Add 8 to both sides.
3k = 7 + 8Add 7 and 8 to get 15.
3k = 15Divide both sides by 3.
k = 15 / 3Divide 15 by 3 to get 5.
k=5 ===> Answer===> Exercise 28b + 9 = −15
Subtract 9 from both sides.
8b= −15 − 9Subtract 9 from −15 to get −24.
8b = −24Divide both sides by 8.
b = -24 / 3Divide −24 entre 8 para obtener −3.
b=−3 ===> Answer===> Exercise 38 = 3x − 13
Swap the sides so that all the terms of the variables are on the left side.
3x −13 = 8Add 13 to both sides.
3x = 8 + 13Add 8 and 13 to get 21.
3x = 21Divide both sides by 3.
x = 21 / 3Divide 21 by 3 to get 7.
x = 7 ===> Answer===> Exercise 46p + 22 = 4
Subtract 22 from both sides.
6p = 4 − 22Subtract 22 from 4 to get −18.
6p = −18Divide both sides by 6.
p = -18 / 6Divide −18 entre 6 para obtener −3.
p = −3 ===> Answer===> Excercise 584 = 51 + 11c
Swap the sides so that all the terms of the variables are on the left side.
51 + 11c = 84Subtract 51 from both sides.
11c = 84 − 51Subtract 51 from 84 to get 33.
11c = 33Divide both sides by 11.
c = 33 / 11Divide 33 by 11 to get 3.
c = 3 ===> AnswerSolution 1 :-
>> 3k - 8 = 7
>> 3k = 7 + 8
>> 3k = 15
>> k = 15 / 3
>> k = 5
Solution 2 :-
>> 8b + 9 = -15
>> 8b = -15 - 9
>> 8b = -24
>> b = -24 / 8
>> b = -3
Solution 3 :-
>> 8 = 3x - 13
>> 3x = 13 + 8
>> 3x = 21
>> x = 21 / 3
>> x = 7
Solution 4 :-
>> 6p + 22 = 4
>> 6p = 4 - 22
>> 6p = -18
>> p = -18 / 6
>> p = -3
Solution 5 :-
>> 84 = 51 + 11c
>> 11c = 84 - 51
>> 11c = 33
>> c = 33 / 11
>> c = 3
Please help me with alg 2 question!
Answer:
J
Step-by-step explanation:
Which best explains whether a triangle with side lengths 5 cm, 13 cm, and 12 cm is a right triangle?
The triangle is a right triangle because 52 + 122 = 132.
The triangle is a right triangle because 5 + 13 > 12.
The triangle is not a right triangle because 52 + 132 > 122.
The triangle is not a right triangle because 5 + 12 > 13.
9
Answer:
the triangle is a right angle triangle. I can't see the correct explanation here so I will explain
Step-by-step explanation:
to work out whether triangles are right angle you do :
square root of (5² + 12²) so it would be 25 + 144 =169 and the square root of 169 is 13 . we do this because the square root of both of the side lengths squares should make ths longer side in this case it makes 13 so it is a right angled triangled
i hope this helps . if you need any more help pls ask :)
The patient recovery time from a particular surgical procedure is normally distributed with a mean of 3 days and a standard deviation of 1.8 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N( , ) b. What is the median recovery time? days c. What is the Z-score for a patient that took 4 days to recover? d. What is the probability of spending more than 3.8 days in recovery? e. What is the probability of spending between 3.2 and 4.2 days in recovery? f. The 90th percentile for recovery times is days.
Using the normal distribution, we have that the desired information is given as follows:
a) X ~ N(3,1.8).
b) 3 days.
c) Z = 0.5556.
d) 0.33 = 33%.
e) 0.2048 = 20.48%.
f) 5.3 days.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 3, \sigma = 1.8[/tex]
Hence the distribution is X ~ N(3,1.8), and, as is standard in the normal distribution, the median is the same as the mean, which is of 3 days.
The Z-score for a patient that took 4 days to recover is Z when X = 4, hence:
Z = (4 - 3)/1.8 = 0.5556.
The probability of spending more than 3.8 days in recovery is one subtracted by the p-value of Z when X = 3.8, hence:
Z = (3.8 - 3)/1.8 = 0.44.
Z = 0.44 has a p-value of 0.67.
1 - 0.67 = 0.33.
The probability is of 0.33 = 33%.
The probability of spending between 3.2 and 4.2 days in recovery is the p-value of Z when X = 4.2 subtracted by the p-value of Z when X = 3.2, hence:
X = 4.2:
Z = (4.2 - 3)/1.8
Z = 0.67.
Z = 0.67 has a p-value of 0.7486.
X = 3.2:
Z = (3.2 - 3)/1.8
Z = 0.11.
Z = 0.11 has a p-value of 0.5438.
0.7486 - 0.5438 = 0.2048 = 20.48%.
The 90th percentile is X when Z = 1.28, hence:
1.28 = (X - 3)/1.8
X - 3 = 1.8 x 1.28
X = 5.3 days.
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PLEASE ASAP - Drag each tile to the correct box. Arrange the figures from least to greatest according to their volumes. Assume the variable h has the same value for each figure.
Assuming that the variable h is the same for each figure, the figures from the least to the greatest is:
Cone with radius of 3 units Cylinder with radius of 3 units Cone with radius of 6 units Cylinder with radius of 6 unitsWhat are the volumes of these shapes?The value of h is the same for all the shape so assume the value of h is 2 units.
The volume of a cylinder is:
= πr²h
First cylinder area:
= 22/7 x 3 x 2
= 56.54867 units
The second cylinder area:
= 22/7 x 6 x 2
= 226.19467 units
The volume of a cone is:
= πr²h/3
First cone volume:
= 22/7 x 3 x 2/3
= 18.84956 units
Second cone volume:
= 22/7 x 6 x 2/3
= 75.39822 units
The order is therefore:
Cone with radius of 3 units < Cylinder with radius of 3 units < Cone with radius of 6 units < Cylinder with radius of 6 units
In conclusion, the shapes with the larger radius of 6 units will have more volume.
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At a furniture manufacturer, worker a can assemble a shelving unit in 5 hours. worker b can assemble the same shelving unit in 3 hours. which equation can be used to find t, the time in hours it takes for worker a and worker b to assemble a shelving unit together? rate (shelving units per hour) time (hours) fraction completed worker a one-fifth t worker b one-third t 5 t 3 t = 1 one-fifth t minus one-third t = 1 one-fifth t one-third t = 1 5 t minus 3 5 = 1
If they work together, they need 15/8 hours to assemble one shelving unit.
What does work mean in math?
In summary, work is done when a force acts upon an object to cause a displacement. Three quantities must be known in order to calculate the amount of work. Those three quantities are force, displacement and the angle between the force and the displacement.According to tittle, we know worker A can assemble a shelving unit in 5 hours , which means worker A can finish 1/5 of work in 1 hour . And worker B can finish 1/3 of work in 1 hour.
If A & B work together , they will spend the same time t to assemble only one shelving .
That means, 1/5t + 1/3 t = 1 (equation)
1/5 t is worker A's workload during time t , 1/3 t is worker B workload.
So, 1/5 t + 1/3t = 1 is the answer
⇒ 5t + 3t = 15
⇒ t = 15/8 hours
If they work together, they need 15/8 hours to assemble one shelving unit.
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Answer:
Letter C is the correct answer or 1/5 t + 1/3t = 1
PLEASE HELP ME SOLVE THE QUESTION BELOW
Ann and Tom want to establish a fund for their grandson's college education. What lump sum must they deposit at 12 % annual interest rate, compounded quarterly , in order to have 20,000$ in the fund at the end of 10 years?
For Ann and Tom to have $20,000 at the end of 10 years, they must deposit a sum of $6,131.14.
What is the principal?
To calculate the sum of money they must deposit, use the compound interest formula.
From the compound interest formula;
P = A / ( 1 + r/n )^(nt)
Given that;
Final amount A = 20,000Interest rate r = 12% = 12/100 = 0.12Compound n = quarterly = 4Time t = 10 yearsPrincipal P = ?P = A / ( 1 + r/n )^(nt)
P = 20,000 / ( 1 + 0.12/4 )^(4×10)
P = 20,000 / ( 1.03)^40
P = 20,000 / 3.26203779
P = $6,131.14
Therefore, for Ann and Tom to have $20,000 at the end of 10 years, they must deposit a sum of $6,131.14.
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6. If x is the largest of three consecutive integers, represent the sum of the three integers.
a) If x is the largest of three consecutive integers, how do we represent the three integers?
b) How do we convert this information into a solvable equation?
c) Find the sum
Answer:
See below
Step-by-step explanation:
x = largest
x-1 previous
x -2 smallest
sum = x + x-1 + x-2
sum = 3x -3
Find x. A. 4–√6 B. 16√6/3 C. 4√6/3 D. 32√3/3
Answer:
Step-by-step explanation:
12
Solve the equation 5(x + 2) = 6x + 3x − 14, and show your work. (5 points)
If the maximum payment of $5,000 is made into a individual retirement account (ira) for 25 years at an annual interest rate of 3.2%, determine the amount in the account.round to the nearest cent. a. $187,159.62 b. $193,148.73 c. $129,082.99 d. $129,427.21
The amount in the ira's account s = $187,159.62.
How do you interest rate?
The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned. The interest rate on a loan is typically noted on an annual basis known as the annual percentage rate (APR).Future Value of an Ordinary Annuity
[tex]s = R(( 1 + i)^{n} - 1 ) / i[/tex]
where
S = the future value;
R = the periodic payment;
i = the interest rate per period;
n = the number of periods.
[tex]s = 5000 ( 1 + 0.032)^{25} - 1)/ 0.032[/tex]
[tex]s = 5000((1.032)^{25} - 1 )/0.032[/tex]
[tex]s = 5000( 2.19782157471 - 1)/0.032[/tex]
[tex]s = 5000(1.19782157471)/0.032[/tex]
[tex]s = 5000 * 37.4319242096[/tex]
s = $187,159.62
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The length and breadth of a rectangular park 25m and 12m. find the distance covered by a boy who takes 4 rounds of the garderean. also find its a
Answer:296 m
I’m assuming “breadth” is width and garderean is just the park.
(25+25+12+12) times 4.
A is never defined
The local gym is offering this new promotion: An enrollment fee of $40 and a monthly fee of $30. Which of the following expressions represents the cost of the gym membership for m months?
40+30m=c40 plus 30 m is equal to c
30+40m=c30 plus 40 m is equal to c
40+30m40 plus 30 m
30+40m
The expression 40 + 30m = c represents the cost of the gym membership for m months option (A) 40 + 30m = c is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
The local gym is offering this new promotion:
An enrollment fee of $40 and a monthly fee of $30.
Let m be the total number of months
Total monthly fee = 30m
Total cost(including the enrollment fee of $40) = 40 + 30m
Let the total cost is c:
c = 40 + 30m
If in the linear expression, one variable is present, then the bis known as the linear expression in one variable.
Thus, the expression 40 + 30m = c represents the cost of the gym membership for m months option (A) 40 + 30m = c is correct.
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Find the circumference of a circle with radius of 4.2in.
Answer: 26.39
Step-by-step explanation:
2xπxr
Hank is currently reading a book that is 250 pages long. if he can read 10 pages every 15 minutes, how many hours will it take him to read the book?
Answer:
The answer is B, 2.78 hours
Step-by-step explanation:
Answer:
6 hours 15 minutes, or 6.25 hours
Step-by-step explanation:
We assume Hank reads at a constant rate. His reading time will be proportional to the number of pages.
ProportionWe know that 15 minutes is 1/4 hour, so the proportion can be written ...
hours/pages = (book hours)/(250 pages) = (1/4 hour)/(10 pages)
Multiplying by 250 pages gives ...
book hours = 250(1/4 hour)/10 = 25/4 hour = 6 1/4 hour
It will take Hank 6 1/4 hours to read the book.
Maria and Franco are mixing sports drinks for a track meet.
Maria uses cup of powdered mix for every 2 gallons of water. Franco uses
1 cups of powdered mix for every 5 gallons of water. Whose sports drink is
stronger? Explain how you found your answer
Answer:Maria
Step-by-step explanation: Maria uses a cup per 2 gallons while Franco uses a cup for 5 gallons. Maria has a 1:16 ratio while Franco has a ratio of 1: 80 because a gallon is 16 cups. It is clear now that Franco has a smaller ratio so, Maria's sports drink is stronger.
Consider the word pencil. if all of the letters are used, and the first letter can’t be n or l, how many ways can the letters be arranged?
480 Ways can the letters be arranged.
What is the meaning of probability ?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.First letter can't be n or l
= 4! × [tex]5P_{3}[/tex]
= 24 × 5! /3!
= 24 × 5 × 4
= 480
Therefore, 480 ways can the letters be arranged.
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Answer: 480 ways
Step-by-step explanation:
Evaluate the following expression. "5 less than 15"
A. -10
B. 8
C. 20
D. 10
Answer: 10
Step-by-step explanation: 5 less than 15 is 10 because 15 - 5 is 10. If it was 15 less from 5, only then it would be -10.
Answer:
5 less than 15 is Option D, 10. This is because using mathematical symbols, it says 15-5 which equals to 10.
Assume you took $5,000 out of the bank to purchase a car worth $5,000. How much did you net worth change?
Your net worth change by zero dollars.
What is net worth?Net worth is the difference between asset and liability.
In other words net worth is the sum of all assets owned by a person or a company, minus any obligations or liabilities.
Therefore, since he took $5,000 out of the bank to purchase a car worth $5,000 his net worth will change by zero dollars.
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What is the shape of the cross section taken parallel to the base of a cylinder? circle rectangle triangle ellipse
The option A is correct. A circle is the shape of the cross section taken parallel to the base of a cylinder.
According to the statement
We have given that the cylinder and we have to tell that the which shape required for the cross section taken parallel to the base of a cylinder.
So, For this purpose,
We know that the
A cylinder is a three-dimensional solid, one of the most basic geometric shapes.
In this shape the surface formed by the points at a fixed distance from a line segment, which is known as the axis of the cylinder.
As the bases of cylinder are two identical circles which are parallel to the curved surface.
The curved surface when we open will be circle rather than the circle.
So, Due to this reason the answer is a circle.
Therefore, a circle is the shape of the cross section taken parallel to the base of a cylinder.
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Help me please! I’ll make you a brainlest show you work!!
The solution to the following mathematical problems are;
5² -3⁴ / (2³-5)(6² ÷ 9) = - 14/320² ÷ {3(5-9)² + 2} = 884/12 + (5-7)² -72 ÷ 6×2 = -13EvaluationSolve using
BODMAS
B - bracketO - offD - division M - MultiplicationA - additionS - Subtraction5² -3⁴ / (2³-5)(6² ÷ 9)
= 25-81 / (8-5)(36÷9)
= -56 / (3)(4)
= -56/12
= - 14/3
20² ÷ {3(5-9)² + 2}
= 400 ÷ {3(-4)² + 2}
= 400 ÷ {3(16) + 2}
= 400 ÷ (48+3)
= 400 ÷ 50
= 8
84/12 + (5-7)² -72 ÷ 6×2
= 7 + (-2)² - 12 × 2
= 7 + (4) - 24
= 11 - 24
= -13
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Please please please help
Answer:r=14°
Step-by-step explanation:
(5r-5)°+ (8r+3)°=180
(Sum of angles on a straight line =180°)
Collect like terms
5r+8r-5+3=180
13r-2=180
13r=180+2
13r=182
r=182/13
r=14°
g(a) = 4a + 5
f(a) = a² + 2a
Find: g(f(a))
Step-by-step explanation:
g(f(a))=4(a²+2a) + 5
= 4a²+8a+5
A coin is flipped 15 times where each flip comes up either heads or tails. How many possible outcomes (a) contain exactly four tails (b) contain at least three heads?
Using the arrangements formula, it is found that:
a) There are 1365 possible outcomes that contain exactly four tails.
b) There are 1,307,674,399,889 possible outcomes that contain at least three heads.
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
When there are repetitions, the number of ways is given as follows:
[tex]A_{n}^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}[/tex]
In which [tex]n_1, n_2, \cdots, n_n[/tex] are the numbers of repetitions.
Item a:
11 heads and 4 tails, hence:
[tex]A_{15}^{11,4} = \frac{15!}{11!4!} = 1365[/tex]
There are 1365 possible outcomes that contain exactly four tails.
Item b:
The total number is:
[tex]A_{15} = 15! = 1,307,674,400,000[/tex]
With no heads:
[tex]A_{15}^{15,0} = \frac{15!}{15!0!} = 1[/tex]
With one head:
[tex]A_{15}^{14,1} = \frac{15!}{14!1!} = 15[/tex]
With two heads:
[tex]A_{15}^{13,2} = \frac{15!}{13!2!} = 95[/tex]
Hence the number of outcomes with less than three heads is:
1 + 15 + 95 = 111
With at least three heads, the number of outcomes is:
[tex]1,307,674,400,000 - 111 = 1,307,674,399,889[/tex]
There are 1,307,674,399,889 possible outcomes that contain at least three heads.
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Find the ratio of 4:25
A function is shown: f(x) = 36x² - 1.
Choose the equivalent function that best shows the x-intercepts on the graph
Based on the given function, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x - 1)(6x + 1)
What are equivalent functions?Equivalent functions are different functions that have equal values when evaluated and compared
How to determin the equivalent function that best shows the x-intercepts on the graph?
The function is given as:
f(x) = 36x^2 - 1
Express 1 as 1^2
f(x) = 36x^2 - 1^2
Express 36x^2 as (6x)^2
f(x) = (6x)^2 - 1^2
Apply the difference of two squares.
This is represented as:
(a + b)(a - b) = a^2 - b^2
So, we have the following equation
f(x) = (6x - 1)(6x + 1)
Based on the given function, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x - 1)(6x + 1)
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Instructions: Find the volume of each figure. Round your answers to the nearest tenth, if necessary.
The volume of the cone is 84.9 km³
How to find the volume of a cone?Volume of a cone = 1 / 3 πr²h
where
h = heightr = radiusTherefore,
radius = 3 km
height = √9.5² - 3²
height = √81.25
height = 9.01387818866
height = 9.014 km
Volume of a cone = 1 / 3 × 3.14 × 3² × 9.014
volume of the cone = 254.732197612 / 3
volume of the cone = 84.9107325372
volume of the cone = 84.9 km³
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A triangle has side lengths of (2b + 5c) centimeters, (10b + 7d) centimeters, and
(4d-3c) centimeters. Which expression represents the perimeter, in centimeters,
of the triangle?
The perimeter of the triangle can be express as follows:
12b + 11d + 2c
How to find perimeter of a triangle?The perimeter of a figure is the sum of the whole sides of the figure.
A triangle has three sides. Therefore, the perimeter of a triangle is the sum of the three sides.
Therefore, the sides of the triangle are of lengths (2b + 5c) centimetres, (10b + 7d) centimetres, and (4d-3c) centimetres.
Hence, the perimeter of the triangle can be represented as follows:
Perimeter of the triangle = 2b + 5c + 10b + 7d + 4d - 3c
Perimeter of the triangle = 2b + 10b + 7d + 4d + 5c - 3c
Perimeter of the triangle = 12b + 11d + 2c
Therefore, the perimeter of the triangle can be express as follows:
12b + 11d + 2c
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jaquan washes cars for his neighbors on the weekends. Jaquan uses the same amount of water for each car he washes. the point on the following coordinate plane show how much water jaquan uses for 2,5, and 8. How much water does Jaquan use for 6 cars?
help me plsss
The amount of water for washing x cars is y = 12x, and 72 gallons would be needed to wash 6 cars.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The standard form of a linear equation is given as:
y = mx + b
Where m is the rate of change and b is the y intercept (initial value of y)
Let y represent the amount of water Jaquan uses to wash x cars, Using the point (2, 24) and (5, 60):
y - 24 = [(60 - 24)/(5- 2)](x - 2)
y = 12x
For 6 cars:
y = 12(6) = 72
The amount of water for washing x cars is y = 12x, and 72 gallons would be needed to wash 6 cars.
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Answer: Jaquan uses 72 L to wash 6 cars
Step-by-step explanation:
The points (2,5) , (3,3) and (k,1) all lie on a straight line
(a) find the value of k
(b) find the equation of the line
Answer:
(a) k = 4
(b) y = - 2x + 9
Step-by-step explanation:
x2-x1, y2-y1
= 3-2, 3-5
= 1,-2
3,3 + 1,-2 = (4,1)
x=4
Which choice is equivalent to the expression below?
5x√2-3√2+x√2
Answer:
You did not list any choices but if you simplify that the answer is 6√2x-3√2
Step-by-step explanation:
If they want you to factor it instead of simplifying the answer is 3√2(2x-1)
Answer:
[tex]6x\sqrt{2} - 3\sqrt{2}[/tex]
Step-by-step explanation:
So you haven't provided any options, but I'm assuming they want it in most simplified form.
To do this, we simply combine like terms, and in this case you can see the [tex]\sqrt{2}[/tex] as a variable, if it makes it easier to think about why we can combine terms. So just like how we can do: [tex]2y + y = 3y[/tex] we can do the same thing here, since sqrt(2) constant and it's in each expression.
So if it makes a bit easier to represent, I'll rewrite the equation such that sqrt(2) = y
[tex]5xy-3y+xy[/tex]
So in here, think of y as the variable and the 5x, -3, and x as the coefficients.
In doing this we can combine the terms by adding them, since they all have the same "variable" (sqrt(2))
[tex](5x-3+x)y[/tex]
Simplify this expression to get
[tex](6x-3)y[/tex]
Now just plug the sqrt(2) back in as y and you get the expression
[tex](6x-3)\sqrt{2}[/tex]
Since we can't combine the 6x and -3 in any way, we we can just distribute this back into the sqrt(2)
[tex]6x\sqrt{2} - 3\sqrt{2}[/tex]