Solution
- The question would like us to solve the following
[tex]\frac{x-3}{2}-4<\frac{x}{3}[/tex]- The solution is outlined below:
[tex]\begin{gathered} \frac{x-3}{2}-4<\frac{x}{3} \\ \\ Collect\text{ like terms:} \\ Add\text{ 4 to both sides and Subtract }\frac{x}{3}\text{ from both sides} \\ \\ \frac{x-3}{2}-\frac{x}{3}<4 \\ \\ We\text{ need the LCM of 2 and 3. } \\ The\text{ LCM is }2\times3=6 \\ \\ Thus,\text{ multiply both sides by 6 in order to remove the denominator} \\ 2\frac{}{} \end{gathered}[/tex][tex]\begin{gathered} 6\left(\frac{x-3}{2}\right?-6\left(\frac{x}{3}\right?<4\times6 \\ \\ 3\left(x-3\right)-2x<24 \\ Expand\text{ the bracket} \\ 3x-9-2x<24 \\ x-9<24 \\ Add\text{ 9 to both sides} \\ x<33 \end{gathered}[/tex]Final Answer
The answer is x < 33
Which answer seems the most reasonable answer to the problem below? *
(-5.6) (3.4) =
-20
18
-15
12
Answer:
-20
Step-by-step explanation:
1- each of the two numbers are inside parenthesis and are beside each other which means they should be multiplied like this: -5.6 * 3.4
2- because 5.6 is negative, the rule in multiplying different signs would result to a negative number
3- and when you accurately multiply them, the answer is 19.04, and the options here are estimated so you should estimate the 19.04 too
4- 1 after it is 9 and nine is a great number, 1 turns to 2 and 9 turns into 0, which equals to 20, and DO NOT forget to add the sign, which is negative as i said previously
What is the exponential form of sq.rt (5^x)?
Answer:
Step-by-step explanation:
Comment and Answer
√5^x
The square root is really 0.5 as a decimal or 1/2 as a fraction. Both are powers.
So the square root of 23 can be written as 23^.5
For your question, you divide the power (x) by 2 so it looks like this.
5^(x/2)
What is the equation of a line that passes through the point (5, −3) and is parallel to 6x+3y=−12?
Enter your answer in the box.
Answer: Slope= -2.000
x-intercept= -2
y-intercept= -4.000
Hope this helps !
aghwhelrrotiuugggdddd
Solution
We have the following info:
Grades Credits
B 2
B 5
B 5
C 2
And we know that A= 4, B= 3, C=2
So we can do this:
[tex]\operatorname{mean}=\frac{3\cdot2+3\cdot5+3\cdot5+2\cdot2}{2+5+5+2}=2.86[/tex]then the weighted average is 2.86
a cyber hacker is trying to identify the mean age of customers that make frequent purchases on the online retail platform. the hacker does not have access to the raw data, however, the hacker had guessed that the age of customers is normally distributed with a standard deviation of 5 years. in addition to the above, the hacker knows that 70% of the time the age of the customers does not exceed 30 years old. calculate the mean age of customers, relying on the above information.
The mean age of customers is 27.35 years.
It is well known that age has a normal distribution with a 5-year standard deviation. Additionally, 30% of the time, customers are under the age of 30.
Mathematically,
P (age ≤ 30) = 0.70
Let μ be the mean age of the customer.
P [z ≤ (30 - μ) / σ] = 0.70
The equivalent of "age" in a conventional normal distribution is the z-score or z. It is evident from the usual normal distribution table that when z=0.53, 0.70 probability is reached.
Thus,
z = (30 - μ) / σ
⇒ 0.53 = (30 - μ) / 5
⇒ μ = 27.35
As a result, the average consumer is 27.35 years old.
The probability at each z-score in a standard normal table is represented by the associated z-score. We will look for the number 0.70 in the table, then the row value of 0.5 and the associated column value of 0.03 will be examined. They add up to 0.53 when combined.
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How do I get n from 2n C n =70?
After evaluating the expression, the value of n is √(70/2C).
What are expressions?An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.) You can think of expressions as being similar to phrases.So, 2nCn = 70:
Now, solve for n as follows:
2nCn =702Cn² = 70n² = 70/2Cn = √(70/2C)Therefore, after evaluating the expression, the value of n is √(70/2C).
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-15/2 = 3x solve for x and simplify your answer as much as possible
Answer:
x = -5/2
Step-by-step explanation:
-15/2 = 3x
multiply both sides by 2:
2(-15/2) = 2(3x)
-15 = 6x
divide both sides by 6:
-15/6 = 6x/6
x = -15/6
this can be reduced to:
x = -5/2
What is the value of this expression.
this is the answer to your equation hope it helps thanks
Answer:
D. [tex]\dfrac{27}{4}\\\\[/tex]
Step-by-step explanation:
[tex]\mathrm{With\;x=\dfrac{1}{8}\;and\;y = \dfrac{3}{16}\;we\;get}\\\\[/tex]
[tex]2\left(\dfrac{1}{8}+4\right)-\left(\dfrac{3}{16}\cdot 8\right)\\\\[/tex]
[tex]\mathrm{Calculate\:within\:parentheses}\:\left(\dfrac{1}{8}+4\right) = \dfrac{1}{8}+\dfrac{32}{8}} = \dfrac{33}{8}\\\\[/tex]
[tex]2\left(\dfrac{1}{8}+4\right) = 2\cdot \dfrac{33}{8} = \dfrac{33}{4}[/tex]
[tex]y \cdot 8 = \dfrac{3}{16} \cdot 8} = \dfrac{3}{2}\\\\[/tex]
So
[tex]2(x + 4) - y\cdot 8 = \dfrac{33}{4} - \dfrac{3}{2}\\\\\\= \dfrac{33-6}{4}\\\\= \dfrac{27}{4}\\\\[/tex]
of all postsecondary degrees awarded in the united states, including master's and doctorate degrees, 21% are associate's degrees, 58% are earned by people whose race is white, and 12% are associate's degrees earned by whites. what is the conditional probability that a degree is earned by a person whose race is white, given that it is an associate's degree? give your answer to three decimal places.
The conditional probability that a degree is earned by a person whose race is white, given that it is an associate's degree, is 0.571.
The percentage of associate's degrees is 21%.
The percentage of degrees earned by people whose race is white is 58%.
The percentage of associate's degrees out of all degrees earned by people whose race is white is 12%.
Let the probability of earning an associate's degree be P(A).
P(A) = 0.21
Let the probability of earning a degree by the people whose race is white be P(B).
P(B) = 0.58
Let the probability of earning an associate's degree by the people whose race is white be P(C).
P(C) = 0.12
P(C) = P(A∩B)
We need to find the conditional probability that a degree is earned by a person whose race is white, given that it is an associate's degree.
P(B/A) = P(A∩B)/P(A)
P(B/A) = 0.12/0.21
P(B/A) = 0.571
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Can someone help me with this
Answer:
1st one- 4
2nd one- 1
3rd one- 5
4th one-6
5th one-3
6th one-2
How many 5's ar in 125 ?
Answer:
There are 25 5's in 125.
Step-by-step explanation:
5 can go in 125 25 times.
(unless you are talking about literally-- there is one 5 in 125)
if f(3)=6, what is the value of f^-1(6)?
If the function f(3) has a value of 6, then the value of f⁻¹(6) is 3
How to determine the composite function?From the question, the definition of the function is given as
f(x)
Such that
The value of f(3) is 6
This is represented as
f(3) = 6
Also, the function can be represented as
y = f(x)
In f(3) = 6, we have
x = 3 and y = 6
When the inverse function is calculated, we have
f⁻¹(y) = x
This means that
f⁻¹(6) = 3
Express as an inverse function
f⁻¹(6) = 3
Hence, the inverse function f⁻¹(6) has a value of 3
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tell me if the way I did it includes what's in this equation like if its commutative, associative, distributive or combined like terms
On the first line the distributive property was used. This property says that the product of a constant with a sum of two numbers is equal to the sum of the products.
On the third line the "associative" property was used. This property says that if you have the sum of three numbers the order at which you sum them doesn't affect the results.
$20 off, 30% original price
Answer:
20%
Explanation:
To know the percentage, we need to identify what percentage of $50 represents $10. So, we can calculate the percentage as:
[tex]\frac{\text{ \$10}}{\text{ \$50}}\times100=0.2\times100=20\text{ \%}[/tex]Therefore, the answer is 20%
A new pet store is offering 12% off for their grand opening! A parakeet originally costs $17. What is the sale price after the discount?
Let:
Oc = original cost = $17
Sp = Sale price
D = Discount percent = 12% = 12/100 = 0.12
The sale price will be:
[tex]\begin{gathered} Sp=Oc-0.12\cdot Oc \\ Sp=17-0.12\cdot17 \\ Sp=17-2.04 \\ Sp=14.96 \end{gathered}[/tex]The sale price is $14.96
2. Mr V bought 2 pajama sets for christmas for $25. He realized that he needed 2 more pajama sets. So now he bought 4 pajama sets for $50. Part A: Is this relationship proportional? Explain. *
We will have that the relationship is proportional because each time he bought more sets they had the same cost, and the total cost added to the sum of the independent cost. And we have the following relationship for the 2 sets and 4 sets:
2 sets:
[tex]\frac{25}{2}=12.5[/tex]So, each individual set is $12.5.
4 sets:
[tex]\frac{50}{4}=12.5[/tex]So, each individual set is $12.5.
So, each individual set for each relationship has the same cost, therefore the relationship is proportional.
A food truck vendor determined that 42% of his customers order a beverage with their food. What is the ratio of customers who order a beverage to customers who do not order a beverage?
Answer:29
Step-by-step explanation:
HELP ASAP-GETS BRAINIEST GETS 100 POINTS.
In a theater with 30 rows the number of seats in a row increases by two with successive row. the front has 15 seats find the total seating capacity of the theater.
Answer:
75
Step-by-step explanation:
15 + 2 × 30
Answer:
1320 seats.
Step-by-step explanation:
The given scenario can be modeled as an arithmetic series.
[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[2a+(n-1)d]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $d$ is the common difference.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
The first term is the number of seats in the front row.
Given that the number of seats in a row increases by 2 with each successive row, the common difference is 2.
The nth term is 30 since there are 30 rows in the theater.
Therefore:
a = 15d = 2n = 30Substitute the values into the arithmetic series formula and solve:
[tex]\implies S_{30}=\dfrac{1}{2}(30)[2(15)+(30-1)2][/tex]
[tex]\implies S_{30}=15[30+(29)2][/tex]
[tex]\implies S_{30}=15[30+58][/tex]
[tex]\implies S_{30}=15[88][/tex]
[tex]\implies S_{30}=1320[/tex]
Therefore, the total seating capacity of the theater is 1320 seats.
Select the correct answer from each drop-down menu.
AABC is translated 6 units up and 3 units left to create AABC
If vertex A is at (-1, 2) and vertex B is at (1, 5), then vertex A' is at
Reset
V
and vertex B is at
Next
From the translation described, If vertex A is at (-1, 2) and vertex B is at (1, 5), then vertex A' is at (-4, 8). See the justification for the same below.
What is a vertex?A vertex is a specific point of a mathematical object that is often where two or more lines or edges intersect. Angles, polygons, polyhedra, and graphs are the most typical places to find vertices. Nodes are another name for graph vertices.
The explanation of the translation is given as follows:
According to the translation rule for translating a point h units left is given as:- (x, y) → (x-h, k)
The translation rule for translating point k units up is given as:
(x,y) → (x, y+k).
Since ∆ABC is translated 6 units up and 3 units left to create ∆A'B'C'. If vertex A is at (-1, 2) and vertex B is at (1, 5).
Then,
The vertex A' =
A (-1, 2) → (-1 -3, 2+6)
= (-4, 8)
Therefore, the vertex A' is at (-4,8).
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From the translation described, the vertex A' is at the point (-4,8).
What is a vertex?A vertex is a specific point of a mathematical object that is often where two or more lines or edges intersect.
Angles, polygons, and graphs are the most typical places to locate the vertices.
The explanation of the translation will be:
Based on the translation rule for translating a point h units left is follows as
(x, y) → (x-h, k)
The translation rule for point k units up is follows as:
(x,y) → (x, y+k).
Since ∆ABC is translated to the 6 units up and 3 units left to create ∆A'B'C'. If vertex A is at (-1, 2) and vertex B is at; (1, 5).
The vertex A' ;
A (-1, 2)
(-1 -3, 2+6)
= (-4, 8)
Therefore, the vertex A' is at the point (-4,8).
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Pls let me see the work!!
The recipe for the waffles presented using rational numbers are as follows;
1. The recipe for 2 waffles is as follows;
[tex] \displaystyle \frac{3}{5} [/tex] cups of flour
[tex] \displaystyle \frac{2}{15} [/tex] teaspoon of salt
[tex] \displaystyle \frac{4}{5} [/tex] teaspoons of baking powder
[tex] \displaystyle \frac{7}{20} [/tex] Cups of milk
[tex] \displaystyle \frac{1}{15} [/tex] Cup of butter
2. The recipe for 5 waffles is as follows;
[tex] \displaystyle 1\frac{1}{2} [/tex] cups of flour
[tex] \displaystyle \frac{1}{3} [/tex] teaspoon of salt
[tex] \displaystyle 2 [/tex] teaspoons of baking powder
[tex] \displaystyle \frac{7}{8} [/tex] Cups of milk
[tex] \displaystyle \frac{1}{6} [/tex] Cup of butter
3. The recipe for 300 waffles is as follows;
900 cups of flour
200 teaspoon of salt
1200 teaspoons of baking powder
525 Cups of milk
100 Cup of butter
4. The required number of waffle irons is 50
5. It would take approximately 6 servers
It would take 34 trips
What is a rational number?A rational number is one that can be expressed as a fraction.
From the given table, we have;
The recipe for 10 waffles includes;
3 cups of flour
[tex] \displaystyle \frac{2}{3} [/tex] teaspoon of salt
4 teaspoons of baking powder
[tex] \displaystyle 1\frac{3}{4} [/tex] Cups of milk
[tex] \displaystyle \frac{1}{3} [/tex] Cup of butter
1. To make 2 waffles, we have;
[tex] \displaystyle 2 = \frac{10}{5} [/tex]
Dividing each of the quantities required to make 10 waffles by 5 gives;
[tex] \displaystyle \frac{3}{5} [/tex] cups of flour
[tex] \displaystyle \frac{2}{3 \times 5} = \frac{2}{15} [/tex] teaspoon of salt
[tex] \displaystyle \frac{4}{5} [/tex] teaspoons of baking powder
[tex] \displaystyle \frac{1\frac{3}{4}}{5} = \frac{7}{20} [/tex] Cups of milk
[tex] \displaystyle \frac{\frac{1}{3}}{5} = \frac{1}{15} [/tex] Cup of butter
2. If each person gets 1 waffle, we have;
Number of waffles = 1 + 4 = 5
[tex] \displaystyle 5 = \frac{10}{2} [/tex]
Dividing the recipe for 10 waffles by 2 gives;
[tex] \displaystyle \frac{3}{2} = 1\frac{1}{2} [/tex] cups of flour
[tex] \displaystyle \frac{2}{3 \times 2} = \frac{1}{3} [/tex] teaspoon of salt
[tex] \displaystyle \frac{4}{2} = 2 [/tex] teaspoons of baking powder
[tex] \displaystyle \frac{1\frac{3}{4}}{2} = \frac{7}{8} [/tex] Cups of milk
[tex] \displaystyle \frac{\frac{1}{3}}{2} = \frac{1}{6} [/tex] Cup of butter
3. When each of 300 people can have one, the number of waffles is 300, which gives;
30 × 10 = 300
Multiplying the quantity of each ingredients required to make 10 waffles by 300 gives;
300× 3 = 900 cups of flour
[tex] \displaystyle 300 \times \frac{2}{3} = 200 [/tex] teaspoon of salt
300 × 4 = 1200 teaspoons of baking powder
[tex] \displaystyle 300 \times 1\frac{3}{4} = 525 [/tex] Cups of milk
[tex] \displaystyle 300 \times \frac{1}{3} = 100 [/tex] Cup of butter
4. Time it takes to cook a waffle = 10 minutes
Number of waffles required = 300
Time allowed = 1 hour = 60 minutes
The number of waffle iron is therefore;
[tex] \displaystyle {n = \frac{300 \times 10}{60} = 50} [/tex]
The number of waffle irons required is 50 waffle irons
5. Number of waffles each server can deliver = 9 waffles
The time it takes each server per trip = 10 minutes
Number of waffles to be delivered = 300
Time in which to deliver the 300 waffles = 1 hour
The number of servers is therefore;
[tex] \displaystyle {n = \frac{300}{9 \times 6} = 5. \overline 5 \approx 6} [/tex]
The number of trips is therefore;
5 servers will deliver 5×9×6 = 270
The sixth server will deliver the remaining 300 - 270 = 30 waffles in 30 ÷ 9 = 3.3 ≈ 4
The number of trips all together is therefore; 5×6 + 4 = 34 trips
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Point(2,8) , (4,7.5) rise over run so what's the answer
The slope of the line with the given coordinates (2,8) and (4,7.5) is -0.25.
What is the slope of the line with the given coordinates?Slope is simply expressed as change in y over the change in x.
Rise over run.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point 1( 2,8) )
x₁ = 2y₁ = 8Point 2( 4,7.5 )
x₂ = 4y₂ = 7.5To find the slope, plug the given x and y values into the slope formula and simplify.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 7.5 - 8 )/( 4 - 2 )
Slope m = ( -0.5 )/( 2 )
Slope m = -0.5 / 2
Slope m = -0.25
Therefore, the slope of the line is -0.25.
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An exterior angle of a rectangle polygon cannot have the measure
The sum of the measures of an exterior angle of a polygon is 360°.
If the given angle divides 360 evenly, then it can be a measure of an exterior angle of a polygon. If otherwise, then it cannot be.
[tex]\begin{gathered} 360\div30=12 \\ 360\div50=7.2 \\ 360\div120=3 \\ 360\div90=4 \\ 360\div40=9 \end{gathered}[/tex]Out of the given angles, only 50 does not divide 360 evenly. Therefore, a regular polygon cannot have an exterior angle measuring 50°. (Option B)
robert has 30 socks in his sock drawer. 16 of the socks are white, 6 are black, 2 are red, and 6 are yellow.what is the prbability that he randomly pulls out a black sock
The Probability that Robert randomly pulls out a black sock is 1/5 .
In the question ,
it is given that
Total number of socks in sock drawer = 30 socks
number of white socks in the drawer = 16 socks
number of black socks in the drawer = 6 socks
number of red socks in the drawer = 2 socks
number of yellow socks in the drawer = 6 socks
So , the probability that he randomly pulls out a black sock = (number of black socks in the drawer) / ( total number of socks in the drawer )
= 6 / 30
= 1/5
Therefore , The Probability that Robert randomly pulls out a black sock is 1/5 .
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sin(40 + 2°) csc(30 + 5°) = 1
sin(40 + 2°) cosec(30 + 5°) = 1 we proved that by the values.
Given,
sin(40 + 2°) cosec(30 + 5°) = 1
To prove the trigonometry function equal to 1.
Now, According to the question:
We know that
Sin 42° = 0.66913061
Cosec 35° = 1.7434468
sin(40 + 2°) cosec(30 + 5°) = 1
sin 42° × cosec 35° = 1
Plug the values of sin and cosec in above function:
0.66913061 × 1.7434468
= 1.16659
But we take the before decimal value i.e., 1
Hence, sin(40 + 2°) cosec(30 + 5°) = 1 we proved that by the values.
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1/2 - 9/4x = -2/3 solve for x and simplify your answer as much as possible
Answer: 14/27
Step-by-step explanation:
the difference between the are of arc length and area of a sector please include the formulas for both in your answer
Person with the correct answer gets brainliest
Triangle ABC is congruent to triangle XYZ. In AABC, AB = 12 cm and AC = 14 cm. In AXYZ, YZ = 10 cm and XZ = 14
!
cm.
What is the perimeter of AABC?
O 36 cm
O 38 cm
О 40 cm
• 50 cm
The perimeter of the triangle ABC is 36 cm. Then the correct option is A.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees. If two triangles are similar, then the ratio of the corresponding sides will remain one.
Triangle ABC is congruent to triangle XYZ. In AABC, AB = 12 cm and AC = 14 cm. In AXYZ, YZ = 10 cm and XZ = 14 cm.
AB = XY = 12 cm
BC = YZ = 10 cm
AC = XZ = 14 cm
Then the perimeter of the triangle ABC is given as,
P = 12 + 10 + 14
P = 36 cm
The perimeter of the triangle ABC is 36 cm. Then the correct option is A.
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is the equation below represent a direct proportion. if so what is the constant 3x + 4 = y
The expression for a linear equation in thee slope-intercept form is ,
y = mx + b
the slope = m= (y2-y1)/ (x2-x1)
y-intercept is (0, b)
___________________
Rearreging tha expresion
y = 3x + 4
The rate is the slope (m) = 3
__________________________
Answer
the constant, in this case, is 3
What are the Missing Angles? Are these triangles the similar or Not similar?
Answer:
The missing angle in Triangle A is 66 degrees
The missing angle in Triangle B is 34 degrees
Because Triangle A has measures of 34 degrees, 80 degrees, and 66 degrees
and
Triangle B has measures of 80 degrees, 66 degrees, and 34 degrees, we can conclude that THEY ARE SIMILAR TRIANGLES
Explanation:
The sum of angles in a triangle is 180 degrees.
Given that triangle A has m<1 = 34 degrees, m<2 = 80 degrees. Let the missing angle be x, then
x + 34 + 80 = 180
x + 114 = 180
Subtract 114 from both sides
x = 180 - 114
= 66 degrees
Triangle B has m<1 = 80 degrees, m<2 = 66 degreess. Let the missing angle be y, then
y + 80 + 66 = 180
y + 146 = `180
Subtract 146 from both sides
y = 180 - 146
= 34 degrees
Triangles A and B are similar, since they have similar measure of angles.
in your own words explain angle addition postulate
This postulate tells us that when we put two angles side by side with a ray touching the ray of the other angle, we are creating a new angle which is the addition of the two, and whose measure is the addition of the measures of the two angles we are contacting via a common ray.