Answer:
-x^2 + 4x + 6
Step-by-step explanation:
(f-g)(x) = f(x) - g(x) =
4x + 1 - (x^2 -5) =
-x^2 +4x + 6
Translate to an algebraic equation then solve. 33. The length of a rectangle is six units longer than the width. Find the length and width if the perimeter of the rectangle is 60 units.
Answer:
length 18 unitswidth 12 unitsStep-by-step explanation:
Let w represent the width of the rectangle. Then the length is w+6, and the perimeter is ...
P = 2(L +W)
60 = 2((w+6) +w) . . . substitute known values
30 = 2w +6 . . . . . . . .divide by 2, collect terms
15 = w +3 . . . . . . . . . divide by 2 again
12 = w
w+6 = 18
The length is 18 units; the width is 12 units.
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.
To learn more about the divide visit:
https://brainly.com/question/28119824
#SPJ12
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.
Learn more about Calculating GPA here:https://brainly.com/question/30641827
#SPJ3
Philip built an addition onto his CD store to expand his floor space for more music. His usable floor space was tripled even after he set aside 150 square feet for a new video arcade. If the floor space of the entire new structure is 1800 square feet, what was the area of the original floor
Answer:
figure to out
Step-by-step explanation:
5 cm
7 cm
15 cm
What is th5 surface area of the figure?
_square centimeters
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
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
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).
Add 5/12 plus 69/10 as an improper fraction in lowest terms
Jared is comparing the interest rates on savings accounts at several banks near his home. He chooses an account that pays 0.85% interest annually. What is 0.85% written as a decimal? (Please remember your rules for turning percents into decimals)
HEELP PLZ fast!
A
0.00085
B
0.0085
C
0.085
D
0.085
Answer:
Option "B" is the correct answer to the following question.
Step-by-step explanation:
Given:
Rate of annual interest = 0.85%
Find
Value of 0.85% in decimal
Computation:
To convert any percent number into a decimal, we have to divide that number by 100.
So,
Value of 0.85% in decimal = [tex]\frac{0.85}{100}[/tex]
Value of 0.85% in decimal = 0.0085
Note: We have to eliminate the percent symbol from the given number.
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:
Multiply 13x-2 by 12
Answer:
156x-24
Step-by-step explanation:
12*(13x-2)=
12*13x+12*(-2)=
156x-24
Hope this helps!
8 customers entered a store over the course of 16 minutes. At what rate were the customers entering the store in minutes per customer?
Answer:
1 customer per 2 minutes or 1/2 of a customer per 1 minute(I would go with the 1st one since you can't have 1/2 of a customer.)
Step-by-step explanation:
The customers were entering at the rate of 1 customer in 2 minutes.
What is unit rate?A unit rate means a rate for one of something.
Given that, 8 customers entered a store over the course of 16 minutes.
8 customers in 16 minutes
1 customer = 16/8 = 2 minutes.
Hence, The customers were entering at the rate of 1 customer in 2 minutes.
For more references on unit rate, click;
https://brainly.com/question/11258929
#SPJ2
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
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°
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:
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?
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.
A broken thermometer reads 33° F, but Kira knows that the temperature is at least 33° F, if not even colder. Which of the following inequalities, shows the possible temperatures?
t ≤ 33° F
t ≥ 33° F
t > 33° F
t < 33° F
Answer:
t ≤ 33°F
Step-by-step explanation:
Answer:
t ≤ 33° F
Step-by-step explanation:
simplify: 11y+3y-y+7x-2x
Answer:
13x + 5x
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]
ake and Nico both measured their thumbs. Jake’s thumb is 55 millimeters long. Nico’s thumb is 5.7 centimeters long. Who has the longer thumb? Explain how you know.
Answer:
Nico
Step-by-step explanation:
We have to convert both to the same units! Think about the units: we have millimeters and centimeters. There are 10 millimeters in a centimeter, so
55 mm = 5.5 cm
We just had to move the decimal point!
Now compare the two measurements in cm. 5.5 and 5.7: which is greater? Look at the tenths place: 5<7, so 5.7 is greater and Nico’s thumb is longer!
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
Sometimes when grouping symbols are use to enclose other grouping symbols, we use __________ instead of parentheses or brackets, to make an expression easier to read.
Example: 2{(3 + 5)[2 −(4 + 5)] + 8
Answer:
Sometimes when grouping symbols are use to enclose other grouping symbols, we use braces instead of parentheses or brackets, to make an expression easier to read.
Step-by-step explanation:
To group numbers or variables, brackets and braces are mostly used. Generally, they are used after parentheses. Parentheses are to be used first, then brackets, and then braces: {[( )]}.
However, instead of brackets or braces, sometimes, the use of larger parentheses will be observed.
Answer:
Square brackets will always be used, to enclose or group several arithmetic operations that involve several simultaneous operations, as described in the example.
The bracket generally groups or implies that the most particular or small operations must be performed until finally breaking it down and thus solving the entire general operation.
Step-by-step explanation:
1. When there are no parentheses or square brackets, we do the multiplications and divisions first if there are any. If there are several positive and negative numbers we group them together and then add them together.
2. When there are parentheses, we first make the calculations for the parentheses if there are any, and then to remove the parentheses we apply the rule of signs, sign that is in front of the parenthesis for each sign that is inside.
3. When there are parentheses and square brackets, we make the parentheses first, we remove them applying the rule of signs. Then we make the brackets and remove them applying the rule of signs. Then we make the products and divisions and finally the sums.
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 repair person charges $25 per hour plus and initial service charge of $30.
Marty received a bill for $155. How many hours did the repair person work?
Answer:
The repair person did 5 hours of work.
Step-by-step explanation:
155 = 25x + 30
125 = 25x
5 = x
Answer:
5 hours
Step-by-step explanation:
155 less 30 initial = 125 divided by 25 an hour = 5
What is the slope intercept form of the equation -7x +14y=-35
Answer:
-7x+14y-35
Step-by-step explanation:
Answer:
y=-1/2x+5/2
Step-by-step explanation:
slope intercept form is y=mx+b
add 7x to both sides to get y alone on the left side of the equal sign
divide by 14 to get y alone
gets your answer y=-1/2x+5/2
Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses. Her goal is 100% of orders shipped within 24 hours. In previous years, neither warehouse has achieved the goal, but the East Coast warehouse has consistently out-performed the West Coast warehouse. Her staff randomly selected 200 orders from the West Coast warehouse (population 1) and 400 orders from the East Coast warehouse (population 2), and reports that 190 of the West Coast orders were shipped within 24 hours, and the East Coast warehouse shipped 372 orders within 24 hours. Maureen's null hypothesis is:
Answer:
Maureen's null hypothesis is, H₀: p₁ ≥ p₂.
Step-by-step explanation:
Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies wants test whether her goal of shipping 100% orders within 24 hours is achieved or not.
After reviewing the order filling operations at her warehouses she determines that neither the East coast nor the West coast warehouse has achieved the goal. But the East Coast warehouse has consistently out-performed the West Coast warehouse.
To check whether this determination is correct or not Maureen's staff randomly selected 200 orders from the West Coast warehouse (population 1) and 400 orders from the East Coast warehouse (population 2).
Of the 200 orders from the West Coast warehouse, 190 were shipped within 24 hours. And of the 400 orders from the East Coast warehouse, 372 were shipped within 24 hours.
The hypothesis can be defined as follows:
H₀: The proportion of orders that were shipped within 24 hours is not more for East Coast warehouse than for West Coast warehouse, i.e. p₁ ≥ p₂.
Hₐ: The proportion of orders that were shipped within 24 hours is more for East Coast warehouse than for West Coast warehouse, i.e. p₁ < p₂.
Thus, Maureen's null hypothesis is, H₀: p₁ ≥ p₂.
Maureen McIlvoy's null hypothesis would likely be that there is no significant difference in the shipment times of the East Coast and West Coast warehouses. Despite the initial data suggesting better performance at the West Coast, more statistical analysis such as a z-test or t-test would be required to confirm if there is a significant difference.
Explanation:In this context, Maureen McIlvoy, who is the owner and CEO of a mail order business for wind surfing equipment, is evaluating the efficiency of order fulfilment at her warehouses. Given her goal is to ship 100% of her orders within 24 hours, she is interested in comparing the performance of the East Coast warehouse to the West Coast warehouse.
When conducting such an analysis, a null hypothesis serves as the baseline or default expectation. In this case, Maureen's null hypothesis could possibly be that there's no difference in the performance between the two warehouses in terms of orders shipped within 24 hours, despite the past performance.
With the given data of 190 out of 200 orders shipped on time at the West Coast, and 372 out of 400 orders shipped on time at the East Coast, we can further analyze the percentages of timely shipping - 95% and 93% respectively. Though the West coast performed better in the examined sample, this is not sufficient to reject the null hypothesis that the performances are identical without further statistical testing such as a z-test or t-test.
On the other hand, her alternative hypothesis could state that there is a significant difference in the efficiency of the two warehouses in achieving the 24-hour shipping target.
Learn more about Null Hypothesis here:https://brainly.com/question/30821298
#SPJ11
Using this formula, what is the acceleration of an object with F=7.92 newtons and m=3.6 kilograms? Express your answer to the nearest tenth.
To find the acceleration of an object with a force of 7.92 N and mass of 3.6 kg, use the formula F = ma to calculate the acceleration as 2.2 m/s².
The force acting on the object can be calculated using the formula F = ma, where F is the force, m is the mass, and a is the acceleration.
Given F = 7.92 N and m = 3.6 kg, plug these values into the formula: F = 7.92 N, m = 3.6 kg.
Calculate the acceleration using the formula: a = F/m = 7.92 N / 3.6 kg = 2.2 m/s².
Therefore, the acceleration of the object with a force of 7.92 N and mass of 3.6 kg is 2.2 m/s².
2. Jeff is trying to "get with" Slater. Being a calculating player, Jeff knows that his population proportion of landing a date is 69 percent. Jeff is going to make advances on Slater until success, so let us model the situation with a geometric distribution.2 (a) What is the probability that Jeff needs exactly 3 advances? (b) What is the probability that Jeff needs at least 3 advances? (c) Given that Jeff already made 4 advances, what is the probability that Jeff will need at least 3 more advances? (d) Show that all of the possibilities do indeed add up to 100 percent.
Answer:
[tex]\bf a) - 0.0663\\b) - 0.31\\c) - 0.021\\d) - 1 or 100%[/tex]
Step-by-step explanation:
[tex]Let\;p = 69\;\% =0.69[/tex]
[tex]So, p(x)=q^{x-1}p[/tex] [tex]-(i)[/tex]
a) - The probability which Jeff requires at exactly three advances that is,
Then, put the value of [tex]x=3[/tex] in eq - i
[tex]p(x=3)=(0.31)^{3-1}(0.69)[/tex]
[tex]p(x=3)=0.0663[/tex]
b) - The probability which Jeff requires at least three advances that is,
[tex]p(x\geq1)=1-p[/tex]
Put the value of [tex]p[/tex] in the eq
[tex]p(x\geq 2)=1-0.69=0.31[/tex]
c) - Considering that he has only made four advances, the probability would be that he will require at least three more advances that is.
[tex]p(\frac{x=7}{x\geq 4}) = \frac{p(x=7\;\cap\;x\geq 4)}{p(x\geq 4)}[/tex]
[tex]p(\frac{x=7}{x\geq 4}) = \frac{p(x=7)}{1-p(x\leq 3)}[/tex]
Then, put the value in the eq - i
[tex]=\frac{(0.31)^{7-1}(0.69)}{1-\sum_{x=1}^{3}(0.31)^{x-1}(0.69)}[/tex]
[tex]=\frac{0.0006}{1-0.9702}[/tex] [tex]=0.0201[/tex]
d) - Display that all possibilities actually added up to 100% that is.
[tex]p(x\geq1)=p(x=1)+p(x=2)+p(x=3)...........[/tex]
[tex]=q^{1-1}p+q^{2-1}p+q^{3-1}p[/tex]
by solving [tex]x=1[/tex] then, we get
[tex]=\frac{p}{1-q} =\frac{0.69}{1-031}[/tex]
So, we get 1 or 100%.
Answer:
A) 0.0066309 ; B) 0.0961 ; D) Proven
Step-by-step explanation:
Geometric Distribution : X ~ [tex]q^(x-1) . p[/tex]
p = 0.69 ; q = 1- p = 1 - 0.69 = 0.31
A) P (x = 3) = [tex](0.31)^(3-1) (0.69) = 0.31^2 (0.69) = 0.0961(0.69)= 0.0066309[/tex]
B) P (x > 3) = 1 - [ P(x =1) + P(x = 2) ]
[tex]1 - [(0.31)^0 (0.69) + (0.31)^1(0.69)] = 1 - (0.69 + 0.2139) = 1 - 0.9039 = 0.0961[/tex]
D) P (x > 1) = P (x =1) + P (x = 2) + P (x = 3) ...............
= p + pq + pq^2 + pq^3 ........ [Geometric series with a = p , r = q]
Sum of infinite geometric series = a / (1- r)
p / (1-q) = 0.69 / (1-0.31) = 0.69 / 0.69 = 1 {Hence Proven}
In a recent survey, a random sample of 199 office managers were asked about overtime, and 76 reported that they regularly work overtime each week. What value of z should be used to calculate a confidence interval with a 98% confidence level
Answer:
2.326
Step-by-step explanation:
They are only asking which z-score should you use. To determine find the confidence interval which is 98% or .98.
Subtract this number by 1 and divide by 2.
1-.98=.02/2=.01
Find the correlating z-score for z.01 on the z-score chart which is 2.326
The z-value for a 98% confidence level in statistics, used in constructing confidence intervals, is approximately 2.33 standard deviations away from the mean.
Explanation:The question falls under the area of statistics, specifically, confidence intervals. In order to find the z-value for a 98% confidence level, we turn to the z-table or use a z-score calculator. The z-value for a 98% confidence level is approximately 2.33. This value represents the number of standard deviations away from the mean that your confidence interval is.
The idea here is that for us to be 98% confident that our interval contains the true population mean or proportion, our interval must extend 2.33 standard deviations on either side of our sample mean or proportion. Thus, in the context of your survey of office managers working overtime, this z-value would be used to calculate your confidence interval for the proportion of all office managers who work overtime.
Learn more about Z-Score for 98% Confidence Level here:https://brainly.com/question/30637686
#SPJ3