Answer:
[tex]12(1 + x)[/tex]
Step-by-step explanation:
We will use order of operations to simplify this expression.
We will evaluate the brackets first.
3(5+7)-6(4-2x) =
[tex]3(12) - 6(4 - 2x) \\ = 36 - 6(4 - 2x) \\ = 36 - 24 + 12x \\ = 12 + 12x[/tex]
You can further simplify it by factorising it:
[tex]12 + 12x \\ = 12(1 + x)[/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3(5 + 7) - 6(4 - 2x)}[/tex]
[tex]\mathsf{= 3(5) + 3(7) - 6(4) - 6(-2x)}[/tex]
[tex]\mathsf{= 15 + 21 - 24 + 12x}[/tex]
[tex]\mathsf{= 36 - 24 + 12x}[/tex]
[tex]\mathsf{= 12 + 12x}[/tex]
[tex]\mathsf{= 12x + 12}[/tex]
[tex]\huge\text{Therefore, your answer should be:\boxed{\mathsf{12x + 12}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
100 POINTS!!! In one area, the lowest angle of elevation of the sun in winter is 21° Find the distance x that a plant needing full sun can be placed from a fence that is 10.5 feet high. Round your answer to the tenths place when necessary.
To find the length of the missing side x, use Tan trigonometric formula
Tan: [tex]\frac{opposite}{Adjacent}[/tex]
Tan 21 = [tex]\frac{10.5}{x}[/tex]
Tan 21 × [tex]\frac{1}{10.5}[/tex] = [tex]\frac{10.5}{x}[/tex]×[tex]\frac{1}{10.5}[/tex]
[tex]\frac{10.5}{Tan 21}=x[/tex]
x=27.4
X= 27.4 ft
Hope it helps!
Answer:
x = 27.4 ft
Step-by-step explanation:
Here given:
opposite side: 10.5 ftadjacent side: x ftto that angle: 21°So, use tan rule:
[tex]\sf tan(\theta) = \dfrac{opposite}{adjacent}[/tex]
insert values
[tex]\sf tan(21) = \dfrac{10.5}{x}[/tex]
make 'x' subject
[tex]\sf x= \dfrac{10.5}{tan(21) }[/tex]
calculate value
[tex]\sf x = 27.35343...[/tex]
rounded to nearest tenth
[tex]\sf x = 27.4 \ ft[/tex]
Volume round to nearest tenth
The total volume of the given figure is:
[tex]V = 311.65cm^3 + 246.97cm^3 = 558.62cm^3[/tex]
How to find the volume of the given figure?
Here we have two simple shapes.
Half a sphere, and a cone.
The volume of half a sphere of radius R is:
[tex]V = \frac{2}{3}*3.14*R^3[/tex]
And here we know that R = 5.3cm, replacing that we get:
[tex]V = \frac{2}{3}*3.14*(5.3cm)^3 = 311.65cm^3[/tex]
For a cone of radius R and height H, the volume is:
[tex]V = \frac{3.14*R^2*H}{3}[/tex]
In this case, R = 5.3cm and H = 8.4cm
The volume of the cone is:
[tex]V = \frac{3.14*(5.4cm)^2*8.4cm}{3} = 246.97cm^3[/tex]
Then the total volume is:
[tex]V = 311.65cm^3 + 246.97cm^3 = 558.62cm^3[/tex]
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THe square root of 10 x 15 x 24 is
[tex]\large\blue\implies \tt \large \: \sqrt{10 \: \times \: 15 \: \times \: 24} [/tex]
[tex]\large\blue\implies \tt \large \: \sqrt{150 \: \times \: 24} [/tex]
[tex]\large\blue\implies \tt \large \: \sqrt{3600} [/tex]
[tex]\large\blue\implies \tt \large \: \sqrt{3600} \: = \: 60[/tex]
[tex]\large\blue\implies \tt \large \:60[/tex]
Which is a term in both the sequence f(n)=f(n-1)+4 and the sequence f(n)=3(5)^n-1 if f(1)=3?
a. 7
b. 15
c. 27
d. 135
Answer:
[tex] \small{\boxed{ \sf{Term \: in \: both \: the \: sequence \: is \: 15}}}[/tex]
Step-by-step explanation:
To determine the common term in both the sequence let's solve for each sequence individually.
Let's solve for first sequence
[tex]f(n) = f(n-1)+4[/tex]
we are already told that f(1) = 3
let's solve for f(2),f(3),f(4)........ and so on till we get the highest digit or more than the highest digit from given option.
f(2) = f(2-1)+4 = f(1)+4
f(2) = 3+4
[tex]\small{ \fbox{f(2) = 7}}[/tex]
f(3) = f(3-1)+4 = f(2)+4
f(3) = 7+4
[tex] \small{\fbox{f(3)= 11}}[/tex]
on solving further..
The series obtained is 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 119, 123, 127, 131, 135.....
Let's solve for second series
[tex]f(n) = 3×5^{n -1}[/tex]
given that f(1) = 3,
f(2) = 3×5¹ = 15
f(3) = 3×5² = 75
f(4) = 3×5³ = 375
The series obtained is 3, 15, 75, 375.....
The term obtained in both the sequence is 15 hence option B is correct Answer.
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A triangle has squares on its three sides as shown below. What is the value of x? 3 cm U x cm 4 cm 3 centimeters 4 centimeters 5 centimeters 07 centimeters A triangle has squares on its three sides as shown below . What is the value of x ? 3 cm U x cm 4 cm 3 centimeters 4 centimeters 5 centimeters 07 centimeters
The value of x is 10 centimeters
How to solve for x?The complete question is in the image
The value of x is calculated using the following Pythagoras theorem
x^2 = 6^2 + 8^2
Evaluate the sum of exponents
x^2 = 100
Take the square roots
x = 10
Hence, the value of x is 10 centimeters
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Need help now due in 5 minutes pls help quick now pls pls pls pls pls
Answer: A and D
Step-by-step explanation:
- Career A's spread is more concentrated while Career B's spread is more dispersed or spread out
- Career A's median is 25 and Career B's median is 30
- Therefore A and D are the correct answers
hope this helps :)
can somebody please explain question (i) and (ii) to me
hey buddy, if u attach your question to this we can help you to find an answer for your question.
☆...hope this helps...☆
_♡_mashi_♡_
Why is it important to use the correct units of measurement when working with conversions? Explain by converting 5 feet into inches.
It is important to use the correct units of measurement when working with conversions because errors may occur. 5 feet = 60 inches.
What is conversion?Conversion means to convert the same thing into different units.
It is important to use the correct units of measurement when working with conversions because errors may occur.
1 foot = 12 inches
Then we have
5 feet = 60 inches
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Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Based on the triangle sum theorem, exterior angle theorem, the true statements are:
m∠5 + m∠6 = 180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
What is the Triangle Sum Theorem and the Exterior Angle Theorem?According to the triangle sum theorem, m∠2 + m∠3 + m∠5 = 180°.
Also, based on the exterior angle theorem, m∠2 + m∠3 = m∠6.
∠5 and ∠6 are a pair of linear angles, therefore: m∠5 + m∠6 = 180°.
In summary, the true statements about the diagram given are:
m∠5 + m∠6 = 180°m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°Learn more about the triangle sum theorem on:
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Need the answer for number 3 please!!
Answer: No
Step-by-step explanation:
The graph is increasing, yet as p increases, the value of 100/p decreases, meaning that the graph should be decreasing.
please solve this question please
Answer:
a) 57
b) 19.476
c) 1.106 (rounded)
Step-by-step explanation:
a) note: the very first step here is to find the number of people of age 21 which is found through subtraction. We have a total of 250 people, and we currently have data on 193 (64 + 60 + 69) people. This means there are (250 - 193 = 57) 57 remaining people of age 21.
The first thing we're trying to find here is the mean, which we sometimes refer to as the average, of this data set.
To find the mean, we add all values together and then divide by the number of values we've combined.
We could write out 18 + 18 + 18... sixty-four times, and then to the same thing for 19's, but that would take a while. So, we can find this value through multiplication (remember, multiplication is the same thing as repeated addition).
18 × 64 = 1152
19 × 60 = 1140
20 × 69 = 1380
21 × 57 = 1197 *see above
Now, we find the sum of our values added together:
Now, we know we have 250 values, so we will divide 4869 by 250:
4869 / 250 = 19.476
So, the mean of this sample is 19.476
Now, we are finding the standard deviation, which is found through the formula:
∑ (x - x^(line over x) ) ²
√ _______
n - 1
(this is hard to write on this website sorry)
find difference between each value and mean (that's what "x - x^(line over x)" is)
18 - 19.476 = -1.476
19 - 19.476 = -0.476
20 - 19.476 = 0.524
21 - 19.476 = 1.524
square each difference: (that's what " (x - x^(line over x))² " is)
now, we need to add up our squared values. But first, we must account for how many of each value there are
now, let's add up our squared values: (that's what "∑" is )
we now need to divide this number by n - 1 (we have 250 samples, so we need to divide by 250 - 1 (249) to find our variance)
now, we find our standard deviation by taking the square root of the variance that's what the "√" is )
we can round this number to:
1.106 (or any other rounded decimal place, I did it this way to match our previous answer)
So, the standard deviation of this set is 1.106 (rounded)
hope this helps! have a lovely day :)
What is the slope of the line shown below?
Answer:
(1/2)
Step-by-step explanation:
From one point, if you go up one and over 2 you will get exactly one block up than from your initial point. And since the graph is pointing down on left side, that means it's positive.
60°
X
x
60°
x = [ ? ]
Ingresar
Answer: 30
Step-by-step explanation:
Since there are two angles that measure [tex]60^{\circ}[/tex], the triangle is equilateral. This means that the angle bisector of the third angle is an altitude, and thus we have two right triangles with acute angles [tex]60^{\circ}[/tex] and [tex]x[/tex]. It follows that x=30.
(a) Write the next whole number after DDD fourteen in the base-fourteen system.
Answer:
1000 in base 14
Step-by-step explanation:
DDD + 1 = 1000 in base 14
What number is 15% of 43
?
43 % of 300 is what
number?
12% of what number is 43?
43 is what percent of 106?
What percent of 43 is 6?
Step-by-step explanation:
So when a question asks what is x% of the y number. It's asking you to convert the x into decimal form by dividing by 100 and then multiply it by y. This gives you the equation: [tex]y * \frac{x}{100}[/tex] which gives you x% of y. so 15% of 43 is [tex]43 * \frac{15}{100} = 6.45[/tex]. 43% of 300 is [tex]300 * \frac{43}{100} = 129[/tex].
the 12% of what number is 43 is a bit more tricky. It's asking you to instead find a number in which 12% of it is equal to 43. So instead of plugging solving for the percentage (which is already given) you solve for y. This gives you the following equation: [tex]y * \frac{12}{100} = 43[/tex]. Now all you do is calculate 12/100 which gives you [tex]y * 0.12 = 43[/tex]. now divide both sides by 0.12 to solve for y. This gives you [tex]y = 358.\overline{33}[/tex]
43 is what percent of 106? This question is also a bit tricky, but instead of solving for y, you're solving for x. So plug in the known values, which gives you the equation: [tex]106 * \frac{x}{100} = 43[/tex]. Divide both sides by 106 to get [tex]\frac{x}{100} \approx 0.406[/tex] and now multiply both sides by 100. this gives you [tex]x \approx 40.57[/tex] which is the answer 40.57%
What percent of 43 is 6. This is asking the same thing just in a different way. So percentage = unknown, entire number = 43, entire number * percentage = 6. With these values we get the equation: [tex]43 * \frac{x}{100} = 6[/tex]. Divide both sides by 43 to get [tex]\frac{x}{100} \approx 0.140[/tex] now multiply by 100 to get [tex]x \approx 13.95[/tex] which is the answer 13.95%
Somebody help please
Answer:
Emily raised $37.50
Justin raised $57.50
Step-by-step explanation:
(Step 1)
Say "x" equals the amount of money Emily made and "y" equals the amount of money Justin made. You can set up an equation with both of these variables because we know that they made a combined $95.
x = Emily's earnings
y = Justin's earnings
Emily + Justin = 95
x + y = 95
(Step 2)
The fact that there are two variables makes it difficult to find how much each person made individually. However, we can eliminate the "y" variable when we remember that Justin made $20 more than Emily. Now, we can substitute "x + 20" in for "y".
x + 20 = y
x + y = 95
x + (x + 20) = 95
(Step 3)
Finally, we can solve for the "x" variable.
x + (x + 20) = 95
2x + 20 = 95 <------ Combine like terms
2x = 75 <------ Subtract 20 from both sides
x = 37.5 <------- Divide both sides by 2
(Step 4)
Since we know the value of "x", we can plug it into one of the equations to find the value of "y".
x + 20 = y
37.5 + 20 = y
y = 57.5
Answer:
Emily raised $37.5 and justin raised $57.5
5. In a high school, 60% of the students live east of the school and 40% live west of the school. Among the students who live east of the school, 30% are in the math club, and among the students who live west of the school, 20% are in the math club. a. Find the probability that a randomly selected student is from east of the school and in the math club. b. Given that a student is from west of the school, what is the probability that he or she is in the math club? c. Is participation in the math club independent from whether a student lives east or west of the school? Justify your answer.
The probability for part (a) is 0.18, for part (b) is 0.08, and for part (c) is 0.26.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
a. Find the probability that a randomly selected student is from east of the school and in the math club:
P(east ∩ math club) = 0.6×0.3 = 0.18
b. Given that a student is from west of the school, what is the probability that he or she is in the math club?
P(west ∩ math club) = 0.4×0.2 = 0.08
c. Is participation in the math club independent of whether a student lives east or west of the school?
P(math club) = P(east ∩ math club) + P(west ∩ math club)
= 0.18 + 0.08
= 0.26
Thus, the probability for part (a) is 0.18, for part (b) is 0.08, and for part (c) is 0.26.
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when a relation is drawn on an xy-plane what is another name for the set of all x values from its graph?
Another name for the set of all x-values for a relation is: domain.
What is the Domain of a Relation?
The domain of a relation can be defined as all the x-values that corresponds to the y-values that are plotted on a graph.
They are referred to as the input or the domain of the relation. Therefore, another name for the set of all x-values plotted for a relation on a graph is: domain.
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A researcher needs to ask a question “what impact does a new curriculum have on a student achievement?” Which of the following is the most appropriate method for answering the question?
A) observation
B)textual analysis
C)experiment
D) survey
Answer:
C) Experiment
Step-by-step explanation:
With a controlled experiment, a researcher can use a student batch that studied the old curriculum as a control group, and the new batch of students as the 'test' group. To measure student achievement, the researcher would need to either:
1. compare test results for the 2 groups
2. do a longitudinal study - follow the 2 groups of students across several years, and track their 'achievements' (university admissions, jobs, income, etc)
With the other 3 options, the results wouldn't necessarily be accurate or relevant.
The area of each circle is exactly
0.56π square inches.
There are 2 identical circles in the cylinder.
So the total area of all the circles is ??? π square inches.
Total area of the circle is 1.12π square inches.
What is Area of circle?The Area of circle is π times the square of the radius.
i.e., A = πr²
Given:
Area of one circle = 0.56π
As the second circle is also identical then the area will be same.
So, the total area of circle is
=2* 0.56π
=1.12π square inches.
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A committee of 4
is being formed randomly from the employees at a school: 4
administrators, 30
teachers, and 4
staff. What is the probability that all 4
members are teachers? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability that all 4 are teachers is 0.0000135.
How to solve for the probabilityThe total number is =
4 + 30 + 4
= 38
The committee of 4 from 38 =
38C4 = 73815
The committee of 4 from 4 teachers =
4C4 = 1 way
The total favorable cases = 1 way
Probability = favorability/ total cases
= 1/73815
= 0.0000135
Hence the probability that all 4 are teachers is 0.0000135.
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Solve for x: 1
04>x>7
04
O-2>x> 1
0-2
Answer: -2 < x < 1
Step-by-step explanation:
move all terms not containing x from the center section of the inequality
1 < x + 3 < 4
subtract 3 from both terms outside the center
1 - 3 = -2
4 - 3 = 1
therefore our answer is:
-2 < x < 1
A regular six-sided die is rolled 1000 times. Use the binomial distribution to determine the standard deviation for the number of times an odd number is rolled
The standard deviation for the number of times an odd number is rolled is 15.8
How to determine the standard deviation?The given parameters are:
Die = regular six-sided die
n = 1000
The probability of rolling an odd number is:
p = 1/2 = 0.5
The standard deviation is then calculated as;
[tex]\sigma = \sqrt{np(1 - p)[/tex]
This gives
[tex]\sigma = \sqrt{1000 * 0.5 * (1 - 0.5)[/tex]
Evaluate the products
[tex]\sigma = \sqrt{250[/tex]
Evaluate the root
[tex]\sigma = 15.8[/tex]
Hence, the standard deviation is 15.8
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Factorize x^2+√4x+2x+2
Answer:
x^2+4x+2
Step-by-step explanation:
PLEASE HELP !!! URGENT!!!
What is the range of f(x)?
O {f(x)
O {f(x)|-∞
O {f(x)|4
O {f(x)|0sf(x)<∞}
Answer:
best ans is { f(x)| –∞ < f(x) ≤ 4}
Step-by-step explanation:
usually to find the range of a fn, u need to see what the value can be. the graph show only a small range of x values. but u can see f(x) is definitely < 4. so the ans is { f(x)| –∞ < f(x) ≤ 4}
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gathmath
The graph of a line has a slope of 3 and passes through the point (–4, –5).
What is the equation of the line in point-slope form?
y – 5 = 3(x – 4)
y – 4 = 3(x – 5)
y + 5 = 3(x + 4)
y + 4 = 3(x + 5)
Answer
(C) y +5 =3(x+4)
We will use the point-slope formula to solve this problem.
We will use the point-slope formula to solve this problem.(y+5)=3(x+4)
)Explanation:
)Explanation:We can use the point slope formula to solve this problem.
)Explanation:We can use the point slope formula to solve this problem.The point-slope formula states: (y−y1)=m(x−x1)
)Explanation:We can use the point slope formula to solve this problem.The point-slope formula states: (y−y1)=m(x−x1)Where m is the slope and (x1y1) is a point the line passes through.
)Explanation:We can use the point slope formula to solve this problem.The point-slope formula states: (y−y1)=m(x−x1)Where m is the slope and (x1y1) is a point the line passes through.We can substitute the slope and point we were given into this formula to produce the equation we are looking for:
)Explanation:We can use the point slope formula to solve this problem.The point-slope formula states: (y−y1)=m(x−x1)Where m is the slope and (x1y1) is a point the line passes through.We can substitute the slope and point we were given into this formula to produce the equation we are looking for:(y−(−5))=3(x--(4))
=> (y+5)=3(x+4)
If the price of a bicycle is increased by 9.09%,
then by 8.33% and then by 7.7%, the price
becomes Rs. 1,274. What is the original price
of the bicycle?
Answer:
Rs 1000.97
Step-by-step explanation:
x = original price
new price = x (1.0909)(1.0833)(1.077) = 1274
x = Rs 1000.97
Need the answer for number 3 please!!!
Answer:
Step-by-step explanation:
Two lines, A and B, are represented by the equations given below:
Line A: y = x − 6
Line B: y = 3x + 4
Which of the following shows the solution to the system of equations and explains why?
(−5, −11), because the point satisfies both equations
(−5, −11), because the point does not lie on any axis
(−3, −5), because the point satisfies one of the equations
(−3, −5), because the point lies between the two axes
The solution to the system of equations (−3, −5)
We have given that,
Two lines, A and B, are represented by the equations given below:
Line A: y = x − 6
Line B: y = 3x + 4
Line A
y = x - 2
Line B
y = 3x + 4
If we equate those 2 equations
x - 2 = 3x + 4
2x = -6
x = -3
y = -5
So the answer is
(−3, −5), because the point satisfies both equations.
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Consider a triangle ABC like the one below. Suppose that A=57°, C=73°, and b = 13. (The figure is not drawn to scale.) Solve the triangle. Round your answers to the nearest tenth. If there is more than one solution, use the button labeled "or".
By using triangle properties and the law of the sines twice, we find that the missing angle is 50° and the missing lengths are 14.232 and 16.229, respectively.
How to determine the missing variables of a triangle
In this triangle we know the length of a side (b = 13) and the measure of two adjacent angles (A = 57°, C = 73°). First, we determine the measure of the missing angle by using triangles properties:
B = 180° - 57° - 73°
B = 50°
Lastly, we determine the missing lengths by the law of the sines:
[tex]a = 13 \times \frac{\sin 57^{\circ}}{\sin 50^{\circ}}[/tex]
a ≈ 14.232
[tex]c = 13 \times \frac{\sin 73^{\circ}}{\sin 50^{\circ}}[/tex]
c ≈ 16.229
By using triangle properties and the law of the sines twice, we find that the missing angle is 50° and the missing lengths are 14.232 and 16.229, respectively.
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