what expressions are equivalent to 45x - 30 ?
Answers
In mathematics, expression is a set of digits, variables, and operators that denotes a quantity or relationship. Expressions can be straightforward and consist only of a single number or variable, or they can be intricate and contain numerous phrases and processes.
There are a few expressions that are equivalent to 45x - 30. One way to find them is to simplify the expression by factoring out the greatest common factor (GCF), which in this case is 15:
45x - 30 = 15(3x - 2)
Now we can see that the expression 45x - 30 is equivalent to 15 times the expression 3x - 2. Therefore, any expression that is equal to 3x - 2 can be used to represent 45x - 30 by multiplying it by 15. Here are some examples:
6x - 4 is equivalent to 45x - 30 when multiplied by 15.
9x - 6 is also equivalent to 45x - 30 when multiplied by 15.
3(15x - 10) is equivalent to 45x - 30, since we can distribute the 3 and get 45x - 30.
In general, we can say that any expression of form 3k - 2, where k is a constant, is equivalent to 45x - 30 when multiplied by 15. This shows that there are infinitely many expressions that are equivalent to 45x - 30, and we can find them by using the GCF and multiplying by a constant.
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Related Questions
A researcher wants to estimate the average amount of calories in a large French Fries order in McDonalds. He wants a 95 % level of confidence with a margin of error of 10 calories. How many orders he needs to sample
Answers
The researcher would need to sample at least 193 large French Fries orders to estimate the average amount of calories with a 95% level of confidence and a margin of error of 10 calories.
To determine the sample size required to estimate the average amount of calories in a large French Fries order in McDonald's, we can use the following formula:
n = (Z^2 * σ^2) / E^2
where:
n = sample size
Z = the z-score associated with the desired confidence level (for a 95% confidence level, Z = 1.96)
σ = the population standard deviation (if unknown, a conservative estimate can be used)
E = the desired margin of error
Since we don't know the population standard deviation, let's assume a conservative estimate of 50 calories based on similar studies. Thus, the formula becomes:
n = (1.96^2 * 50^2) / 10^2 = 192.08
Rounding up to the nearest whole number, the researcher would need to sample at least 193 large French Fries orders to estimate the average amount of calories with a 95% level of confidence and a margin of error of 10 calories.
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give it a line segment containing the points AB and C in order if AB is four and BC is 16 then what is the length of AC
Answers
pls give the answer
Answers
Answer:
It should be 245 m
Step-by-step explanation:
Separate it like this:
chop of the rectangle part and find the area of that and then add it to the trapezoid part
10*20 = 200.
Area of a trapezoid = 5+10/2 *6.
5+10 = 15. 1
5/2 = 7.5.
7.5*6 = 45.
45 + 200 = 245
an automobile emissions testing center has six inspectors and tests 50 vehicles per hour. each inspector can inspect 12 vehicles per hour. how many inspectors would the center require to have a target utilization of 90 percent? question 50 options: two three seven five
Answers
Total number of inspectors required = Time required by the inspectors / Time taken by a single inspectorTotal number of inspectors required = 3.75 / 1Total number of inspectors required = 3.75So, the center would require 4 inspectors to have a target utilization of 90 percent.Option 3, that is, seven is not correct.
An automobile emissions testing center has six inspectors and tests 50 vehicles per hour. Each inspector can inspect 12 vehicles per hour.
How many inspectors would the center require to have a target utilization of 90 percent?
The target utilization is 90 percent which implies that 90 percent of the total available time is used by the inspectors in the automobile emissions testing center. We can calculate the total available time using the formula,
Total available time = Total number of vehicles / Number of vehicles inspected by a single inspector Total available time = 50 / 12 (since each inspector can inspect 12 vehicles per hour)Total available time = 4.17 hours (approx)The total available time is 4.17 hours. This implies that the center requires 90% of the total available time to be used by the inspectors. Hence, the time required by the inspectors is given as,Time required by the inspectors = \(4.17 * 0.9\)Time required by the inspectors = 3.75 hours (approx)Now, we can calculate the total number of inspectors required to inspect the vehicles in the given time.
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The following ordered pairs (x,y) define the relation Q.is Q a function (3,-2), (-3,1), (-2,-2), (1,-3)
Answers
The correct answer is: Yes, relation Q is a function,because there is exactly one y-value for every x-value.
To determine whether the given relation Q is a function, we need to check if each x-value is associated with a unique y-value. If there is any x-value that corresponds to multiple y-values, then the relation is not a function.
Let's examine the ordered pairs in relation Q: (3, -2), (-3, 1), (-2, -2), (1, -3).
We can see that each x-value in Q is associated with a unique y-value:
For x = 3, the y-value is -2.
For x = -3, the y-value is 1.
For x = -2, the y-value is -2.
For x = 1, the y-value is -3.
Since each x-value is paired with a unique y-value in relation Q, we can conclude that Q is a function.
In a function, every input (x-value) maps to a single output (y-value). If there were any repeated x-values with different y-values in the relation, it would indicate a violation of this rule and Q would not be a function. However, in this case, all the x-values have distinct y-values, satisfying the criteria for a function.
It's worth noting that we can also visualize this relation on a coordinate plane and check if there are any vertical lines that intersect the graph at more than one point. If there are no such lines, it confirms that the relation is a function.
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Two cans of pumpkin roll down a loading dock ramp. They have identical inertias, but one of them has a larger radius (and a shorter length) than the other.
Which one, if either, makes it down the ramp first?
A. The can with the larger radius reaches the ground first.
B. The can with the smaller radius reaches the ground first.
C. The cans don't reach the ground at all.
D. The cans reach the ground at the same time.
Answers
Two cans of pumpkin roll down a loading dock ramp. They have identical inertias, but one of them has a larger radius (and a shorter length) than the other. D. The cans reach the ground at the same time.
The rate at which an object rolls down a ramp depends on its rotational inertia (moment of inertia) and the distribution of mass around its axis of rotation. In this case, both cans have identical inertias, indicating that their mass distributions are the same relative to their respective axes of rotation.
The radius and length of the cans do not affect their inertias in this scenario since both cans have the same inertia. Therefore, both cans will experience the same gravitational force and will roll down the ramp at the same rate.
The cans with different radii but identical inertias will reach the ground at the same time when rolled down the ramp.
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which ratios form a proportion?
1/6 and 3/8 or 2/3 and 8/12 or 3/4 and 9/16 or 2/5 and 5/2
Answers
Answer:
2/3 and 8/12.
Step-by-step explanation:
£490 is divided between Richard, Stephen & Bridget so that Richard gets twice as much as Stephen, and Stephen gets three times as much as Bridget. How much does Stephen get?
Answers
Answer:
Stephen gets £147
Step-by-step explanation:
Given
Let
\(S = Stephen; B = Bridget; R = Richard\)
So:
\(S + B + R = 490\)
\(R = 2S\)
\(S = 3B\)
Required
Find S
Make B the subject in \(S = 3B\)
\(B = \frac{S}{3}\)
Substitute: \(R = 2S\) and \(B = \frac{S}{3}\) in \(S + B + R = 490\)
\(S + \frac{S}{3} + 2S = 490\)
Take LCM
\(\frac{3S + S + 6S}{3}= 490\)
\(\frac{10S}{3}= 490\)
Solve for S
\(S = \frac{490 * 3}{10}\)
\(S = 49 * 3\)
\(S = 147\)
Stephen gets £147
Last year, Greg had $20000 to invest. He invested some of it in an account that paid 7% simple interest per year, and he invested the rest in an account that paid 5% simple interest per year. After one year, he received a total of $1340 in interest. How much did he invest in each account?
Answers
The amount invested into 7% simple interest and 5% simple interest is $17,000 and $3,000 respectively.
How much was invested in each account?Let
x = 7% simple interesty = 5% simple interestx + y = 20,000
0.07x + 0.05y = 1340
From (1)
x = 20,000 - y
Substitute into (2)
0.07x + 0.05y = 1340
0.07(20,000 - y) + 0.05y = 1340
1,400 - 0.07y + 0.05y = 1340
- 0.07y + 0.05y = 1340 - 1400
-0.02y = -60
y = -60 / -0.02
y = 3,000
Substitute y = 3,000 into (1)
x + y = 20,000
x + 3,000 = 20,000
x = 20,000 - 3,000
x = 17,000
Therefore, $17,000 and $3,000 was invested into into 7% simple interest and 5% simple interest respectively.
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An object dropped from a height of h feet will take t seconds to fall all the way to the ground, according to the
following equation.
16t2 - h = 0
The Eiffel Tower in Paris, France is 900 feet tall.
How many seconds will it take an object dropped from that height to fall all the way to the ground?
Answers
Answer:
7.5 seconds.
Step-by-step explanation:
16t^2 - h = 0
16t^2 - 900 = 0
t^2 = 900/16
t = √900/√16
= 30/4
= 7.5 seconds.
Simplify the expression below. Make sure to reduce all fractions.
8sec(x)/-7csc(x)
Answers
Answer:
16/7sin(2x)
Step-by-step explanation:
-8×1/cos(x)×⅐×1/sin(x)
-8/7cos(x)sin(x)
-8/⁷/²×sin(2x)
-8/7sin(2x)/2
16/7sin(2x)
Answer:
- \(\frac{8}{7}\) tanx
Step-by-step explanation:
Using the identities
secx = \(\frac{1}{cosx}\) , cscx = \(\frac{1}{sinx}\) , tanx = \(\frac{sinx}{cosx}\)
Given
\(\frac{8secx}{-7cscx}\)
= \(\frac{\frac{8}{cosx} }{\frac{-7}{sinx} }\) ← multiply numerator/ denominator by sinx
= \(\frac{8\frac{sinx}{cosx} }{-7}\)
= - \(\frac{8}{7}\) tanx
a vector graphic consists of a set of instructions for creating a picture.
Answers
Answer:
A vector graphic consists of a set of instructions for creating a picture is a true statement.
Step-by-step explanation:
A vector graphic is an image format that represents images as a set of mathematical instructions or geometric primitives such as lines, curves, and shapes. Instead of using a grid of pixels like raster graphics, vector graphics define images based on mathematical formulas and coordinates.
These instructions or mathematical representations describe the shapes, colors, and other visual attributes of the image. They allow the image to be scaled, resized, and manipulated without loss of quality since the instructions can be recalculated and redrawn at any resolution or size.
Vector graphics are often created and edited using specialized software such as Adobe Illustrator, CorelDRAW, or Inkscape. They are commonly used for logos, illustrations, diagrams, typography, and other graphical elements where scalability and flexibility are important.
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What is the significance of the mean of a probability distribution? It is the expected value of a discrete random variable. In most applications, continuous random variables represent counted data, while discrete random variables represent measured data.
Answers
It is important to note that continuous random variables typically represent measured data, such as the weight or height of an individual, while discrete random variables typically represent counted data, such as the number of heads in a series of coin flips.
The mean of a probability distribution, also known as the expected value, is a measure of central tendency that represents the average value of a random variable in the long run. It is calculated by taking the weighted average of all possible values that the random variable can take, with the weights being the probabilities of each value occurring.
In the case of a discrete random variable, the mean is calculated by multiplying each possible value by its probability and then summing the results. For a continuous random variable, the mean is calculated by integrating the product of the value and its probability density function over the entire range of possible values.
The mean is significant because it provides a measure of the central tendency of a probability distribution, which can be used to make predictions about future outcomes. It is also used in various applications, such as calculating the expected value of a financial investment or the expected number of occurrences of an event in a given time period.
It is important to note that continuous random variables typically represent measured data, such as the weight or height of an individual, while discrete random variables typically represent counted data, such as the number of heads in a series of coin flips.
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Due May 4Attendance Question (5/4/21) A cab company charges a$5 boarding rate in addition to its meter which is $3 forevery mile. What equation represents the rate of thiscompany?
Answers
Explanation
Step 1
Let x represents the number of hours
Let y represents the rate of the company
and
cost per hour = $3
so, the total cost per time is
cost per time= 3* number of hours
cost per time==3x
now, the company charges a $5 boarding rate
so, the rate is
\(\begin{gathered} \text{rate= boarding rate}+\text{cosper times} \\ reaplce \\ y=\text{ \$5+\$3x} \\ \text{reorder} \\ y=\text{ \$3x}+\text{\$5} \end{gathered}\)I hope this helps you
If y = 4x, what is y if the x = 5?
9
45
54
20
Help I will give brainliest
Answers
Answer:
20
Step-by-step explanation:
Substitute x in y = 4x for 5. So now the equations stands as y = (4)(5). 4 times 5 equals 20
It’s 20 because 4(5) equals 20.
i. The uniform probability distribution's shape is a rectangle. ii. The uniform probability distribution is symmetric about the mode. iii. In a uniform probability distribution, P(x) is constant between the distribution's minimum and maximum values. Multiple Choice (ii) and, (iii) are correct statements but not (i). (i). (ii), and (iii) are all false statements. (i) is a correct statement but not (ii) or (iii). (i) and, (iii) are correct statements but not (ii).
Answers
The correct option is: (i) and (iii) are correct statements but not (ii).
The correct answer is:
(i) The uniform probability distribution's shape is a rectangle.
(ii) The uniform probability distribution is symmetric about the mode.
(iii) In a uniform probability distribution, P(x) is constant between the distribution's minimum and maximum values.
Therefore, the correct option is: (i) and (iii) are correct statements but not (ii).
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vic's favorite cookie recipe uses 250 250250 grams of flour for every 170 170170 grams of butter. imani made cookies using 750 750750 grams of flour for every 630 630630 grams of butter. what will vic think of the amount of butter in imani's cookies? choose 1 answer:
Answers
Vic would think that the amount of butter in Imani's cookies is appropriate since the ratio of flour to butter used in Imani's recipe is the same as the ratio used in Vic's favorite cookie recipe, which is 250:170 grams of flour to butter.
Specifically, in Vic's recipe, there are approximately 1.47 grams of flour for every gram of butter (250/170), while in Imani's cookies, there are approximately ratio 1.19 grams of flour for every gram of butter (750/630). This means that there is relatively more butter in Imani's cookies compared to Vic's recipe. Based on this difference, Vic might expect Imani's cookies to have a richer, denser texture and a stronger buttery flavor than his favorite recipe.
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What is the simplified value of the exponential expression 27 1/3
Answers
Answer:
3
Step-by-step explanation:
Arrange the following values from least to greatest.
1. √4.1
2. 0
3. |-2|
4. -4
5. |-3|
Answers
.4, .2, .3, .1, .5
A contractor bought 12.6ft2 of sheet metal. He used 4.9ft2 so far and has 123.20 worth of sheet of metal remaining. The equation 12.6x-4.9x=123.2 how much sheet metal is remaining and cost of the remaining amount. How much does sheet of metal cost per square foot?
Answers
Answer:
Step-by-step explanation:
12.6x-4.9x=123.2
63x over 5 -4.9x-123.2
You inherit $5,000 from your Uncle Harold. The bad news is that the money must sit in a bank account for the next 10 years until you can use it. The account earns 7.2% interest, compounded annually. This means that you will need to multiply the amount of money by 1.072 to determine how much money remains at the end of the next year.
HELPPP PLEASEE
Answers
Answer:
what the world is this question its so long and hard
-4(7.5x-8)=-5(6.3x+8)
Answers
Answer:
x = -48
Step-by-step explanation:
-4(7.5x - 8) = -5(6.3x + 8)
-30x + 32 = -31.5x - 40
-30x + 31.5x = -40 - 32
1.5x = -72
x = -72/(1.5)
x = -48
please help me with my question
Answers
The volume of a triangular prism is given by the following expression:
\(V=A_{\text{base}}\cdot h\)Where V is the volume, Abase is the area of the base and h is the height of the prism. For this prism the base has a rectangular shape, so it can be calculated as shown below:
\(A_{\text{base}}=\text{length}\cdot\text{width}=18\cdot12=216cm^2\)Using this value on the first expression:
\(V=216\cdot9=1944cm^3\)The correct option is A.
Which verbal expression is represented by 2(x + 4)?
A. twice the sum of a number and four
B. the sum of two times a number and four
C. two times the difference of a number and four
D. twice the product of a number and four
Answers
Answer:
A.
Step-by-step explanation:
The sum of a number, x, and 4 just means x + 4.
If we take twice this sum, it implies that we take the resulting number and multiply it by 2.
Our resulting number is x + 4, so we are left with 2(x + 4).
I hope this helps!
The correct answer is twice the sum of a number and four.
What is an expression?Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given an expression, 2(x+4)
The sum of a number, x, and 4 just means x + 4.
Taking twice of the sum, it implies that we take the resulting number and multiply it by 2.
The resulting number is x + 4, so it is 2(x + 4).
Hence, The correct answer is twice the sum of a number and four.
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Three people are selected at random. Find the probability: a) all 3 are born on Tuesday b) all 3 are born on a different day of the week
Answers
a) The probability of all 3 people being born on Tuesday is 1/343, calculated by multiplying the probability of each person being born on Tuesday (1/7) together.
b) The probability of all 3 people being born on different days of the week is 30/343, calculated by multiplying the probability of each person being born on a different day of the week (7/7, 6/7, 5/7) together.
a) To find the probability that all 3 people are born on Tuesday, we need to first determine the probability that one person is born on Tuesday, which is 1/7 (assuming all days of the week are equally likely). Since each person's birthday is independent of the others, the probability that a second person is also born on Tuesday is also 1/7, and the probability that a third person is born on Tuesday is also 1/7. To find the probability that all three people are born on Tuesday, we multiply the probabilities together: (1/7) x (1/7) x (1/7) = 1/343. So the probability that all 3 people are born on Tuesday is 1/343.
b) To find the probability that all 3 people are born on a different day of the week, we need to first determine the probability that one person is born on any given day of the week, which is 1/7. Once one person's birthday has been determined, the probability that the second person is born on a different day of the week is 6/7 (since there are only 6 other days of the week to choose from). Similarly, the probability that the third person is born on a different day of the week from the first two is 5/7. To find the probability that all three people are born on different days of the week, we multiply the probabilities together: (1/7) x (6/7) x (5/7) = 30/343. So the probability that all 3 people are born on different days of the week is 30/343.
a) To find the probability that all 3 people are born on a Tuesday, you simply calculate the probability of each person being born on a Tuesday and then multiply these probabilities together. Since there are 7 days in a week, the probability of being born on any specific day (including Tuesday) is 1/7. So, the probability of all 3 being born on Tuesday is:
(1/7) x (1/7) x (1/7) = 1/343
b) To find the probability that all 3 people are born on different days of the week, first consider the probability for each person. The first person can be born on any day (7/7 chance). For the second person, they have a 6/7 chance of being born on a different day than the first person. Finally, the third person has a 5/7 chance of being born on a different day than the first two. Multiply these probabilities together:
(7/7) x (6/7) x (5/7) = 210/343
So, the probability of all 3 people being born on different days of the week is 210/343.
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6/7 times 3/4 = x
IN SIMPLEST FORM
Answers
Answer:
I believe 6/7 times 3/4 in the simplest form is 9/14 because you aren't able to put anything in both of those numbers
Step-by-step explanation:
The value of x in the equation (6/7) × (3/4) = x is 9/14.
To find the value of x in the equation (6/7) × (3/4) = x.
We can simply multiply the two fractions together.
Multiplying the numerators and denominators gives us:
(6 × 3) / (7 × 4)
= 18/28
The fraction 18/28 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2.
(18/2) / (28/2)
= 9/14
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What is the greatest common factor of:
10 – 25t
Answers
Answer:
maybe 15?? sorry if I'm wrong
1. Find the GCF of 8 and 12.
List the factors of 8.
List the common factors.
Find the GCF of 15 and 20.
Math
Answers
Step-by-step explanation:
8-1,2,4,8
12-1,2,3,4,6,12
15-1,3,5,15
20-1,2,4,5,10,20
An independent basic service set (IBSS) consists of how many access points?
Answers
An independent basic service set (IBSS) does not consist of any access points.
In an IBSS, devices such as laptops or smartphones connect with each other on a peer-to-peer basis, forming a temporary network. This type of network can be useful in situations where there is no existing infrastructure or when devices need to communicate with each other directly.
Since an IBSS does not involve any access points, it is not limited by the number of access points. Instead, the number of devices that can be part of an IBSS depends on the capabilities of the devices themselves and the network protocols being used.
To summarize, an IBSS does not consist of any access points. Instead, it is a network configuration where wireless devices communicate directly with each other. The number of devices that can be part of an IBSS depends on the capabilities of the devices and the network protocols being used.
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Determine which of the following relations is a function. (Lesson 1-7)
A.{(–4, 3), (−2, −2), (0, 2), (0, 5)}
B.{(−3, 1), (−3, 3), (−2, −1), (0, 5)}
C.{(−4, −1), (−2, −1), (−1, −1), (3, 3)}
D.{(2, −5), {−1, −1), (0, 4), (2, −3)}
Answers
Answer:
c
Step-by-step explanation:
c is a function because the x variables don't repeat. You can't have the same number in x variable position repeat.