Solve the equation \(\sqrt{x+3} +4 = 5\) Show each step of your solution process.
Answer:
-2
Step-by-step explanation:
We start off by subtracting 4 on both sides giving us:
sqrt(x+3) = 5-4 = 1
So,
sqrt(x+3) = 1, and squaring both sides we get x+3 = 1
Therefore,
x = -2
Answer:
x = -2 & -4
Step-by-step explanation:
√(x + 3) + 4 = 5
√(x + 3) = 5 - 4
√(x + 3) = 1
[√(x + 3)]² = (1)²
x² + 9 + 6x = 1
x² + 9 - 1 + 6x = 0
x² + 8 + 6x = 0
x² + 6x + 8 = 0
x² + (4x + 2x) + 8 = 0
x² + 4x + 2x + 8 = 0
x(x + 4) + 2(x + 4) = 0
(x + 4)(x + 2) = 0
x = -2 & -4
Hence,
Value of x is -2 & -4
HOT DOGS Costco's beef franks (hot dogs) come in a packet with 15 beef franks inside.
Julian decides to buy 8 packs which is a grand total of 120 beef franks for his Super Bowl
Party. Julian and 3 friends each cooked a fraction of the beef franks on the grill. Julian
cooked 5/12 of the beef franks. Angel cooked 3/20 of the beef franks. Pedro cooked 1/6 of the
beef franks. Miguel cooked the rest of the beef franks. What fraction of the beef franks did
Miguei cook.
*Make sure your answer is SIMPLIFIED!
Answer:
Step-by-step explanation:
Julian bought a total of 8 packs of beef franks, each containing 15 beef franks. So the total number of beef franks is:
8 packs × 15 beef franks/pack = 120 beef franks
Julian, Angel, Pedro, and Miguel together cooked all 120 beef franks. Let's add up the fractions they cooked:
5/12 + 3/20 + 1/6 + Miguel's fraction = (25 + 9 + 10M + 60M) / (60*20)
= (34 + 70M) / 120
We know that this fraction must equal 1 (since they cooked all the beef franks), so we can set up an equation:
(34 + 70M) / 120 = 1
Solving for M, we get:
34 + 70M = 120
70M = 86
M = 43/35
Therefore, Miguel cooked 43/35 of the beef franks. This fraction can be simplified:
43/35 = 1 + 8/35
So Miguel cooked 1 and 8/35 of the beef franks.
-4x4x(-3x2+9) what is the answer this question on my math homework
Answer:
-48
Step-by-step explanation:
-4x4x(-3x2+9)=-48
Answer:
12x^7−36x^5
Step-by-step explanation:
PLEASE HELP................
1. The scale factor here in the dilation is 4/3.
2. Yes, dilation occurred on the coordinate plane below. The scale factor for the dilation is -4/3.
What is dilation?During the process of dilatation, an object must be reduced in size or changed. It is a transformation that uses the given scale factor to shrink or expand the objects. The image is the new figure that forms as a result of dilatation, whereas the pre-image is the original figure. There are two kinds of dilation:
A rise in an object's size is referred to as expansion.
Contraction is the term used for a reduction in size.
Here in the question,
The coordinates of the point B change from (-3,6) to (-4,8).
The scale factor here is -4/-3=4 or 8/6=4/3.
Now, when the dilation happens below the plane, the coordinates will be (x,-y)
So, the dilation factor will be -4/3.
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Karen runs 3 miles in 28 minutes. At the same rate, how many miles would she run in 42 minutes?
Answer:
4.5
Step-by-step explanation:
Well, she runs 3 miles in 28 minutes.
42 = 28 ⋅ 1.5
So, her journey would just be running
1.5
times, with each time running
28
minutes.
So, she runs a total of
1.5 ⋅ 3 = 4.5 miles
READ No link or bot and answer the question 20 points I give Brainliest to the best answer
Answer:
1- 5 to the 2nd power=25 / 25-11=14 / 14+2=16 /16+8=24
3- 6 to the 3rd power= 216/ 216-9= 207/207+1=208/ 208+4+8=220
4- 6-3=3/ 3x9=27/ 3x-9= -27/ -27+27=0
Step-by-step explanation:
I can't do all of them cuz im in 5th G but i can help u wit some
sorry i can tell this is very overwhelming also i'm am also sorry if this is wrong if this is not for work and your just practicing (thank god).
have a great day
Heather invests $2,975 in an account with a 3.5% interest rate, making no other deposits or withdrawals. What will Heather’s account balance be after 9 years if the interest is compounded 4 times each year?
Heather's account balance will be approximately $4,179.60 after 9 years if the interest is compounded 4 times each year.
What is interest?Interest is the cost of borrowing money or the compensation received for lending money. It is usually expressed as a percentage of the amount borrowed or lent, and it is calculated based on the principal (the initial amount borrowed or lent), the interest rate, and the time period for which the money is borrowed or lent.
What is compounding?Compounding refers to the process of earning interest on both the principal amount and the accumulated interest earned over time. In other words, it is the interest earned on interest.When interest is compounded, the interest earned in each compounding period is added to the principal amount, and the new total becomes the basis for calculating interest in the next period.
In the given question,
We can use the formula for compound interest to find Heather's account balance after 9 years:
A = P * (1 + r/n)^(n*t)
where A is the account balance, P is the principal (initial investment), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
Plugging in the given values, we get:
A = 2975 * (1 + 0.035/4)⁴ˣ⁹
Simplifying this expression, we get:
A = 2975 * (1.00875)³⁶
Using a calculator or a computer, we can evaluate this expression to get:
A ≈ $4,179.60
Therefore, Heather's account balance will be approximately $4,179.60 after 9 years if the interest is compounded 4 times each year.
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4.91666666667 as a fraction
Answer:
Up to 6 decimal places are supported for decimal-to-fraction conversion.
Step-by-step explanation:
According to Descartes rule what is a possible number of positive and negative roots
Answer:
sepalacola
Step-by-step explanation:
What is the trigonometric ratio for cos N?
Enter your answer, as a simplified fraction.
Answer
=12/13
Step-by-step explanation:
I have done it before:)
Which expression correctly represents "six more than the quotient of three and a number, decreased by eight"?
6+3/n-8
6+n/3-8
6+3/n+8
6+n/3+8
The option A is correct because the value of the statement is 6+3/n-8.
According to the statement
we have given that the statement and we have to write the statement in the numerical form.
So, For this purpose
we know that the given statement is
"Six more than the quotient of three and a number, decreased by eight".
In this statement "Six more than" indicates the sum between the quotient and 6.
And "The quotient of three and a number" indicates a fraction where the numerator is 3 and the denominator is , a number.
"Decreased by eight" indicates a subtraction between the quotient an 8 units".
If we unit all parts of the statements, we would have
6+3/n-8
So, From the given statement, The option A is correct because the value of the statement is 6+3/n-8.
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Write the equation that passes through the following points:
(5,0) and (-10, — 5)
-
1
Basic Funcs Trig
X
Y
X
X
π
✓ N
8
DNE
↑
→→→→
1
X
\((\stackrel{x_1}{5}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{-10}~,~\stackrel{y_2}{-5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{-10}-\underset{x_1}{5}}} \implies \cfrac{ -5 }{ -15 } \implies \cfrac{1 }{ 3 }\)
\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{ \cfrac{1 }{ 3 }}(x-\stackrel{x_1}{5})\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x-\cfrac{5}{3} \end{array}}\)
I need help I don’t understand
Answer:
Decreases
Step-by-step explanation:
As 'n' increases the value of the (1/4) will decrease.
Say, n=1 ; 1/4
n=2 ; 1/4 * 1/4 = 1/16(because n=2, there are two 1/4s)
n= and so on
A study of 800 homeowners in a certain area showed that the average value of the homes was $82,000, and the standard deviation was $5000. How many of these homes have a value greater than $83,500.
Round to a whole number.
I got 62 it says that is wrong answer.
Answer:
400
Step-by-step explanation:
it says average which probably means 400
33.36% of these homes have a value greater than $83,500.
The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
\(z=\frac{x-\mu}{\sigma} \\\\where\ x \ is\ raw\ score,\mu=mean,\sigma=standard\ deviation\)
Given that μ = $82000, σ = $5000.
For x > 83500:
\(z=\frac{83500-82000}{5000} =0.43\)
From the normal distribution table, P(x > 83500) = P(z > 0.43) = 1 - P(z < 0.43) = 1 - 0.6664 = 33.36%
33.36% of these homes have a value greater than $83,500.
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If Audrey wanted to solve this equation using the square root method, which answer shows the correct sequence of steps?
x2 + 5 = 41
a. Take the square root of both sides
b. Subtract 41 from both sides, then square root both sides.
c. Subtract 5 from both sides, then square root both sides.
d. Add 5 to both sides, then square root both sides
Answer:
C
Step-by-step explanation:
subtract 5 from both sides
"Jessica deposits one-third of her weeklypaycheck into her savings account. If the amount she deposits each week is $105, how much is her paycheck (P)?”
Answer:
105 x 3 = 315
p = $315
Step-by-step explanation:
The table and the graph each show a different relationship between the same two variables, x and y: у X у 850 3 270 680 510 4 360 340 170 5 450 0 2 4 6 8 10 6 540 How much more would the value of y be in the table, than its value on the graph, when x = 11? (1 point) 55 95 O 100 215
Answer:
The difference between value of y at x=11 is 385, the correct option is third
Step-by-step explanation:
(the / is a fraction bar)
Kati has 2/3 of a bag of frozen fruit. She used 1/4 of the fruit to make smoothies. Which equation represents the amount of fruit Kati used to make smoothies?
A. 1/4 + 2/3 = 11/2 of a bag
B. 2/3 - 1/4 = 5/12 of a bag
C. 1/4 x 2/3 = 1/6 of a bag
D. 1/4 ÷ 2/3 = 3/8 of a bag
Answer:
bbbbbbbbbbbbbbbb
im a math god
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Given f(x) = x^3 - 2x^2 - x + 2,
the roots of f(x) are
Answer:
Domain: -∞ < x < ∞
Range: -∞ < f(x) < ∞
Derivative: 3x² - 4x - 1
Roots: x1=-1
x2=1
x3=2
Estimate 147+14+85 by first rounding each number to the nearest ten.
Answer:
250
Step-by-step explanation:
because 147 rounded is 150 14 is 10 and 85 is 90 these added together are 250
of the exam form that you MUST che
Question 1 Multiple choice Worth points)
(08.02)The calculated average of a data set best describes which of the re
Mean
The calculated average of a data set best describes which of the following?
Answer:
A. Mean
Step-by-step explanation:
Mean can also be described as the average of a data set.
The calculated average of a data set is the sum of all data values divided by the number of data values we have in a data set. This is the same as the mean.
For example, let's say you bought 5 t-shirts. The cost of the 5 t-shirts can be regarded as a data set, which are: $10, $10, $11, $12, and $15.
The average cost of t-shirt bought by you can be calculated as:
Average = Mean = (10 + 10 + 11 + 12 + 15)/5
= 58/5
= 11.6
The average cost of t-shirt you bought, which is also the mean cost of t-shirt is $11.6
Use this graph of velocity vs. time for two objects to answer the question.
Which statement makes an accurate comparison of the motions for objects C and D?
A. Object C has an acceleration that is greater than the acceleration for D.
B. Objects C and D have different velocities but the same acceleration.
C. Object D has an acceleration that is greater than the acceleration for C.
D. Objects C and D have different accelerations but the same velocity throughout the motion.
Answer:
Object C has an acceleration that is greater than the acceleration for D
- I just took the quiz and got 100%
Using derivatives, it is found that the correct option is:
A. Object C has an acceleration that is greater than the acceleration for D.
The acceleration is the derivative of the velocity, given by change in velocity divided by change in time, that is:
\(a = \frac{\Delta_v}{\Delta_t}\)
In this problem:
The change in time for objects C and T is the same.The change in velocity for object C is greater, thus, it has a greater acceleration, and the correct option is:A. Object C has an acceleration that is greater than the acceleration for D.
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Which of the following is NOT an irrational number?
Answer:
I'm gonna go with the first choice because it's rational.
Step-by-step explanation:
Answer:
pi is the answer
Step-by-step explanation:
Two wires are attached to a pole and create similar triangles with the ground. The longer wire is attached to the ground 32 feet from
the base of the pole and the shorter wire is attached to the ground 16 feet from the base of the pole.
If the cosine of the angle formed by the shorter wire and the ground is 8/41, what is the length of the longer wire?
Please help im so confused!
The length of the longer wire is 82 feet.
Let's denote the length of the longer wire as L. According to the given information, the shorter wire is attached to the ground 16 feet from the base of the pole, and the longer wire is attached to the ground 32 feet from the base of the pole.
We can form two similar right triangles using the wires. The height of each triangle is the height of the pole, and the base of each triangle is the distance from the base of the pole to where the wire is attached to the ground.
In the first triangle, the shorter wire creates an angle with the ground. Let's denote this angle as θ. Since we are given the cosine of this angle, we can use the cosine function to find the height of the pole in terms of θ and the base of the triangle:
cos(θ) = adjacent/hypotenuse = 16/L
Given that cos(θ) = 8/41, we can substitute this value into the equation:
8/41 = 16/L
To solve for L, we can cross-multiply and solve for L:
8L = 41 * 16
L = (41 * 16)/8
L = 82
Therefore, the length of the longer wire is 82 feet.
In summary, the length of the longer wire is 82 feet, as determined by using the cosine of the angle formed by the shorter wire and the ground, and considering the similarity of the triangles formed by the wires and the pole.
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Suppose you select 4 skittles at random from the bowl. What is the proba- bility exactly 1 of those skittles is green
Answer:
1/4
Step-by-step explanation:
4 skittles and one being green
Answer:
4/5
Step-by-step explanation:
According to the Wrigley's Consumer Care Department, the fruit candies are produced in equal proportions— 20% of each of the five colors (green, red, orange, yellow, and purple). However, although these candies are made in equal proportions, the individual Skittles bags are filled by weight and by machines but on average I'd say 4/5 chance its a green.
Which measure is equivalent to 1.5 kg?
1. 15 g
2. 150 g
3. 1500 g
4. 15,000 g
Answer:
number 2.) 1,500g
Step-by-step explanation:
i just know..
For a sample of transformers built for heavy industry, the mean and standard deviation of the number of sags per weeks were and , respectively; also, the mean and standard deviation of the number of swells per week were and , respectively. Consider a transformer that has sags and swells in a week. Complete parts a and b below.
1. Would you consider 314 sags per week unusual, statistically? Explain.
A. No. The Z-score is meaning that the number of sags is not unusual and is not an outlier.
B. No. The Z-score is meaning that less than approximately 68% of transformers have a number of sags closer to the mean.
C. Yes. The Z-score is meaning that this is an outlier and almost every other transformer has fewer sags.
D. Yes. The Z-score is meaning that this is an outlier and almost every other transformer has more sags.
E. This cannot be determined, since the IQR is not provided and cannot be found from the provided information.
2. Would you consider 243 swells per week unusual, statistically? Explain.
A. No. The Z-score is meaning that less than approximately 68% of transformers have a number of swells closer to the mean.
B. Yes. The Z-score is meaning that this is an outlier and almost every other transformer has more swells.
C. Yes. The z-score is meaning that this is an outlier and almost every other transformer has fewer swells.
D. No. The Z-score is meaning that the number of swells is not unusual and is not an outlier.
E. This cannot be determined, since the IQR is not provided and cannot be found from the provided information.
Answer:
The correct options are:
(1) A
(2) C
Step-by-step explanation:
The complete question is:
For a sample of 119 transformers built for heavy industry, the mean and standard deviation of the number of sags per weeks were 338 and 22, respectively; also, the mean and standard deviation of the number of swells per week were 174 and 15, respectively. Consider a transformer that has sags 375 and 120 swells in a week.
(1)
A z-score less than -2 or more than 2 are considered as unusual.
Compute the z-score for 314 sags per week as follows:
\(z=\frac{x-\mu}{\sigma}\)
\(=\frac{314-338}{22}\\\\=-1.091\)
The z-score for 314 sags per week is -1.091.
This value is more than -2.
Thus, the correct option is:
A. No. The Z-score is -1.091 meaning that the number of sags is not unusual and is not an outlier.
(2)
Compute the z-score for 243 swells per week as follows:
\(z=\frac{x-\mu}{\sigma}\)
\(=\frac{243-174}{15}\\\\=4.6\)
The z-score for 243 swells per week is 4.6.
This value is more than 2.
Thus, the correct option is:
C. Yes. The z-score is 4.6 meaning that this is an outlier and almost every other transformer has fewer swells.
1). The decision regarding the consideration of 314 sags every week unusually would be:
a). No. The Z-score is meaning that the number of sags is not unusual and is not an outlier.
2). The decision regarding the consideration of 243 swells every week every week unusually would be:
c). Yes. The z-score is meaning that this is an outlier and almost every other transformer has fewer swells.
a). Given that
No. of transformers = 119
Mean = 338
Standard Deviation for the week = 22
Now,
z-score for sags = (No. of sags - Mean)/Standard Deviation
\(= (314 - 338)/22\\= -1.091\)
Since it is greater than -2, option A is the correct answer.
b). Given that
No. of swells = 243
Mean for swells = 174
Standard Deviation = 15
Now,
z-score for sags = (No. of sags - Mean)/Standard Deviation
\(= (243 - 174)/15\\= 4.6\)
Since it is greater than 2, it exemplifies an outlier. Thus, option C is the correct answer.
Thus, options A and C are the correct answers.
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If a couple plans to have 9 children, what is the probability that there will be at least one boy? Assume boys and girls are equally likely. Is that probability high enough for the couple to be very confident that they will get at least one boy in 9 children?
Answer:
It is a 9/10 chance of having at least one boy. The probability is also high enough for the couple to be very confident in having at least one boy in 9 children.
Step-by-step explanation:
I listed all of the possible combinations below
GGGGGGGGG BGGGGGGGG
BBGGGGGGG BBBGGGGGG
BBBBGGGGG BBBBBGGGG
BBBBBBGGG BBBBBBBGG
BBBBBBBBG BBBBBBBBB
Total number of combinations with at least one boy is 9/10
This is a very high percentage, which means the couple is very likely to have at least one boy.
A bucket contains six white balls and five red balls. A sample of four balls is selected
at random from the bucket, without replacement. What is the probability that the
sample contains...
Exactly two white balls and two red balls?
At least two white balls?
To solve this problem, we can use the formula for probability:
P(event) = number of favorable outcomes / total number of outcomes
First, let's find the total number of outcomes. We are selecting 4 balls from 11 without replacement, so the total number of outcomes is:
11C4 = (11!)/(4!(11-4)!) = 330
where nCr is the number of combinations of n things taken r at a time.
Now let's find the number of favorable outcomes for each part of the problem.
Part 1: Exactly two white balls and two red balls
To find the number of favorable outcomes for this part, we need to select 2 white balls out of 6 and 2 red balls out of 5. The number of ways to do this is:
6C2 * 5C2 = (6!)/(2!(6-2)!) * (5!)/(2!(5-2)!) = 15 * 10 = 150
So the probability of selecting exactly two white balls and two red balls is:
P(2W2R) = 150/330 = 0.45 (rounded to two decimal places)
Part 2: At least two white balls
To find the number of favorable outcomes for this part, we need to consider two cases: selecting 2 white balls and 2 red balls, or selecting 3 white balls and 1 red ball.
The number of ways to select 2 white balls and 2 red balls is the same as the number of favorable outcomes for Part 1, which is 150.
To find the number of ways to select 3 white balls and 1 red ball, we need to select 3 white balls out of 6 and 1 red ball out of 5. The number of ways to do this is:
6C3 * 5C1 = (6!)/(3!(6-3)!) * (5!)/(1!(5-1)!) = 20 * 5 = 100
So the total number of favorable outcomes for selecting at least two white balls is:
150 + 100 = 250
And the probability of selecting at least two white balls is:
P(at least 2W) = 250/330 = 0.76 (rounded to two decimal places)
Sales tax is ,
to the price
Sales tax is a percentage of the sale price of an item that is then added on to the total price of the item.
Example:
let's say you are buying an item priced at $10.00 and the sales tax rate is 6%. Sales tax rates can vary from state to state and even within counties or cities.