explanation:
first we get the cone formula because a melted ice cream cone will have a flat top, making it a cone
the cone formula is π*r^2 * h /3
so we input radius and height
π*2^2 * 6 /3
then we simplfy
π * 4 * 6 /3
12.56 *6/3
75.398/3
25.13
Suppose a subdivision on the southwest side of Denver, Colorado, contains 1,400 houses. The subdivision was built in 1983. A sample of 110 houses is selected randomly and evaluated by an appraiser. If the mean appraised value of a house in this subdivision for all houses is $227,000, with a standard deviation of $8,500, what is the probability that the sample average is greater than $228,500?
Answer:
3.22% probability that the sample average is greater than $228,500
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
[tex]\mu = 227000, \sigma = 8500, n = 110, s = \frac{8500}{\sqrt{110}} = 810.44[/tex]
What is the probability that the sample average is greater than $228,500?
This is 1 subtracted by the pvalue of Z when X = 228500. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{228500 - 227000}{810.44}[/tex]
[tex]Z = 1.85[/tex]
[tex]Z = 1.85[/tex] has a pvalue of 0.9678
1 - 0.9678 = 0.0322
3.22% probability that the sample average is greater than $228,500
What do dinosaurs use to run their cars?
Answer:
Probably the engine from their helicopter
Step-by-step explanation:
There are 3 feet in 1 yard. This is equivalent to 12 feet in 4 yards. Which proportion can be used to represent this? StartFraction 12 over 1 EndFraction = StartFraction 4 over 12 EndFraction One-third = StartFraction 12 over 4 EndFraction StartFraction 3 over 1 EndFraction = StartFraction 4 over 12 EndFraction StartFraction 3 over 1 EndFraction = StartFraction 12 over 4 EndFraction
Answer:
[tex]\dfrac{3}{1}=\dfrac{12}{4}[/tex]
Step-by-step explanation:
If you write the proportion as ratios of feet to yards, you have ...
[tex]\dfrac{3\,\text{ft}}{1\,\text{yd}}=\dfrac{12\,\text{ft}}{4\,\text{yd}}\\\\\boxed{\dfrac{3}{1}=\dfrac{12}{4}}\qquad\text{without the units}[/tex]
__
Please note that a proportion is a true statement. Here, you need only pick the true statement from those offered. For example, here's the first choice written in more readable form:
[tex]\dfrac{12}{1}=\dfrac{4}{12}\qquad\text{FALSE statement}[/tex]
Answer:
d: 3/1 12/4
Step-by-step explanation:
Kim spent 40/100 of a dollar on a snack write as a money amount she has left.
[tex]\frac{60}{100}[/tex] of a dollar
A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.
Kim spent [tex]\frac{40}{100}[/tex] of a dollar on a snack.
So, she has been left with [tex]1-\frac{40}{100}=\frac{60}{100}[/tex] of a dollar on a snack.
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Final answer:
Kim spent 40/100 of a dollar (40 cents) on a snack, so she has 60 cents left.
Explanation:
The question requires converting a fraction of a dollar into a money amount. Kim spent 40/100 of a dollar on a snack. A dollar is equivalent to 100 cents, so Kim spent 40 cents on her snack. To find out how much she has left, we subtract her spending from the total amount of one dollar.
To perform the calculation: 100 cents - 40 cents = 60 cents.
Therefore, Kim has 60 cents left after purchasing the snack.
One study estimated that bears populate the Kenai Peninsula of Alaska at a rate of 424242 bears per 1,000 \text { km}^21,000 km 2 1, comma, 000, start text, space, k, m, end text, squared of available habitat. According to this study, about how many bears would you expect to find in a habitable region of this peninsula 8,500 \text { km}^28,500 km 2 8, comma, 500, start text, space, k, m, end text, squared in size?
Answer:
357 bears
Step-by-step explanation:
Given;
Population density of bears in the Kenai Peninsula of Alaska = 42 bears per 1000km^2
Area of habitable region of this peninsula = 8500 km^2
how many bears would you expect to find in a habitable region of this peninsula N;
N = population density × area
N = 42/1000 × 8500
N = 357 bears
What is the point-slope form of a line with slope-3 that contains the point
(10,-1)?
O A. y+1 = 3(x+10)
O B. y+ 1 = 3(x-10)
O C. x+ 1 =-3(y-10)
OD. y+ 1 = -3(x-10)
Answer:
D.) [tex]y+1=-3(x-10)[/tex]
Step-by-step explanation:
The original point slope form equation is as follows:
[tex]y - y_1 = m(x-x_1)[/tex]
When you input a negative or positive value into the equation, the sign may or may not change. In this case, we input a negative y value -- this caused the sign to change to '+1' rather than stay at '-1'
Select the graph that represent the equation (x-6)^2+(y+7)^2=16
Answer:
This is a circle with centre (6,-7) and radius 4.
Step-by-step explanation:
The equation of a circle has the following format:
[tex](x - x_{0})^{2} + (y - y_{0})^{2} = r^{2}[/tex]
In which r is the radius(half the diameter) and the centre is the point [tex](x_{0}, y_{0})[/tex]
In this question:
[tex](x-6)^{2} + (y+7)^{2} = 16[/tex]
So
[tex]x_{0} = 6, y_{0} = -7[/tex]
[tex]r^{2} = 16[/tex]
[tex]r = \pm \sqrt{16}[/tex]
The radius is the positive value.
[tex]r = 4[/tex]
So this is a circle with centre (6,-7) and radius 4.
Answer:
Given equation
(x-6)^2+(y+7)^2=16
centre (6,-7) and radius 4.
Step-by-step explanation:
The equation of a circle is (x - a)² + (y - b)² = r²
the radius is r
the centre is (a, b)
Given equation
(x-6)^2+(y+7)^2=16
so ,
a = 6
b = - 7
r² = 16
[tex]r = \pm \sqrt{16}[/tex]
r = 4
Therefore, the circle with centre (6,-7) and radius 4.
The phone company A Fee and Fee has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 290 minutes, the monthly cost will be $87. If the customer uses 980 minutes, the monthly cost will be $225. A) Find an equation in the form y = m x + b , where x is the number of monthly minutes used and y is the total monthly of the A Fee and Fee plan.
Final answer:
The equation representing the total monthly cost of the A Fee and Fee plan based on the number of minutes used is y = 0.20x + 29, where y is the total monthly cost and x is the number of minutes.
Explanation:
To find an equation in the form y = mx + b, where x is the number of monthly minutes used and y is the total monthly cost of the A Fee and Fee plan, we first need to determine the slope (m) and the y-intercept (b).
We have two points based on the information given: (290, 87) and (980, 225). The slope (m) is calculated by the difference in cost divided by the difference in minutes:
m = (225 - 87) / (980 - 290)
m = 138 / 690
m = 0.20
Now that we have the slope, we can use one of the points to find b, the y-intercept.
Using the point (290, 87) and the slope 0.20:
87 = 0.20(290) + b
b = 87 - 58
b = 29
The equation representing the total monthly cost (y) based on the number of minutes used (x) is therefore:
y = 0.20x + 29
Brian makes a cleaning solution using a ratio of 4cups of water to 1 cup of vinegar. Which equationcould be used to find c, the number of cups ofvinegar that Brian should use with 12 cups of water?
A. 4/12 =c
B. 4/1 =12/c
C 4/1 = c/12
D. 4+1 = 12+c
Answer:
Option B could be used to find c, the number of cups ofvinegar that Brian should use with 12 cups of water
Step-by-step explanation:
Brian makes a cleaning solution using a ratio of 4 cups of water to 1 cup of vinegar.
Let c be the number of cups of vinegar that Brian should use with 12 cups of water.
1 cup of vinegar uses cup of water = 4
c cups of vinegar uses cup of water = 4c
We are c, the number of cups ofvinegar that Brian should use with 12 cups of water
So, 4c=12
[tex]4=\frac{12}{c}[/tex]
So, equation =[tex]\frac{4}{1}=\frac{12}{c}[/tex]
So, Option B could be used to find c, the number of cups ofvinegar that Brian should use with 12 cups of water
"If a ball of mass M is dropped from a height h onto a spring with spring constant k (whose equilibrium positions is at height 0), compresses the spring an additional distance (L/2), and then rebounds, what height will the ball reach? Express your answer symbolically."
So I was thinking something along the lines of h= M*k*(L/2) but I'm not sure :/ Any guidance?
Answer:[tex]h=\dfrac{kL^2}{8mg}[/tex]
Step-by-step explanation:
Given
Mass of ball is M is dropped from a height h
spring constant is k
Here we can use conservation of energy
Mass has a Potential energy of E=mgh
and when it falls on the spring then it compresses it a length of 0.5 L
Now potential energy is converted into Elastic potential energy and then spring unleashes this energy to the mass and again provide kinetic energy to mass to move upward .
In this way energy is conserved. So, mass must move to an initial height h
[tex]mgh=\frac{1}{2}k(\frac{L}{2})^2[/tex]
[tex]h=\dfrac{kL^2}{8mg}[/tex]
considering [tex]h >> 0.5L[/tex]
What is the area of a square with side length of 4 and one-fourth m?
Answer:18.0625m^2
Step-by-step explanation:
Length =4 1/4 m
Area= length x length
Area=4 1/4 x 4 1/4
Area=(4x4+1)/4 x (4x4+1)/4
Area=17/4 x 17/4
Area=(17x17)/(4x4)
Area=289/16
Area=18.0625m^2
David wants to buy a 6-foot long sandwich for a birthday party. If the sandwich costs $72.00, what is the cost per foot?
Answer:
$12 per foot
Step-by-step explanation:
$72.00 divided by 6 is $12
Answer:
The cost per foot of the sandwich is $12.
Step-by-step explanation:
You need to use division for this problem.
Pretend you are cutting the 6-foot sanwhich into 1-foot pieces. You will have 6 pieces. You have to give each piece an equal amount of money. Think about your 6-times tables. What times 6 = 72?
__ x 6 =72
or
72/6 = __