To simplify the expression 2(4x + 3) + (x - 3), we need to use the distributive property of multiplication over addition, and then combine like terms.
The expression 2(4x + 3) + (x - 3) contains parentheses and addition and multiplication operations, so we need to follow the order of operations to simplify it. The order of operations is:
1. Simplify any expressions inside parentheses.
2. Evaluate any exponents.
3. Perform multiplication and division, from left to right.
4. Perform addition and subtraction, from left to right.
Let's follow these steps to simplify the expression,
1. Simplify any expressions inside parentheses.
There are two sets of parentheses in the expression: (4x + 3) and (x - 3).
We can use the distributive property of multiplication over addition to eliminate the parentheses:
2(4x + 3) + (x - 3) = 8x + 6 + x - 3
2. Evaluate any exponents,
There are no exponents in the expression.
3. Perform multiplication and division, from left to right.
There is no multiplication or division to perform.
4. Perform addition and subtraction, from left to right.
We can now simplify the expression by combining like terms:
8x + 6 + x - 3 = (8x + x) + (6 - 3) = 9x + 3
Therefore, the simplified expression is 9x + 3.
In summary, the correct procedure to simplify the expression 2(4x + 3) + (x - 3) is to use the distributive property to eliminate the parentheses, and then combine like terms to obtain the simplified expression 9x + 3.
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please help me i dont understand this
Answer: 57
Step-by-step explanation: I recommend learning angle properties, pictures on the internet might help ya out
the process standard deviation is 0.15 , and the process control is set at plus or minus 2.4 standard deviations. units with weights less than or greater than ounces will be classified as defects. what is the probability of a defect (to 4 decimals)?
The probability of a defect (weights less than -0.36 ounces or greater than 0.36 ounces) is approximately 0.0521 × 2 = 0.1042 or 10.42% to four decimal places.
To find the probability of a defect, we need to determine the range of weights that would be considered as defects. The process control limit is set at plus or minus 2.4 standard deviations, which means that any weight outside the range of mean ± 2.4× standard deviation would be considered a defect. Let's calculate the mean weight (μ): μ = 0
And the control limit (LCL and UCL):
LCL = μ - (2.4 × standard deviation)
= 0 - (2.4 × 0.15) = -0.36 UCL
= μ + (2.4 × standard deviation)
= 0 + (2.4 × 0.15) = 0.36.
Since the standard deviation is 0.15 ounces and the normal distribution is symmetrical, the probability of a weight being less than -0.36 ounces or greater than 0.36 ounces is equal. To calculate the probability, we can use the cumulative distribution function (CDF) of a standard normal distribution. Using a standard normal table or a calculator with statistical functions, we can find that the probability of a standard normal distribution being less than -0.36 or greater than 0.36 is about 0.0521 or 5.21%. So, the probability of a defect (weights less than -0.36 ounces or greater than 0.36 ounces) is approximately 0.0521 × 2 = 0.1042 or 10.42% to four decimal places.
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53. The cutting tool on a lathe moves 3/128 in. along the piece being turned for each revolution of work. The piece revolves at 45 revolutions per minute. How long will it take to turn a length of 9 9/64-in. Find in one operation?
Using the concept of rates, the machine will complete 9 9/64 inches in 8.67 minutes
How long will it take to turn a particular length
To determine how long it will take to turn a particular length of iron, we can calculate the rate at which it works and it must be in a definite proportion.
If the lathe moves 3/128 in one revolution.
And the machine completes 45 revolutions in 1 minutes, we can determine how many inches in moves in that minute.
3/128 in = 1 rev
x in = 45
45 * (3/128) = 45 revolutions = 1 minute
1.054 inches in 1 minute.
We can further use this to determine the time it takes to move 9 9/64 inches
1.054 inches = 1 minute
9 9/64 inches = x minute
cross multiply both sides and solve
x = 8.67 minutes
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jake and kim share some money in the ratio 1:3
kim gets $90 more than jake.
how much does kim get
Answer: $135
Step-by-step explanation:
We have the ratio 1 : 3.
Kim gets $90 more than Jake.
So 1 : 3 can also be written as x : x+90
If x * 3 equals x+90, we can create the equation 3x=x+90. Solving this results in x being equal to 45
Kim gets $135 (x+90=45+90=135)
solve for angle BD only
Answer: BD = 60.34
Step-by-step explanation:
8x -33 = 2x+37
Take away 2x from both sides ( the 2x will cancel out)
= 6x - 33= 37
Add the 33 to both sides. (The -33 will cancel out)
Now you are left with 6x = 70
Divide both sides by 6.
x = 11.67 (rounded by the hundredth) (11.66666...)
Now to figure out BD your new equation is 2(11.67) + 37
After multiplying you get 23.34 + 37.
BD = 60.34
Hope this helps. This is the way I learned.
Kelly had 64 plums. She gave her friend 16 and her sister 32 . What percentage of the plums did she have remaining. Show working
8. On the graph below, plot the points (-6,-6) and (6, 6). Find the distance
between the two points.
Answer:
You are correct it is 12.
Step-by-step explanation:
Answer: Square root of 288, or estimated 16.97
Step-by-step explanation:
Conveniently, the points form a diagonal line as you show, so we can use the Pythagorean Theorem to find the distance.
The x-component of this is the distance between -6 and 6, which is 12, and the y-component is again the distance between -6 and 6, which is also 12.
Therefore, the distance is the square root of 12^2 + 12^2, or the squareroot of 288.
A soccer player has a large cylindrical water cooler that measures 3.5 feet in diameter and is 2 feet tall. If there are approximately 7.48 gallons of water in a cubic foot, how many gallons of water are in the water cooler when it is completely full? Use π = 3.14 and round to the nearest hundredth.
The volume of the water in the water cooler when it is completely full is 82.21 gallons.
What is a cylinder?
One of the most fundamental curvilinear geometric shapes, a cylinder has traditionally been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In many contemporary branches of geometry and topology, a cylinder can also be defined as an infinitely curvilinear surface.
Given that the height of a cylinder is 3.5 feet. The diameter of the cylinder is 2 feet.
The radius of the cylinder is half of the diameter.
The radius of the cylinder is 2/2 = 1 foot.
The volume of a cylinder is πr²h.
r = radius, h = height
The volume of the cylinder is
π×1²×3.5
= 3.14 × 3.5
= 10.99 cubic foot
= 10.99 × 7.48 gallons
= 82.205 gallons
= 82.21 gallons
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prove, that 32^5-16^5+2^19 is divisible by 63 help asap
ill award brainlist
Step-by-step explanation:
Use PEMDAS (Order of operations).
Simplify exponents
33554432 - 1048576 + 54288
Add and subtract (left to right)
33030144
63 goes into 33030144 524288 times.
Answer:
2^19(63)
Step-by-step explanation:
(2^5)^5-(2^4)^5+2^19
2^25-2^20+2^19
2^19(2^6-2+1)
2^19(64-2+1)
2^19(63)
Convert the Senary (base 6 number 54724 to decimal
Answer: To convert a Senary (base 6) number to decimal, we can use the following formula:
Decimal = (5 * 6^4) + (4 * 6^3) + (7 * 6^2) + (2 * 6^1) + (5 * 6^0)
= (5 * 1296) + (4 * 216) + (7 * 36) + (2 * 6) + (5 * 1)
= 6480 + 864 + 252 + 12 + 5
= 7603
So the Senary (base 6) number 54724 is equivalent to the decimal number 7603.
Step-by-step explanation:
I really need help with this
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
To check if a curve represents a function, draw vertical lines all over the graph intersecting the curve at different regions.
Now, check how many times a line cuts the curve, if all the vertical lines cuts the curve at a single point then it represents a function, and if the vertical line cuts the curve at more than one point, then its not a function.
By keeping the above instructions in mind, conclusion can be made that :
Functions : (i), (ii), (iii), (iv) and (vi)
Non function : (v) and (vii)
4. John and Mitchell are buying snack from the break cart at school. John bought 2 bags of chips and 3
candy bars for $8.50. Mitchell bought 4 bags of chips and 2 candy bars for $11. How much did each item
cost?
Define your variables. x =
Write a system of equations.
Solve using any method.
y=_
3/5 divided by 4/7 id ont get this can so,eome help
The expression which is equivalent to the given expression 3/5 divided by 4/7 is given by option d. 3/5 multiply 7/4.
The expression which is equivalent to the expression 3/5 divided by 4/7 is:
3/5 divided by 4/7 can be expressed as
= ( 3 / 5 ) ÷ ( 4 / 7 )
Convert division sign into multiplication sign we get,
= ( 3 / 5 ) × [ 1 / ( 4 / 7 ) ]
= ( 3 / 5 ) × ( 7 / 4 )
= 3/5 multiply 7/4
Therefore, the correct way of representing the expression 3/5 divided by 4/7 is equivalent to option d. 3/5 multiply 7/4.
The above question is incomplete, the complete question is:
Which of these expression is the same as 3/5 divided by 4/7?
a 3/5 divided 7/4
b 4/7 divided 3/5
c 3/5 multiply 4/7
d 3/5 multiply 7/4
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philips metal costs $14.50 at the local restaurant. the server did their job very well and philip would like to leave a 20% tip. what amount of money should he leave as a tip?
Answer: The tip is $2.90
Step-by-step explanation: 20% of 14.50 is 2.9
a group of 100 people contains 60 democrats and 35 republicans. if there are 60 women and 40 of the democrats are women, what is the probability that a person selected at random is a democrat or a woman?
The probability of selecting a person who is either a Democrat or a woman is 0.8, or 80%.
Probability is a branch of mathematics that deals with the study of random events. It is used to predict the likelihood of an event occurring.
Let's start by finding the probability of selecting a Democrat. We are given that there are 60 Democrats in the group of 100 people. Therefore, the probability of selecting a Democrat at random is:
P(Democrat) = 60/100 = 0.6
Next, let's find the probability of selecting a woman. We are given that there are 60 women in the group of 100 people. Therefore, the probability of selecting a woman at random is:
P(Woman) = 60/100 = 0.6
Now, we need to find the probability of selecting both a Democrat and a woman. We are given that 40 of the Democrats are women. Therefore, the probability of selecting a woman who is also a Democrat is:
P(Democrat and Woman) = 40/100 = 0.4
To find the probability of selecting a person who is either a Democrat or a woman, we add the probabilities of selecting a Democrat and selecting a woman, and then subtract the probability of selecting both a Democrat and a woman. Therefore, the probability of selecting a person who is either a Democrat or a woman is:
P(Democrat or Woman) = P(Democrat) + P(Woman) - P(Democrat and Woman)
= 0.6 + 0.6 - 0.4
= 0.8
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Which figures have equal area? Choose all that are correct.
Equivalence means to be same, whether it be value, temperature, size, etc.
Let's take a look at shape 1.
Shape 1 has a base of 3, and a height of 4, but there is a gap with a width of 1 and a height of 2. So, we can use this equation to figure out the area:
(3 × 4) - (1 × 2) = 10So, shape 1 has an area of 10 units.
Let's look at shape 2.
Shape 2 has a base of 2, and a height of 4, but there is also a gap, with a width of 1 and a height of 3. So, we can use this equation to figure out the area:
(2 × 4) - (1 × 3) = 5So, shape 2 has an area of 5 units.
Let's look at shape 3.
Shape 3 consists of 4 right triangles, put together to form an arrowhead. The shape has a base of 4, and a height of 2. So, we can use this equation to figure out the area:
(4 × 2) ÷ 2 = 4So, shape 3 has an area of 4 units.
Let's look at shape 4.
Shape 4 consists of 4 right triangles, put together to form a diamond. The shape has a base of 4, and a height of 2. So, we can use this equation to figure out the area:
(4 × 2) ÷ 2 = 4So, shape 4 has an area of 4 units.
Looking to the final shape (5), we can see it consists of a long rectangle and 2 right triangles. Instead of calculating the base and height of the entire shape, we can break it into pieces, making a rectangle that has a base of 3, and a height of 1. Then we are left a shape that has a base of 2, and a height of 3. So, we can use this equation to figure out the area:
(3 × 1) + ([2 × 3] ÷ 2) = 6So, shape 5 has an area of 6 units.
Let's compare the area of all of the shapes.
Has an area of 10 square units. Has an area of 5 square units. Has an area of 4 square units. Has an area of 4 square units. Has an area of 6 square units.Therefore, the two figures that have equal areas are shapes 3 and 4.
the coordinates of the endpoints of rs are r(1,11) and s(6,1). point t is on rs and divides it such that rt:st is 4:1. what are the coordinates of t?
The coordinates of the endpoints of rs are r(1,11) and s(6,1). point t is on rs and divides it such that rt:st is 4:1.
the coordinates of the point t are (5, 3)
We may utilise the notion of section formula to get the coordinates of point T, which states that if we have two points A(x1, y1) and B(x2, y2) and a point P splitting the line segment AB in the ratio m:n, then the coordinates of point P can be calculated using the following formula:
P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n))
In this situation, we have the coordinates of points R and S, as well as the ratio of T divided by RS. So, let's enter the following values into the formula to determine T's coordinates:
Let the coordinates of point T be (x, y), and the ratio of T to RS be 4:1, implying that RT:ST = 4:1. This means that RT = 4/5 (RS length) and ST = 1/5. (length of RS).
RS length =[tex]sqrt((6-1)^2 + (1-11)^2)[/tex] = [tex]sqrt (146)[/tex]
RT=[tex](4/5) * sqrt(146)[/tex] = [tex](4/5) * 12.083[/tex] = 9.666
ST =[tex]1/5* sqrt(146)[/tex] = [tex]1/5* 12.083[/tex] = 2.4166
We get the following using the section formula:
x = (4×6 + 1×1)/(4+1) = 5
y = (4×1 + 1×11)/(4+1) = 3
T = (5, 3)
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A Set of Speakers costs $35 and Songs cost $195 each. The sales tax
rate is 8.25%. The expression 0.0825(35+ 195s) can be used to determine
the amount of sales tax due on the entire purchase of a set of Speakers
and S.Songs. Expand the expression and round to the nearest hundredth.
The amount of sales tax due on the entire purchase of a set of speakers and s songs is given by expression 2.8875+16s
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that :
Cost of speaker = $35
Cost per song = $195
Sales tax rate = 8.25%
Expression to obtain the amount of sales tax on entire purchase : 0.0825(35+ 195s)
Using distributive law to expand the expression :
0.0825(35+ 195s)
= 2.8875+16s
Hence, the amount of sales tax due on the entire purchase of a set of speakers and s songs is given by expression 2.8875+16s
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brianna is driving on a long road trip. she created the graph below to represent the gallons of gas left in her tank. what does the x-intercept in the graph represent?
The x-axis represents the distance traveled (in miles).
Considering that the x-axis shows the distance travelled (in miles) and the y-axis represents the amount of gas left in the tank (in gallons), the x-intercept would represent the point at which Brianna's gas tank is empty, and she would need to refill her tank to continue traveling. In other words, the x-intercept is the distance Brianna can travel before running out of gas, assuming her car's fuel efficiency remains constant and she does not refill her tank.
Two key lines known as the x and y axes are the building blocks of a graph.
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Question 7(Multiple Choice Worth 1 points)
(06.02 MC)
Three friends, Martin, Tyreese, and Braydon, are collecting donations to help in their community's clean-up initiative. Their total contribution goal is represented by the expression
7x²-4xy+8. The friends have already collected the following amounts
Martin: 5xy + 16
Tyreese: x²
Braydon: 4x²-7
Which expression represents the amount of money the friends still need to collect to meet their goal?
A.2x²-9xy-1
B.2x² + xy +17
C.5x²+5xy+9
D.12x² + xy + 17
The algebraic expression that represents the amount that they still need to raise is given as follows:
A. 2x² - 9xy - 1.
How to obtain the algebraic expression?The total amount that the three friends want to raise is defined as follows:
7x² - 4xy + 8.
The total amount raised is obtained adding the amounts raised by each of the friends, as follows:
5xy + 16 + x² + 4x² - 7 = 5x² + 5xy + 9.
Then the remaining amount to be raised is obtained by the subtraction of the total amount by the amount raised, as follows:
7x² - 4xy + 8 - (5x² + 5xy + 9) = 7x² - 5x² - 4xy - 5xy + 8 - 9
7x² - 4xy + 8 - (5x² + 5xy + 9) = 2x² - 9xy - 1.
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Find tn Will mark branliest!
The sequence is an arithmetic sequence
The equation of tn is Tn = -k^2 - k + 1 + (n - 1) * (k^2 + 2k + 3)
How to determine the equation of the functionFrom the question, we have the following parameters that can be used in our computation:
-k^2 - k + 1, k + 2, k^2 + 3k + 3, 2k^2 + 5k + 4
The above sequence is an arithmetic sequence
And the common difference (d) is
d = k + 2 + k^2 + k + 1
d = k^2 + 2k + 3
The nth term is then calculated as
Tn = a + (n - 1)d
So, we have
Tn = -k^2 - k + 1 + (n - 1) * (k^2 + 2k + 3)
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Clear my choice
Which expression is equivalent to
(-√8 -√2) + √-36
The expression equivalent to (-√8 -√2) + √-36 is -3√2 + 6i.
What are complex numbers?A real number and an imaginary number are effectively combined to create a complex number. The complex number is written as a+ib, where a and ib are real and imaginary numbers, respectively. Additionally, I = -1 and both a and b are real numbers.
Consequently, a complex number is a straightforward illustration of the addition of two integers, specifically a real number and an imaginary number. It consists of two parts: one that is entirely real, the other entirely fantastical.
The given expression is:
(-√8 -√2) + √-36
The expression can be written as:
(-2√2 - √2) + √(i)²(6)²
Taking the common term:
√2(-2 - 1) + 6i
Simplifying the expression:
-3√2 + 6i
Hence, the expression equivalent to (-√8 -√2) + √-36 is -3√2 + 6i.
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sean gets an average of 20 calls during his 8 hour work day. what is the probability that sean will get at most 9 calls in a 4 hour portion of his work day? round the final answer to three decimal places.
The probability that Sean will get at most 9 calls in a 4 hour portion of his work day is 0.037.
The probability that Sean will get at most 9 calls in a 4 hour portion of his work day can be calculated by using the Poisson distribution formula. The formula is [tex]P(x)=e^-μ(μ^x/x!)[/tex].
In this case, μ = 20/4 = 5.
Therefore, [tex]P(x=9) = e^-5(5^9/9!) = 0.037[/tex]
Rounding the answer to three decimal places, the probability that Sean will get at most 9 calls in a 4 hour portion of his work day is 0.037.
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i need help guysss
schoology
Solving an equation we will see that the measure of angle a is 68°.
How to find the measure of the missing angle?We want to find the measure of angle a. On the image we can see that we have 3 angles, and the sum of these 3 angles should be equal to 180°, then we can write the equation:
28° + 90° + a = 180°
(the 90° angle is the one with the square).
Solving that equation for a, we will get:
a = 180° - 90° - 28°
a = 90° - 28°
a = 62°
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how much does 3.26 m of lace cost if 0.8m costs $5.60?
1. Laquan is hosting a brunch and buying pastries for himself and each of his 12 guests. If each pastry costs $3.50, how much will he spend?
Answer:
$45.5
Step-by-step explanation:
12 guests and himself : 13×3.50=45.5
to find m∠JML, you can stop when you get the step 3x=126 degrees, right?
No, you cannot stop at the step 3x = 126 degrees. The measure of angle JML is approximately 56.67 degrees
What is the measure of angle θ?
A radian is the length of an arc formed by an angle that, when shown as a central angle, equals the length of the circle's radius.
No, you cannot stop at the step 3x = 126 degrees.
To find the measure of angle JML, we need to solve for x and then use that value to find the measure of the angle.
We can start by using the fact that the angles in triangle JLM must add up to 180 degrees. We have:
m∠JLM + m∠JML + m∠LMJ = 180
Substituting the given values, we get:
4x + (2x + 18) + (3x - 12) = 180
Simplifying and combining like terms, we get:
9x + 6 = 180
Subtracting 6 from both sides, we get:
9x = 174
Dividing both sides by 9, we get:
x = 19.33...
Now that we have the value of x, we can use it to find the measure of angle JML. We have:
m∠JML = 2x + 18
Substituting x = 19.33..., we get:
m∠JML = 2(19.33...) + 18 = 56.67...
Therefore, the measure of ∠JML is approximately 56.67 degrees
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(PLEASE HELP ME ASAP THIS IS DUE TODAY)
An image of a parallelogram is shown.
A parallelogram with a base of 22 and one-half feet and a height of 19 and one-fourth feet.
What is the area of the parallelogram?
423 1/2 ft
427 1/2 ft
433 1/8 ft
455 1/8 ft
Answer:
433 1/8ft
Step-by-step explanation:
this is my answer
find the following arc measures
Answer:
m angleJ= 53, m angle JML = 63.5
Step-by-step explanation:
As this is a circle, KJ and KL are radii, which are equal
If we join J and L to form JL, Triangle KJL becomes and isosceles triangle( two sides equal).
That means, the angles J and L are equal (isosceles triangle thm).
Therefore- m angleJ = 180 - 127
m angleJ = 53
Join J and K, and L and K
Another circle theorem- The angle subtended by an arc/chord on the centre is double the angle subtended by the chord on any other point on the circle.
Therefore- angle JML = (1/2)127
So, m angleJML = 63.5
15 solids and 15 liquids found in the kitchen.
Please help.
15 liquids that can be found in a kitchen include:
WaterMilkJuice Cooking oil VinegarWineSoy sauceHoneySoupKetchupMustardMayonnaiseSalad dressingEggnogCocktail mixers15 solids in a kitchen are:
FlourSugarSaltRiceBaking sodaBaking powderSpices NutsPastaButterCheeseBreadMeat Vegetables FruitsWhat are some solids and liquids in kitchens ?When it comes to solids in the kitchen, we can mostly find either food ingredients, such as salt, flour, and spices, or actual food that can be prepared such as meat, vegetables, and bread.
As for liquids, these can be anything from drinks such as juice, water and wine, to liquids used for cooking such as oil, soy sauce and vinegar.
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