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
Help please I really do need help
Answer:
P'(-6, -4)
Step-by-step explanation:
The (x, y) coordinates of the plotted point P are (-2, 2).
Putting those values into the translation formula, you get ...
(x, y) ⇒ (x -4, y -6)
(-2, 2) ⇒ (-2 -4, 2 -6) = (-6, -4)
The coordinates of the translated point P' are ...
P'(-6, -4)
When playing American roulette, the croupier (attendant) spins a marble that lands in one of the 38 slots in a revolving turntable. The slots are numbered 1 to 36, with two additional slots labeled 0 and 00 that are painted green. Consider the numbers 0 and 00 as neither even nor odd. Half the remaining slots are colored red and half are black. Assume a single spin of the roulette wheel is made. Find the probability of the marble landing on a 00 or even slot. The total number of outcomes is and the number of outcomes in the event is
Answer:
Check the explanation
Step-by-step explanation:
1) probability for odd or 00 = (18+1)/38 = 0.5
2) expected value can be calculated as follows :
14 * win probability - 13 * lose probability
=14 * (18/38) - 13*(20/38)
= -0.21
Using it's concept, it is found that there is a 0.5 = 50% probability of the marble landing on a 00 or even slot.
A probability is the number of desired outcomes divided by the number of total outcomes.
In this problem:
There are 38 slots, hence [tex]T = 38[/tex].Of those, 18 are even, plus 00, hence [tex]D = 19[/tex]The desired probability is:
[tex]p = \frac{D}{T} = \frac{19}{38} = 0.5[/tex]
0.5 = 50% probability of the marble landing on a 00 or even slot.
A similar problem is given at https://brainly.com/question/15536019
Triangle MNO is reflected over the x-axis and then translated up 4 and right 3. On a coordinate plane, triangle O M N has points (1, 3), (2, 1), (negative 1, 2). Triangle O prime M prime N prime has points (4, 1), (5, 3), (2, 2). How can the transformation be amended such that the translation can occur before the reflection and have the image remain in the same position?
Answer: the answer is i think* A, Translate the pre-image down 4 and right 3 and then reflect the figure over the x-axis.
Step-by-step explanation: it's the only one that makes sense im takin the test
Answer:
A, Translate the pre-image down 4 and right 3 and then reflect the figure over the x-axis.
Step-by-step explanation:
I took the test hope this helps!!!!!!!!!!!!!!
Given z1 and z2 below. Calculate z1/z2 and write your answer in rcistheta form.
z1=-3+3sqrt(3)i
z2=27i
Answer:
(2/9)cis(30°)
Step-by-step explanation:
We can express the two numbers in magnitude∠angle form, then find their ratio.
|z1| = 3√((-1)² +(√3)²) = 3√4 = 6
∠z1 = arctan((3√3)/(-3)) = -arctan(√3) = 120°
z2 = 27∠90°
So, the ratio is ...
z1/z2 = (6∠120°)/(27∠90°) = (6/27)∠(120°-90°)
z1/z2 = (2/9)∠30°
Please answer! Will mark as Brainliest if correct.
Pedro, Lena, Harriet, and Yermin each plot a point to approximate the square root of 0.50.
(See picture)
Whose point is the best approximation of the square root of 0.50?
A: Pedro
B: Lena
C: Harriet
D: Yermin
Answer:Harriet
Step-by-step explanation:
Answer:
The aNSWER IS d
Step-by-step explanation: i JUST DID THE TEST
Commercial real estate prices and rental rates suffered substantial declines in 2008 and 2009. These declines were particularly severe in Asia; annual lease rates in Tokyo, Hong Kong, and Singapore declined by 40% or more. Even with such large declines, annual lease rates in Asia were still higher than those in many cities in Europe. Annual lease rates for a sample of 30 commercial properties in Hong Kong showed a mean of 1,114 per square meter with a standard deviation of 230. Annual lease rates for a sample of 40 commercial properties in Paris showed a mean lease rate of 989 per square meter with a standard deviation of 195. On the basis of the sample results, can we conclude that the mean annual lease rate is higher in Hong Kong than in Paris? Develop appropriate null and alternative hypotheses. At the 5% level of significance, what is your conclusion?
Answer:
Conclusion
The average rental rate in Hong Kong are higher than in Paris
Step-by-step explanation:
From the question we are told that
The sample size for Hong Kong is [tex]n_1 = 30[/tex]
The mean for Hong Kong is [tex]\mu_h = 1,114 \ m^2[/tex]
The standard deviation for Hong Kong is[tex]s = 230[/tex]
The sample size for Paris is [tex]n_2 = 40[/tex]
The mean for Paris is [tex]\mu_p = 989 \ m^2[/tex]
The standard deviation for Paris is [tex]s_p = 195[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The Null Hypothesis is
[tex]H_o : \mu_1 - \mu_2 = 0[/tex]
The alternative hypothesis is
[tex]H_a: \mu_1 - \mu_2 >0[/tex]
The test statistics is mathematically represented as
[tex]t = \frac{\mu _1 - \mu_2 - d }{\sqrt{(\frac{s^2}{n1} )+(\frac{(s_p^2}{n_2} )}}[/tex]
Substituting values
[tex]t = \frac{1114 - 989 - 0 }{\sqrt{(\frac{230^2}{30} )+(\frac{(195^2}{40} )}}[/tex]
[tex]t = 2.399[/tex]
Since the value of the test statistics is higher than the significance level then there is enough evidence to conclude that the average rental rate in Hong Kong are higher than in Paris
Using the t-distribution, it is found that since the test statistic is more than the critical value, there is enough evidence to conclude that the mean annual lease rate is higher in Hong Kong than in Paris.
At the null hypothesis, it is tested if the average is not higher in Hong Kong, that is, the result of the subtraction if not greater than 0.
[tex]H_0: \mu_H - \mu_P \leq 0[/tex]
At the alternative hypothesis, it is tested if it is higher, that is:
[tex]H_1: \mu_H - \mu_P > 0[/tex]
The standard errors for both samples are:
[tex]s_H = \frac{230}{\sqrt{30}} = 42[/tex]
[tex]s_P = \frac{195}{\sqrt{40}} = 30.83[/tex]
The distribution of the differences has mean and standard deviation given by:
[tex]\overline{X} = \mu_H - \mu_P = 1114 - 989 = 125[/tex]
[tex]s = \sqrt{s_H^2 + s_P^2} = \sqrt{42^2 + 30.83^2} = 52.1[/tex]
The test statistic is:
[tex]t = \frac{\overline{X} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.
Hence, the value is:
[tex]t = \frac{125 - 0}{52.1}[/tex]
[tex]t = 2.4[/tex]
The critical value, for a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.05 and 30 + 40 - 2 = 68 df, is [tex]t^{\ast} = 1.67[/tex]
Since the test statistic is more than the critical value, there is enough evidence to conclude that the mean annual lease rate is higher in Hong Kong than in Paris.
A similar problem is given at https://brainly.com/question/16402495
What’s 5 times 5 in math
Answer:25
Step-by-step explanation:
Because 5x5 equals 25
Answer:
25 Count by five with your five fingers
Step-by-step explanation:
5x5=25
Eastman Company purchased a delivery truck for $35,000 on January 1, 2008. The truck was
assigned an estimated useful life of 5 years and has a residual value of $10,000. Compute
depreciation expense using the double-declining-balance method for the years 2008 and 2009
BE 3
Answer:
The depreciation expense of the truck in 2008 and 2009 are $14,000 and $8,400 respectively.
Step-by-step explanation:
The double declining depreciation method depreciates assets twice as fast as the traditional declining balance method.
The method records larger depreciation expenses during the earlier years of an asset’s useful life, and smaller ones in later years.
As a result, companies opt for the method for assets that are likely to lose most of their value early on, or which will become obsolete faster.
For double declining depreciation method,
- Divide “100%” by the number of years in the asset’s useful life, this is the straight-line depreciation rate.
- Then, multiply that number by 2 and that is the Double-Declining Depreciation Rate. - In this method, depreciation continues until the asset value declines to its salvage value.
Number of useful lives = 5 years.
- Divide 100% by 5 years
100% / 5 = 20%
- Then, multiply that percentage by 2
20% x 2 = 40%
The Double-Declining Depreciation rate is 40%.
Value of the truck at the start of 2008 = $35,000
Depreciation in 2008 = 40% × 35000 = $14,000
Book Value of the truck at the start of 2009 = $35000 - $14000 = $21000
Depreciation in 2009 = 40% × 21000 = $8,400
Hope this Helps!!!
please help :'(
dhjehdkhkduiu
Answer:
lol good luck with that but you add them
Step-by-step explanation:
Carlos tiene una produccion semanal de 500kg de papas negras y 600kg de batatas al cabo de 12 semanas de ¿cuanto sera la produccion de papas? ¿Y de batatas? ¿De cuanto sera la produccion total?
The production of black potatoes is 6000 kg, the production of sweet potatoes is 7200 kg, and the total production of both types of potatoes is 13200 kg.
To find the total production of black potatoes and sweet potatoes, we need to multiply the weekly production by the number of weeks (12 weeks).
For black potatoes:
Weekly production = 500 kg
Total production of black potatoes = Weekly production * Number of weeks
= 500 kg/week * 12 weeks
= 6000 kg
For sweet potatoes:
Weekly production = 600 kg
Total production of sweet potatoes = Weekly production * Number of weeks
= 600 kg/week * 12 weeks
= 7200 kg
Now, to find the total production:
Total production = Total production of black potatoes + Total production of sweet potatoes
= 6000 kg + 7200 kg
= 13200 kg
So, the production of black potatoes is 6000 kg, the production of sweet potatoes is 7200 kg, and the total production of both types of potatoes is 13200 kg.
Complete question:
Carlos has a weekly production of 500kg of black potatoes and 600kg of sweet potatoes after 12 weeks. How much will the production of potatoes be? And of sweet potatoes? How much will the total production be?
What is the volume of a hemisphere with a radius of 62 cm rounded to the nearest tenth of a cubic centimeter?
Answer:
499,153.0 cm^3
Step-by-step explanation:
The volume of a sphere is given by the formula ...
V = (4/3)πr^3
The volume of a hemisphere will be half that, or ...
(2/3)πr^3 = (2/3)π(62 cm)^3 = (158885 1/3)π cm^3
≈ 499,153.0 cm^3
_____
Comment on this result
We have used a value of pi sufficiently accurate to give the result to 7 significant figures. If you use 3.14, you will get an answer somewhat different from this.
Answer: 499,153.0 cm^3
You
12 cupcakes needs 100 grams butter. How much in each cupcake
Answer:
The answer is 8.3 repeating. If you round it the answer is 8.
Answer:
8.3... grams in each cupcake
Step-by-step explanation:
you basically divide 100 by 12
Which of these numbers of simulations of an event would be most likely to produce results that are closest to those predicted by probability theory?
A. 50
B. 60
C. 30
D. 40
Answer:
60. Got it wrong, but oh well.
Step-by-step explanation:
What is there area to this?
Answer:
The total area of the figure is 52 in²
Step-by-step explanation:
This figure requires you to find the area of the square and the triangle separately, and then subtract the area of the triangle from the area of the square.
Find the area of the square
l=8in
A=l²
A=8²
A=64 in²
The area of the square is 64 in²
Find the area of the triangle
b=8in
h=3in
A=(bh)/2
A=(8*3)/2
A=24/2
A=12 in²
The area of the triangle is 64 in²
Now we need to subtract the areas
64-12=52 in²
The total area of the figure is 52 in²
Los $15000 del premio del consurso de ceramica,se repartieron entre ignacio,mariela y laura .Igancio recibio los 3/5partes,mariela las 4/25 y laura el resto ¿Cuanto dinero recibio cada uno? Y que parte del premio recibieron Ignacio y Mariela?
Answer:
a. Ignacio recibió $9000. Mariela recibió $2400 y Laura, $3600. b. Ignacio y Mariela recibieron [tex] \\ \frac{19}{25}[/tex] del total del premio (diecinueve veinticincoavos) ($11400).
Step-by-step explanation:
Tenemos un total de $15000, que fue el premio del concurso, el cual fue repartido entre tres personas: Ignacio, Mariela y Laura.
Lo que tenemos que hacer es multiplicar cada fracción por la totalidad del premio ($15000), para determinar cuánto recibió cada uno.
Recordemos que para resolver estos casos, la regla general es que sólo tenemos que multiplicar el numerador de la fracción por dicho total ($15000) y luego dividir el producto resultante entre el denominador de la fracción.
De esta manera, procedemos a resolver cada caso.
Lo recibido por Ignacio
Si Ignacio recibió las 3/5 partes del premio: ¿cuánto recibió Ignacio?
Como ya sabemos, la respuesta es multiplicar la fracción por el total del premio. Es decir:
[tex] \\ \frac{3}{5}*15000[/tex]
[tex] \\ \frac{3*15000}{5}[/tex]
[tex] \\ \frac{45000}{5}[/tex]
[tex] \\ 9000[/tex]
Que podemos también resolver de la siguiente manera, considerando que es más fácil dividir 15000 entre 5, por ser 5 un divisor de 15000:
[tex] \\ \frac{15000}{5}*3[/tex]
[tex] \\ 3000*3[/tex]
[tex] \\ 9000[/tex]
Es decir, Ignacio recibió $9000.
Lo recibido por Mariela
Para el caso de Mariela, aplicamos el mismo procedimiento.
Como Mariela recibió las 4/25 (cuatro veinticincoavos) del premio, tenemos entonces:
[tex] \\ \frac{4}{25}*15000[/tex]
[tex] \\ \frac{4*15000}{25}[/tex]
[tex] \\ \frac{60000}{25}[/tex]
[tex] \\ 2400[/tex]
También lo hubiéramos resuelto, sin tener que hacer una multiplicación y división extensas, si consideramos que 15000 y 25 son múltiplos de 5. Por lo tanto:
[tex] \\ \frac{4}{25}*15000[/tex]
[tex] \\ \frac{15000}{25}*4[/tex]
Es decir, dividir 15000 entre 25, y luego multiplicamos por cuatro. Así:
[tex] \\ 600*4[/tex]
[tex] \\ 2400[/tex]
Obteniendo el mismo resultado
De esta manera, Mariela recibió $2400.
Lo recibido por Laura
Laura recibió el resto de lo dejado por Ignacio y Mariela. Podemos resolver ésto de diversas formas. Una de ellas es restar del total del premio la suma de lo recibido por Ignacio y Mariela.
[tex] \\ 15000 - (9000 + 2400)[/tex]
[tex] \\ 15000 - 11400[/tex]
[tex] \\ 3600[/tex]
De esta manera, Laura recibió $3600.
¿Qué parte del premio recibieron Ignacio y Mariela?
En otras palabras, qué parte del premio recibieron Ignacio y Mariela en conjunto, en forma de fracción.
Una manera de resolver esta pregunta es sumando las fracciones que recibió cada uno, es decir, [tex] \\ \frac{3}{5} + \frac{4}{25}[/tex].
Hay varias maneras de sumar ambas fracciones. Una de ellas (la manera más general) es multiplicar el denominador de cada fracción por el numerador de la otra fracción, sumar cada producto obtenido y luego dividirlo entre el producto de los denominadores de cada fracción.
[tex] \\ \frac{3}{5} + \frac{4}{25}[/tex]
[tex] \\ \frac{3*25 + 5*4}{5*25}[/tex]
[tex] \\ \frac{75 + 20}{125}[/tex]
[tex] \\ \frac{95}{125}[/tex]
Podemos observar que 95 y 125 son múltiplos de 5, así que podemos simplificar el numerador y el denominador de la fracción dividiendo a ambos entre 5:
[tex] \\ \frac{95}{125}[/tex]
[tex] \\ \frac{\frac{95}{5}}{\frac{125}{5}}[/tex]
[tex] \\ \frac{19}{25}[/tex]
El número 19 es un número primo y no podemos simplificar más la fracción.
De esta manera, Ignacio y Mariela recibieron [tex] \\ \frac{19}{25}[/tex] del total del premio (diecinueve veinticincoavos), lo cual podemos comprobar si multiplicamos esta fracción por el total del premio y lo comparamos con la suma de los resultados para Ignacio y Mariela:
[tex] \\ \frac{19}{25}*15000[/tex]
[tex] \\ \frac{15000}{25}*19[/tex]
[tex] \\ 600*19[/tex]
[tex] \\ 11400[/tex]
Lo que es igual a la suma de lo recibido por Ignacio ($9000) y Mariela ($2400), es decir $11400.
Laura, por lo tanto recibió [tex] \\ \frac{6}{25}[/tex]
Por cuanto
[tex] \\ \frac{6}{25} + \frac{19}{25} = \frac{6+19}{25} = \frac{25}{25} = 1[/tex]
Es decir, la suma de las fracciones de lo recibido por Ignacio y Mariela más lo que recibió Laura debe sumar la totalidad, es decir, la unidad (1).
Ella drew 40 different pictures for an art show. Twenty of them include a dog in the picture. If she shuffles the pictures and picks one at random to give to her friend, what is the probability that she will pick one that includes a dog?
A.
0.2
B.
0.05
C.
0.1
D.
0.5
Answer:
0.05
Step-by-step explanation:
)) In a right triangle, a and b are the lengths of the legs and c is the length of the
hypotenuse. If b = 8.8 kilometers and c = 9.3 kilometers, what is a? If necessary, round to
the nearest tenth.
Answer:
3.008 km or 3.0 km
Step-by-step explanation:
According to the Pythagoras theorem:
[tex] {c}^{2} = {a}^{2} + {b}^{2} \\ \therefore \: {a}^{2} = {c}^{2} - {b}^{2} \\ \therefore \: {a}^{2} = {(9.3)}^{2} - {(8.8)}^{2} \\ \therefore \: {a}^{2} = {(9.3 + 8.8)}{(9.3 - 8.8)} \\ \therefore \: {a}^{2} = 18.1 \times 0.5 \\ \therefore \: {a}^{2} = 9.05 \\ \therefore \: {a} = \sqrt{9.05} \\ \therefore \: {a} = 3.00832179 \\ \therefore \: {a} = 3.0 \: km[/tex]
Alannah is a student who is not old enough to work, but would like to make some money. She
decides to make her own hand sanitizer to sell to her family and neighbors. She makes 2
different size bottles: large and small. The small bottle sells for $5.00 and the large sells for
$12.00. On her first day, she sold all 45 of the hand sanitizer bottles she had made and
collected $435. how many small bottles of hand sanitizer did Alannah sell? how many large bottles of hand sanitizer did Alannah sell?
Answer:
15 small bottles
30 large bottles
Step-by-step explanation:
Let the number of small bottle sold=s
Let the number of large bottle sold=l
She sold all 45 of the hand sanitizer bottles, therefore:
s+l=45The small bottle sells for $5.00
The large sells for $12.00
She collected a total of $435
5s+12l=435We solve the two equations simultaneously to obtain s and l.
From the first equation, s=45-l
Substitute s=45-l into 5s+12l=435
5(45-l)+12l=435
225-5l+12l=435
7l=435-225
7l=210
Divide both sides by 7
l=30
Recall: s=45-l
Therefore, s=45-30=15
Allanah sold 15 small bottles and 30 large bottles of hand sanitizer.
Suppose that a fast food restaurant decides to survey its customers to gauge interest in a breakfast menu. After surveying multiple people, the restaurant created a 95% confidence interval for the proportion of customers interested in a breakfast menu. The confidence interval is ( 0.349 , 0.433 ) . Use the confidence interval to find the point estimate and margin of error for the proportion. Give your answer precise to three decimal places.
Answer:
The point estimate is 0.391 and the margin of error is 0.042.
Step-by-step explanation:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
The margin of error is the absolute value of the difference between the point estimate and any of the two bounds.
In this problem, we have that:
Lower bound: 0.349
Upper bound: 0.433
Point estimate:
(0.349+0.433)/2 = 0.391
Margin of error:
|0.391 - 0.433| = |0.391 - 0.349| = 0.042
The point estimate is 0.391 and the margin of error is 0.042.
Final answer:
The midpoint of the confidence interval (0.349, 0.433) provides the point estimate, which is 0.391. The margin of error is calculated by subtracting the point estimate from the upper bound of the interval, resulting in 0.042.
Explanation:
The confidence interval (0.349, 0.433) can be used to find the point estimate and margin of error for the proportion of customers interested in a breakfast menu at a fast food restaurant. To find the point estimate, we take the midpoint of the confidence interval, which is the average of the lower and upper bounds.
Point Estimate = (Lower Bound + Upper Bound) / 2
Point Estimate = (0.349 + 0.433) / 2
Point Estimate = 0.391
To find the margin of error, we subtract the point estimate from either the upper or lower bound of the confidence interval.
Margin of Error = Upper Bound - Point Estimate
Margin of Error = 0.433 - 0.391
Margin of Error = 0.042
Therefore, the point estimate is 0.391 and the margin of error is 0.042 for the proportion of customers interested in the breakfast menu.
Which expression is equivalent to 4(x+2)?
A:6x
B:4(x)+4(2)
C:4(x)+4
D:8x
Please answer fast !
Answer:
B:4(x)+4(2)
Step-by-step explanation:
(4 × x)+(4 × 2)
You cant do anything in the parentheses so you have to distribute 4
Answer: B:4(x)+4(2)
Step-by-step explanation:
(4 × x)+(4 × 2)
You cant do anything in the parentheses so you have to distribute 4
Step-by-step explanation:
Add 5/12 plus 69/10 as an improper fraction in lowest terms
To compute a student's Grade Point Average (GPA) for a term, the student's grades for each course are weighted by the number of credits for the course. Suppose a student had these grades:
3.9 in a 5 credit Math course
2.4 in a 2 credit Music course
2.7 in a 4 credit Chemistry course
3.1 in a 6 credit Journalism course
What is the student's GPA for that term? Round to two decimal places.
The student's GPA for that term would be 3.16.
Given that;
A student had these grades:
3.9 in a 5 credit Math course
2.4 in a 2 credit Music course
2.7 in a 4 credit Chemistry course
3.1 in a 6 credit Journalism course
Now for the student's GPA for the term, calculate the weighted average of the grades.
First, calculate the total grade points earned by multiplying each grade by the corresponding number of credits:
Grade points for Math course = 3.9 × 5
= 19.5
Grade points for Music course = 2.4 × 2
= 4.8
Grade points for Chemistry course = 2.7 × 4
= 10.8
Grade points for Journalism course = 3.1 × 6
= 18.6
Hence, the total grade points earned:
Total grade points earned = 19.5 + 4.8 + 10.8 + 18.6
= 53.7
Finally, divide the total grade points earned by the total number of credits:
Total credits = 5 + 2 + 4 + 6
= 17
Use the formula;
GPA = Total grade points earned / Total credits
GPA = 53.7 / 17
GPA = 3.16
Therefore, the student's GPA for that term is 3.16.
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To compute a student's GPA, we need to calculate the weighted average of their grades. Multiply each grade by the corresponding number of credits, sum the products, and divide by the total number of credits.
Explanation:To compute the student's GPA for the term, we need to calculate the weighted average of their grades. The weighted average is calculated by multiplying each grade by the corresponding number of credits and then summing up these products. Finally, we divide the sum by the total number of credits.
For the student in question, let's calculate their GPA:
Multiply the Math grade (3.9) by the number of credits (5): 3.9 * 5 = 19.5Multiply the Music grade (2.4) by the number of credits (2): 2.4 * 2 = 4.8Multiply the Chemistry grade (2.7) by the number of credits (4): 2.7 * 4 = 10.8Multiply the Journalism grade (3.1) by the number of credits (6): 3.1 * 6 = 18.6Sum up the products: 19.5 + 4.8 + 10.8 + 18.6 = 53.7Divide the sum by the total number of credits: 53.7 / (5 + 2 + 4 + 6) = 53.7 / 17 = 3.16The student's GPA for that term is 3.16 when rounded to two decimal places.
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In the theory of learning, the rate at which a subject is memorized is assumed to be proportional to the amount that is left to be memorized. Assume that the rate at which material is forgotten is proportional to the amount memorized. Suppose M denotes the total amount of a subject to be memorized and A(t) is the amount memorized in time t > 0. Determine a differential equation for the amount A(t) when forgetfulness is taken into account. (Assume the constants of proportionality for the rate at which material is memorized and the rate at which material is forgotten are k1 > 0 and k2 > 0, respectively. Use A for A(t).)
Answer: equation = dA/dt = K₁ (M - A) - K₂A
Step-by-step explanation:
Let us follow this carefully to get our equation right.
From the question we are told to (Assume the constants of proportionality for the rate at which material is memorized and the rate at which material is forgotten are k1 > 0 and k2 > 0, respectively. Use A for A(t) ).
The Rate of memorizing the material is ∝ [Total amount to be memorized] - [Amount memorized]
remember using A for A(t).
where A rep the amount memorized at a time t and M is the Total amount memorized.
so we have that dA/dt ∝ M - A
which is dA/dt = K₁ (M - A) ---------------(*)
remember it was stated that forgetfulness is taken into account
Forgetfulness, F ∝ A
F = K₂A --------------- (**)
which implies the rate of memorization is decreased as a result of forgetting;
this leads to
dA/dt = K₁ (M - A) - K₂A
The rate of differential equation is ⇒ dA/dt = K₁ (M - A) - K₂A
cheers i hope this helped!!!!
what’s the measure of the angle theta?
Answer:
∅ = 50°
Step-by-step explanation:
YOU NEED A CALCULATOR TO SOLVE THIS!
You need to use Law of Sines
[tex]\frac{a}{sinA} =\frac{b}{sinB} = \frac{c}{sinC}[/tex]
Here you will be doing [tex]\frac{a}{sinA} =\frac{c}{sinC}[/tex]
a and c are the lengths, while A and C are the angles
[tex]\frac{3.46}{sinA} = \frac{2.54}{sin43}[/tex] you want to get the denominators out from underneath so multiply both sides by sinA and sin43
[tex]3.46sin43 = 2.54sinA[/tex]
Now you want to get sinA alone so divide both sides by 2.54
[tex]\frac{3.46sin43}{2.54} = sinA[/tex] now get A alone
[tex]sin^{-1} (\frac{3.46sin43}{2.54}) = A[/tex] put that into the calculator
[tex]49.61741033 = A[/tex]
simplify: 11y+3y-y+7x-2x
Answer:
13x + 5x
Step-by-step explanation:
A circle has a radius of 9cm and a sector of the circle has an arc length of 9.7
Answer:62
Step-by-step explanation:
emily is adding 51 and 29 which steps can she use to add the numbers
Answer:
51 + 29+ 80
Step-by-step explanation:
she got this by adding 51 + 29
A random sample of 8989 eighth grade students' scores on a national mathematics assessment test has a mean score of 282282. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 280280. Assume that the population standard deviation is 3838. At alphaαequals=0.050.05, is there enough evidence to support the administrator's claim? Complete parts (a) through (e).
Answer:
[tex]t=\frac{282-280}{\frac{38}{\sqrt{89}}}=0.497[/tex]
Now we can calculate the p value for the test
We are conducting a right tailed test so then the p value is given by:
[tex]p_v =P(z>0.497)=0.310[/tex]
Since the p value is higher than the significance level we have enough evidence to conclude that the true mean is not significantly higher than 280 so then the administrator claim is not true
Step-by-step explanation:
Data provided
[tex]\bar X=282[/tex] represent the mean for the assesment test
[tex]\sigma=38[/tex] represent the population deviation
[tex]n=89[/tex] sample size
[tex]\mu_o =280[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to determine if the mean score for the state's eighth graders on this exam is more than 280, so then the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 280[/tex]
Alternative hypothesis:[tex]\mu > 280[/tex]
Since we know the population deviation we can use a z test for the true mean and the statistic is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Replacing the info given by the problem we got:
[tex]t=\frac{282-280}{\frac{38}{\sqrt{89}}}=0.497[/tex]
Now we can calculate the p value for the test
We are conducting a right tailed test so then the p value is given by:
[tex]p_v =P(z>0.497)=0.310[/tex]
Since the p value is higher than the significance level we have enough evidence to conclude that the true mean is not significantly higher than 280 so then the administrator claim is not true
To determine if there is enough evidence to support the administrator's claim, we need to perform a hypothesis test. By comparing the z-score to the critical value at α=0.05, we can reject the null hypothesis and conclude that there is enough evidence to support the administrator's claim.
Explanation:To determine if there is enough evidence to support the administrator's claim, we need to perform a hypothesis test. The null hypothesis (H0) is that the mean score for the state's eighth graders is <=280. The alternative hypothesis (Ha) is that the mean score is >280.
To conduct the test, we can calculate the z-score using the formula z = (x - μ) / (σ / sqrt(n)), where x is the sample mean, μ is the hypothesized population mean (280), σ is the population standard deviation (38), and n is the sample size (8989). Plug in the given values, we get z = (282 - 280) / (38 / sqrt(8989)) = 3.055.
Next, we compare the z-score to the critical value at α=0.05. For a one-tailed test, the critical value is 1.645. Since 3.055 > 1.645, we reject the null hypothesis and conclude that there is enough evidence to support the administrator's claim that the mean score for the state's eighth graders on this exam is more than 280.
What is the solution for a in the following question? 2b-a=5
Answer:
5
Step-by-step explanation:
so you can think of it as b is 5 and 2 times by 5 is 10. you can then make 10 - 5 which is 5. so a is 5
What is the area of the parallelogram below?
A. 7 in
B. 14 in
C. 15 in
D. 12 in
Answer:
D. 12 in²
Step-by-step explanation:
The area of a parallelogram is given by the formula ...
A = bh
Substituting the given values for the length of the base (b) and the height (h), we have ...
A = (4 in)(3 in)
A = 12 in²
The area is 12 square inches.
Answer:
D 12
Step-by-step explanation:
I just did the lesson and got it right.