Answer:
To solve this equation, we need to perform the operations in the correct order according to the order of operations. The order of operations is a set of rules for determining the sequence in which operations should be performed in a mathematical expression to get the correct result. The order of operations is typically abbreviated as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Applying the order of operations to the given equation, we first need to evaluate the expression inside the parentheses, which is 3(x - 6). To do this, we need to subtract 6 from x, which gives us 3(x - 6) = 3(11 - 6) = 3(5) = 15. Next, we need to multiply the result of this operation by 3, which gives us 3 * 15 = 45. Therefore, the final result of the equation is 45.
Here is how you can solve the equation step by step:
1. Evaluate the expression inside the parentheses: 3(x - 6) = 3(11 - 6) = 3(5) = 15
2. Multiply the result of the previous step by 3: 3 * 15 = 45
Therefore, the final result of the equation is 45.
Step-by-step explanation:
The price of licorice is proportional to its length. It costs $0.50 to buy 5in. How much licorice can you get for $1.80
Answer: 18in
Step-by-step explanation:
0.50x 3 = 1.50
50 divided by 5 is 10
1in every 10 cent
. about 19% of young adults have high blood pressure. consider the proportion of people with high blood pressure in random samples of 45 young adults. what is the standard deviation of this sample proportion?
The standard deviation of the sample proportion is 10.
In math standard deviation is defined as the statistical measure of diversity or variability in a data set.
Here we have given that about 19% of young adults have high blood pressure. consider the proportion of people with high blood pressure in random samples of 45 young adults.
And we need to find the the standard deviation of this sample proportion
Let us assume the expected population standard deviation to be 10, and employing t-distribution to estimate sample size, the study would require a sample size of: 44 to estimate a mean with 67% confidence and a precision of 1.5.
Which means that, if you select a random sample of 44 from a population, and determine the mean to be say y, you would be 67% confident that the mean in the population lies somewhere between y - 1.5 and y + 1.5.
To know more about Standard deviation here.
https://brainly.com/question/16555520
#SPJ4
show your work please
Answer:
Correct Answer is A
Step-by-step explanation:
5×14 = 70
using the addition law of indices
(x¹. x⁷) ( y⁰. y⁵)
Add the powers
Therefore: x^(1+7) = x⁸
y^(0+5) = y⁵
Answer: 70x⁸y⁵
two numbers have a sum of 30,000 if 7% of the first number is added to 10% of the second, the result is 2,400. find the numbers
The numbers x and y values are the integer x = 29,288 and y = 713.
What is a linear equation?
Ax+By=C represents a two-variable linear equation in its standard form.
A linear equation with one variable has the conventional form Ax + B = 0. x is a variable, A is a coefficient, and B is constant in this situation.
An equation is used to show the relationship between variables, and numbers.
Let's call the two numbers x and y, where x is the first number and y is the second number. We are given that x + y = 30,000 and that 0.07x + 0.1y = 2,400.
Using substitution, we can solve for one variable in terms of the other and then substitute this expression into the other equation.
From the first equation, we can solve for y: y = 30,000 - x
Substituting this expression into the second equation, we get:
0.07x + 0.1(30,000 - x) = 2,400
0.07x + 3,000 - 0.1x = 2,400
Combining like terms, we get:
-0.03x = -600
Dividing both sides by -0.03, we get:
x = 20,000
Substituting this value back into the first equation, we can solve for y:
y = 30,000 - x
y = 30,000 - 20,000
y = 10,000
Therefore, the two numbers are x = 20,000 and y = 10,000.
Alternatively, we could have used elimination to solve the system. We can do this by adding the two equations together:
x + y = 30,000
0.07x + 0.1y = 2,400
0.07x + 0.1y + x + y = 30,000 + 2,400
0.17x + 1.1y = 32,400
Dividing both sides by 0.17, we get:
x + 6.47y = 190,588
Multiplying both sides of the first equation by 6.47, we get:
6.47x + 6.47y = 194,490
Subtracting the second equation from the first, we get:
5.47y = 3,902
Dividing both sides by 5.47, we get:
y = 712.5
Substituting this value back into the first equation, we can solve for x:
x = 30,000 - y
x = 30,000 - 712.5
x = 29,287.5
Since x and y must be positive integers, we can round these values to the nearest integer to get x = 29,288 and y = 713. These values are very close to the actual solution, which is x = 20,000 and y = 10,000. This is because we introduced some error when we divided both sides of the equation 0.17x + 1.1y = 32,400 by 0.17.
Hence, the numbers x and y values are the integer x = 29,288 and y = 713.
To learn more about the linear equation visit,
https://brainly.com/question/28732353
#SPJ1
HELPPPP
find three consecutive integers such that the sum of twice the second and three times the third is five less than six times the first.
Answer:
13, 14, 15
Step-by-step explanation:
The three integers are consecutive so let those integers be x, (x+1), (x+2)
As per the question,
2(x+1) + 3(x+2) = 6x-5
or, 2x+1+3x+6 = 6x-5
or, 8+5 = 6x-5x
or, x = 13
So, x+1 = 13+1 = 14
x+2 = 13+2 = 15
a fair coin is tossed 29 times. what is the probability that at most 27 heads occur? a) 0.00000006 b) 0.00000081 c) 0.00000076 d) 0.99999994 e) 0.99999919 f) none of the above.
Option- D is correct that is the probability that at most 27 heads occur is 0.99999994.
Given that,
A fair coin is tossed 29 times.
We have to find what is the probability that at most 27 heads occur.
We know that,
A fair coin is tossed 29 times.
n=29
Probability of heads p=1/2
q= 1-p
q=1-1/2=1/2
We get
P (X=x) = ⁿCₓ qⁿ⁻ˣ pˣ
Now, the probability that at most 27 heads occurs is
P(X<27)
=1-[P(X=28)+ P(X=29)]
=1-[²⁹C₂₈(1/2)²⁹⁻²⁸(1/2)²⁸- ²⁹C₂₉(1/2)²⁹⁻²⁹(1/2)²⁹]
=1-[²⁹C₂₈(1/2)²⁹- ²⁹C₂₉(1/2)²⁹]
=1-[28+1](1/2)²⁹
=1-29×0.00000000186
=0.999999945
Therefore, Option- D is correct that is the probability that at most 27 heads occur is 0.99999994.
To learn more about probability visit: https://brainly.com/question/11234923
#SPJ4
If a taxpayer does not have enough taxes withdrawn from her paychecks throughout the year to equal the total tax she is required to pay that year, she will owe the government the remaining balance. On the other hand, if the taxpayer has more money withheld for taxes than she is required to pay that year, she will receive a refund for the difference.
Katie has determined that, based on her annual income of $42,000, her federal income tax for the year is $6,328. Katie gets paid on a bi-weekly basis, giving her 26 paychecks throughout the 52 week year.
What is the minimum amount Katie must have withheld from each of her 26 bi-weekly paychecks in order to avoid owing the federal government at the end of the year?
The minimum amount Katie must have withheld from each of her 26 bi-weekly paychecks in order to avoid owing the federal government at the end of the year is $243.
What is income tax?
An income tax is a charge levied against people or organizations in relation to the income or profits they make. In most cases, income tax is calculated as the sum of the tax rate and the amount of taxable income. The type of taxpayer and the type of income are two factors that can affect the tax rate.
Given:
Katie has determined that, based on her annual income of $42,000, her federal income tax for the year is $6,328.
Katie gets paid on a bi-weekly basis, giving her 26 paychecks throughout the 52 week year.
We can calculate the amount that should be withheld every two weeks by dividing Katie's estimated annual income taxes by 26 weeks:
$6328 / 26 weeks = $243.38 ≈ $243.
Hence, the minimum amount Katie must have withheld from each of her 26 bi-weekly paychecks in order to avoid owing the federal government at the end of the year is $243.
To know more about income tax, click on the link
https://brainly.com/question/28414951
#SPJ1
How many ways can 4 people each choose a piece of cake from 7 total (no sharing).
The number of ways 4 people each choose a piece of cake from 7 total is 840.
What is the Permutations?Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol nPr is used to denote the number of permutations of n distinct objects, taken r at a time.
Given that, 4 people each choose a piece of cake from 7.
We know that, P(n,r) = n!/(n-r)!
Here, P(7, 4) =7!/(7-4)!
= (7×6×5×4×3!)/3!
= 7×6×5×4
= 840
Therefore, the number of ways 4 people each choose a piece of cake from 7 total is 840.
To learn more about the permutation visit:
https://brainly.com/question/3867157.
#SPJ1
(T/F) in slicing, if the end index specifies a position beyond the end of the string, python will use the length of the string instead.
True, If the end index for slicing specifies a location after the end of the alphabet, Python will use the list's length instead.
What is slicing?
In Python, there is a concept of string, list and tuples. Sometimes it is required to access part of those string, list and tuples. This is known as slicing.
In case of slicing, suppose the the end index specifies a position beyond the end of the list, Python will return to the default length of the string. So there will be no error if the end index specifies a position beyond the end of the list.
So the above sentence is a true sentence.
To learn more about slicing, refer to the link-
brainly.com/question/19660645
#SPJ4
The midpoint of AB is MI(-2, -6). If the coordinates of A are (1, -4), what are
the coordinates of B?
Complex conjugate (attached image) PLEASE HELP
A & D are complex conjugates because the sum of A and D is a real number. Also, A & D are complex conjugate because the product of A and D is a real number.
Options A and D are the correct answer
How to determine which two points are complex conjugates?The complex conjugate of a complex number is the number obtained by changing the sign of its imaginary part. The complex conjugate is written with a bar over the complex number, like this:
z = a + bi
z* = a - bi
where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1
For example, the complex conjugate of the complex number 3 + 4i is 3 - 4i.
The complex conjugate has several important properties. For example, the product of a complex number and its complex conjugate is always a real number:
(a + bi)(a - bi) = a²+ b²
Also, the sum of a complex number and its complex conjugate is always a real number:
(a + bi) + (a - bi) = 2a
These properties are useful for simplifying expressions involving complex numbers.
Let's examine the points on the graph:
A = -2 + 3i
B = 2 + 3i
C = 3 + 2i
D = -2 - 3i
A x D = ( -2 + 3i) x (-2 - 3i) = (-2)²- (3i)² = 4- (-9) = 13
A + D = ( -2 + 3i) + (-2 - 3i) = -2-2 + 3i-3i = -4
Thus, points A and D are complex conjugates because the sum and product of A and D are real numbers
Learn more about complex conjugates on:
brainly.com/question/17203594
#SPJ1
if you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a heart or 2? (your answer must be in the form of a reduced fraction.)
Answer:
Step-by-step explanation:
total no of outcome = 52 cards
favorable outcomes = 16 cards
probability of getting a heart or 2 = no . of favorable outcomes
no . of total outcomes
= 16 = 4
52 13
If 50+2(4x-1)=72, then the value of x is
options are....
(a) 1
(b) 2
(c) 3
(d) 4
Answer:
C. 3
Step-by-step explanation:
First, use the distributive property. Multiply 4x and 1 each by 2.
This gives us the equation 50 + 8x - 2 = 72.
Next, subtract 2 from 50 to get 48. Subtract 2 from 2 to cancel it out.
Then, we have 48 + 8x = 72.
Subtract 48 from both sides. This leaves 8x = 24.
Divide both sides by 8 to get x = 3.
Trader Joe's sold 3481 bags of tortilla chips recently. If 2173 of these bags were fat free, find the percent that were fat free. Round your answer to the nearest percent.
To find the percent of bags of tortilla chips that were fat free, we need to divide the number of fat-free bags by the total number of bags and multiply the result by 100%.
The percentage of bags that were fat-free is:
(2173 fat-free bags / 3481 total bags) * 100% = 62.72%
Rounded to the nearest percent, the percentage of bags that were fat-free is 63%.
Answer: About 62%
Step-by-step explanation: About 62% of the bags were fat-free. I hope this helps ;)
Find the reciprocal of -1
The reciprocal value of -1 is 1/-1 which is equal to -1.
What is Fraction?A fraction represents a part of a whole.
We need to find the reciprocal of -1.
The reciprocal (or multiplicative inverse) of a number is whatever value must be multiplied to that number to equal 1.
Let a be a number and b be its reciprocal.
So ab=1
b=1/a
Substitute for a.
b=1/-1
b=-1
Hence, -1 is the reciprocal of -1.
To learn more on Fractions click:
https://brainly.com/question/10354322
#SPJ1
Alda is measuring the growth of a plant. Its initial height was 14 centimeters (cm), and the plant has consistently grown 32 cm each day.
Which linear equation represents the plant height, (y), after a given number of days, (x)?
Answer:
Step-by-step explanation:
y=32x+14
I got this equation because the initial height is the starting so that would be the y-int which comes after the slope, the slope is 32 because it says that the plant has grown that amount of centimeters each day, and each day should refer to the rate meaning slope. That would be the equation that you would use to find the plant's height after a given number of days,
For example..
y=32(5) + 14
I plugged in a 5 for x meaning 5 days. so you'd multiply 32 by 5 which is 160 and then you'd add 14 and you'd get 174. Meaning that after 5 days the plant has grown 174 cm...
(hopefully that helps a bit..if not then I'm sorry)
Which of these values for P and a will cause the function f(x)-Pa to be an
exponential growth function?
O
○ A P = 1²; a = 2
OB. P= 5; a = 1
C. P = 5; a = 1/1/2
○ D. P= 1/2; 0 = 1/1/2
The values of P and a that will make f(x)=Pa^x to be an exponential growth function is; A P = 1²; a = 2
How to identify an exponential growth function?The general formula for exponential growth function is;
y = a(b)ˣ
When a is a positive value and 'b' is the base greater than 1,
In order to represent exponential growth, a must be a positive number larger than 1. If a is a fraction less than 1, we are basically taking a percent (less than 100) of the number and this will make it smaller, which would the become a decay function. If a is a negative, the values would alternate between positive and negative.
The only option where a is a positive number larger than 1 is P = 1²; a = 2
Read more about exponential growth function at; https://brainly.com/question/27161222
#SPJ1
What’s a? Please help!!
Answer:
a = - 3
Step-by-step explanation:
r² - 6r + 9
consider the factors of the constant term (+ 9) which sum to give the coefficient of the r- term (- 6)
the factors are - 3 and - 3 , since
- 3 × - 3 = + 9 and - 3 - 3 = - 6 , then
r² - 6r + 9
= (r - 3)(r - 3)
= (r - 3)² ← in the form (r + a)²
with a = - 3
Marneashia has a total of 14 chickens . If she has 2 times as many chickens as dogs write and solve an equation to determine the number of dogs she has.
The correct answer is 2x = 14; x = 7
How did we figure this out?For this equation we are going to divide the numbers to find are answer.Divide by 2 on both sides of the equal sign, 14 divided by 2 is 7.Therefore, The correct answer is 2x = 14; x = 7
Carly took a total of 15 quizzes over the course of 5 weeks. How many weeks of school will Carly have to attend this quarter before she will have taken a total of 24 quizzes? Assume the relationship is directly proportional.
Answer:
Carly will have to attend school for 8 weeks before she takes a total of 24 quizzes.
Step-by-step explanation:
To determine the number of weeks Carly will have to attend school before she takes a total of 24 quizzes, we need to first calculate the proportion of quizzes taken to weeks attended by dividing the number of quizzes taken by the number of weeks attended:
Proportion = Number of quizzes taken / Number of weeks attended
Proportion = 15 quizzes / 5 weeks
Proportion = 3 quizzes / week
Next, we can use this proportion to calculate the number of weeks Carly will have to attend school before she takes 24 quizzes by multiplying the number of quizzes Carly wants to take by the reciprocal of the proportion:
Number of weeks = Number of quizzes / Proportion
Number of weeks = 24 quizzes / 3 quizzes/week
Number of weeks = 8 weeks
Therefore, Carly will have to attend school for 8 weeks before she takes a total of 24 quizzes.
Cian is buying movie tickets for a group. He wants to have at least 30 tickets and spend no more than $400. Adult tickets cost $12.50 and child tickets cost $7.50. Which system of inequalities can be used to find the number of each type of ticket Cian could buy?
A. x + y ≥ 30
7.5x + 12.5y ≤ 400
B. x + y ≤ 30
7.5x + 12.5y ≥ 400
C. x + y ≥ 30
7.5x + 12.5y ≥ 400
D. x + y ≤ 30
7.5x + 12.5y ≤ 400
The system of linear inequalities for each ticket is (a) x + y ≥ 30, 7.5x + 12.5y ≤ 400
How to determine the system of linear inequality that describes the situation.From the question, we have the following parameters that can be used in our computation:
Budget = No more than $400Tickets = At least 30Children (x) = $7.50Adults (y) = $12.50When the total number of tickets is represented as an equation/inequality, we have
x + y ≥ 30
For the spendings, we have
7.5x + 12.5y ≤ 400
So, we have the following representations (inequality)
x + y ≥ 30
7.5x + 12.5y ≤ 400
Hence, the system of linear inequalities is (a)
Read more about inequalities at
https://brainly.com/question/25275758
#SPJ1
This is do today Pleaseeee helpppp
Answer:
A
Step-by-step explanation:
It is A definitely I'm sure
caitlyn has found that the total fertility rate for montana is 1.73. what other piece of information would caitlyn need to predict how many babies will be born this year in montana?
Caitlyn would need to know the population size of Montana in order to predict how many babies will be born this year in the state.
In order to predict how many babies will be born this year in Montana, Caitlyn needs to have access to the population size of Montana. The total fertility rate for Montana is 1.73, which is the average number of children a woman can expect to have throughout her lifetime. Knowing the population size of Montana will allow Caitlyn to have a better understanding of how many babies are likely to be born this year, as this number is directly correlated to the total fertility rate. By having access to both the population size and the total fertility rate, Caitlyn will be able to make a more informed prediction about the number of babies that will be born this year in Montana.
Learn more about population here
https://brainly.com/question/19538277
#SPJ4
What is the next step for the construction
Answer:Step 6, put the compass on point L
Step-by-step explanation:
Making a small arc from point L will make a little "X" at the point where you should draw the line through.
Answer:
See the answer above
Step-by-step explanation:
Open your eyes and direct your attention to the answer above.
Find the rate of change between the points
Answer: D. 3/8
Step-by-step explanation:
The rate of change or slope is rise/run
We see that the y decreases by 9 and the x decreases by 24, so our slope is -9/-24 = 3/8 because negative and negative will be positive.
So the answer is D
Answer:
C. -3/8
Step-by-step explanation:
To find the rate of change is the same as finding the slope. To find the slope between two points you'd use the slope formula, which is y2-y1 over x2-x1.
You'd get -8-1 over -8-16. -8-1 is -9. -8-16 is -24 so you'd get -9/-24.
Because that isn't one of the answer choices you have to simplify it. To simplify it you would divide both numbers by the same number. A common number they both share is 3. So then you'd divide -9 by 3 and you'd divide -24 by 3. -9 divided by 3 is -3. -24 divided by 3 is -8 so you'd get -3/-8. Which should be C. -3/8. Because both numbers are negative the answer should have a negative sign so you'd cross b and d out. And a isn't right because the 8 is supposed to be in the denominator and not in the numerator.
(Hopefully you understood this, if not then I'm sorry.)
benjamin works as a salesperson at an electronics store and sells phones and phone
accessories. benjamin earns a $10 commission for every phone he sells and a $4
commission for every accessory he sells. On a given day, made a total of
$180 in commission from selling a total of 27 phones and accessories. Graphically
solve a system of equations in order to determine the number of phones sold, x, and
the number of accessories sold, y.
y Click twice to plot each line. Click a line to delete it.
The required number of phones and accessories sold are x = 12, y = 5,
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
Let the number of phones sold be x and the number of accessories sold be y.
According to the question,
He sold a total of 27 phones and accessories,
x + y = 27 - - - - -(1)
And, made a total of $180 in commission,
10x + 4y = 180 - - - - -(2)
Graph both the equation,
From the graph, the solution of the system of equations is given as,
x = 12, y = 5,
Since, when two intersect each other, is the point of a solution of the system of equation.
Thus, the solutions gives the number of phones and accessories sold as x = 12, and y = 5.
Learn more about simultaneous equations here:
https://brainly.com/question/16763389
#SPJ1
there have been 136 earthquakes in the magnitude range 4.0-5.0 in the san francisco area over the past 30 years. what is the mean recurrence interval of earthquakes in this magnitude range?
HELP HELP HELP HELP HELPPPPPPPPPPPPP
Answer:
The ratio of x-values to y-values in the table is 2:3
Step-by-step explanation:
8 / 12 = 2/3
10 / 15 = 2/3
12 / 18 = 2/3
Each has a ratio of 2 to 3.
2.
12
Bo
5
13
xº
Which measures shown in the triangle are
equivalent to ? (MGSE9-12.G.SRT.6)
5
13
A. sin a Only
B. cos ß Only
C. sin a and cos B
D. sin ß and cos a
on solving the provided question, we can say that - 5/13 measure shown in the triangle are equivalent to sin [tex]\alpha[/tex] and cos [tex]\beta[/tex].
what are trigonometric functions?Trigonometry uses the first six fundamental trigonometric functions. Trigonometric ratios are these functions. The six fundamental trigonometric functions are the sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function. A right-angled triangle's side ratio corresponds to the trigonometric functions and identities. In order to determine the sine, cosine, tangent, secant, and cotangent values, trigonometric formulae are applied to the perpendicular side, hypotenuse, and base of a right triangle.
as cos x = base/ hypotenuse
and, sin x = perpendicular/ hypotenuse
To know more about trigonometric functions visit:
https://brainly.com/question/6904750
#SPJ1
Can someone please help me I’ll mark as brainlist
Answer:
u=14, v=2
Step-by-step explanation:
Here's my attempt:
Proving triangle congruency:
We need to prove that the two triangles are congruent.
First, we need to see which sides/angles correspond (basically how the two triangles overlap each other).
Well, we can see that m∠F = 90° and that m∠D = 90°, so we know that ∠F and ∠D are congruent, and so they correspond.
So, if you drag ΔHFG over to ΔCDE, then sides DC and FH would be right on top of each other. (try drawing this to make it clearer)
Solving for v:
So if sides DC and FH are congruent, then their values are also equal.
DC = 17v and FH = v+32
So if DC=FH, then 17v=v+32
Then, we simplify this:
17v=v+32 [original equation]
16v=32 [subtract v from both sides]
v=2 [divide both sides by 16 to isolate v]
So, we have our value for v: v=2
Solving for u:
Now, it's time to find u: (also, it doesn't matter if you found v first or u first in this problem)
When we overlapped ΔHFG and ΔCDE, we saw that EC = GH
So, using the same method as we used to find v, we can say that
EC=7u and GH = 10u-42
If EC=GH, then 7u=10u-42
Then, we simplify:
7u=10u-42 [original equation]
-3u=-42 [subtract 10u from both sides to get u on just one side]
u=14 [subtract both sides by -3 to isolate u]
Finally, we have our value for u: u=14
But we're not done yet: let's check our work:
Firstly, let's plug our answer for v into our equation for v:
17v=v+32
17(2)=(2)+32
34=34 It works!
Next, we'll plug in our answer for u into our equation for u:
7u=10u-42
7(14)=10(14)-42
98=140-42
98=98 It works!
I hope you read through my explanation and that it helped! :D