Answer:
[tex]{ \tt{ {x}^{2} + 2 = 0 }} \\ \\ { \tt{ {x}^{2} = - 2 }} \\ \\ { \tt{x = \sqrt{ - 2} }}[/tex]
- At this point, we can't operate the square root. Let's introduce the imaginary part of a value
From complex numbers;
[tex]{ \boxed{ \tt{{ \red{note} \: {\rightarrow{i \times i = - 1 = {i}^{2} }}}}}}[/tex]
Therefore;
[tex]{ \tt{x = \sqrt{2 \times {i}^{2} } }} \\ \\ { \boxed{ \rm{ \: x = i \sqrt{2} \: \: }}}[/tex]
HELP PLEASE!!!
In a recent year, 26% of all college students were enrolled part-time. If 4.4 million college students were enrolled part-time that year, what was the total number of college students? Round your answer to the nearest million.
Answer: 17 million
Step-by-step explanation:
We will set up a proportion to solve. We also will divide 26% by 100 to get a decimal, 0.26. We know that 26% of college students was 4.4 million, but we want to find 100%.
[tex]\displaystyle \frac{0.26}{4.4\text{ million}} =\frac{1}{x\text{ million}}[/tex]
Now, we will cross-multiply.
0.26 * x = 1 * 4.4
0.26x = 4.4
Lastly, we will divide both sides of the equation by 0.26. Then, we will round to the nearest million.
x = 16.923
x ≈ 17 million
Question 19 Here are the fuel efficiencies (in mpg) of 8 new cars. 44, 19, 51, 12, 34, 21, 15, 24 What is the percentage of these cars with a fuel efficiency less than 24 mpg?
The percentage of these cars with a fuel efficiency less than 24 mpg is 50 %.
What is percentage?Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.
Given data:
44, 19, 51, 12, 34, 21, 15, 24
fuel efficiency less than 24 mpg is 19, 12, 21, 15
So, the percentage is
=4 / 8 x 100
= 1/2 x 100
= 50%
Hence, the percentage of these cars with a fuel efficiency less than 24 mpg is 50 %.
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If the quotient of a number and 8 is added to 1/4 the result is 7/8. Find the number.
Answer:
5
Step-by-step explanation:
Let n be the unknown number.
The quotient is the result obtained by dividing one number by another.
Therefore, the quotient of a number and 8 is ⁿ/₈.
If the quotient of a number and 8 is added to 1/4 the result is 7/8:
[tex]\implies \dfrac{n}{8}+\dfrac{1}{4}=\dfrac{7}{8}[/tex]
To solve, make the denominators of all the fractions the same:
[tex]\implies \dfrac{n}{8}+\dfrac{1 \cdot 2}{4 \cdot 2}=\dfrac{7}{8}[/tex]
[tex]\implies \dfrac{n}{8}+\dfrac{2}{8}=\dfrac{7}{8}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]
[tex]\implies \dfrac{n+2}{8}=\dfrac{7}{8}[/tex]
Multiply both sides by 8:
[tex]\implies \dfrac{8(n+2)}{8}=\dfrac{7 \cdot 8}{8}[/tex]
[tex]\implies n+2=7[/tex]
Subtract 2 from both sides:
[tex]\implies n+2-2=7-2[/tex]
[tex]\implies n=5[/tex]
Therefore, the number is 5.
As an estimation we are told £3 is €4. Convert £12 to euros.
Well, here is the answer . . .
£12 = 13.73€
A designer has designed different tops, pants, and jackets to create outfits. How many different outfits can the models wear if she has designed the following pieces?
seven tops, two pants, eight jackets
There are a total of different outfits
The most appropriate choice for combination will be given by-
Models can wear 112 different types of outfit.
What is combination?
Combination determines the number of ways of selecting some number of particular items from a group of given item, here the order of selection do not matter.
If there are n objects and from there, r objects are chosen, number of ways will be given by
[tex]n \choose r[/tex] = [tex]\frac{n!}{(n - r)! \times r!}[/tex]
Here,
Number of tops = 7
Number of pants = 2
Number of jackets = 8
From 7 tops the designer can choose 1 top in [tex]7 \choose 1[/tex] ways
= [tex]\frac{7!}{(7-1)!\times 1 !}[/tex]
= [tex]\frac{7!}{6!}[/tex]
= [tex]7[/tex]
From 2 pants the designer can choose 1 pant in [tex]2 \choose 1[/tex] ways
= [tex]\frac{2!}{(2-1)!\times 1 !}[/tex]
= [tex]\frac{2!}{1!}[/tex]
= [tex]2[/tex]
From 8 jackets the designer can choose 1 jacket in [tex]8 \choose 1[/tex] ways
= [tex]\frac{8!}{(8-1)!\times 1 !}[/tex]
= [tex]\frac{8!}{7!}[/tex]
= [tex]8[/tex]
Total number of different outfits models can wear = [tex]7 \times 2 \times 8[/tex]
= 112
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I need help please with number 5 initially. I have attached a scanned document of my book problems.
Considering the z-test formula, it is found that:
a) Increasing the difference between the sample mean and the original population mean increases the test statistic.
b) Increasing the population standard deviation decreases the test statistic.
c) Increasing the sample size increases the test statistic.
What is the z-test formula?Considering a z-test, the formula for the test statistic is given by the following rule:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which the parameters are defined as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.In item a, increasing the difference between the sample mean and the original population mean is increasing the numerator [tex]\overline{x} - \mu[/tex], meaning that the test statistic z will be increased.
In item b, increasing the population standard deviation [tex]\sigma[/tex] means that the denominator of the formula will be increasing, hence the test statistic will be decreased.
In item c, increasing the sample size n means that the denominator will be decreased, as the denominator is a fraction which is inverse proportional to the sample size, hence the test statistic z will be increased.
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Given the graph of a function f. Identify the function by name. Then Graph, state the domain and range, use set notation forA) 1/2f(x)B) 2f(x)
From the graph, we can determine that the function f(x) is quadratic. The function f(x) is defined as:
[tex]f(x)\text{ = }x^2[/tex]The graph of (a) 1/2 f(x):
This implies that f(x) is compressed vertically by a factor of 1/2.
Using the points:
(-4, 8) , (-2, 2), (0,0), (2,2), (4, 8)
The graph of the function using a graphing calculator is shown below:
The graph of (b) 2 f(x)
This implies that the original function was stretched vertically by a factor of 2
Using the points:
(-4, 32), (-2, 8), (0,0), (2,8), (4,32)
The graph using a graphing calculator is shown below:
The domain:
This is a set of allowable x-values
Using interval notation:
[tex](-\infty,\text{ }\infty)\text{ or All real numbers}[/tex]The range:
This is a set of allowable y-values:
Using interval notation:
[tex]\lbrack0,\text{ }\infty)\text{ }[/tex]Complete.
:14=15:21
Someone please answer how to solve
Answer:
The missing number is 10Step-by-step explanation:
Given ratiox : 14 = 15 : 21Multiply both sides by 14 to find the missing value:
x = 14*15/21 x = 10A model rocket is launched straight up into the air. The height y (in feet) of the rocket after t seconds can be modeled by y=-16t^2+128t. How many seconds is the rocket in the air?
Answer:
8
Step-by-step explanation:
To find the time the rocket is in the air, we can find the time when the height is 0 (remember this time is not 0).
[tex]-16t^2+128t=0 \\ \\ t^2-8t=0 \\ \\ t(t-8)=0 \\ \\ t=0,8 \\ \\ t \neq 0 \implies t=8[/tex]
Use the figure for 5 and6.
And 7
So I’m doing this assignment and got stuck on this question can anyone help me
Explanation:
The question involves dividing radicals
To resolve the question, we will follow the steps below
Step 1: Write the expression
[tex]\sqrt{50x^3}\div\sqrt{32x^2}[/tex]Step 2: simplify the expression in parts and apply the laws
[tex]\begin{gathered} \sqrt{50x^3}=\sqrt{25\times2\times x^2\times x} \\ =\sqrt{25\times2\times x^2\times x}=\sqrt{5^2\times2\times x^2\times x}=\sqrt{5^2}\times\sqrt{x^2}\times\sqrt{2x} \end{gathered}[/tex]Thus
[tex]\begin{gathered} \sqrt{50x^3}=\sqrt{5^2}\times\sqrt{x^2}\times\sqrt{2x}=5\times x\times\sqrt{2x} \\ Therefore \\ \sqrt{50x^3}=5x\sqrt{2x} \end{gathered}[/tex]For the second part
[tex]\sqrt{32x^2}=\sqrt{16\times2\times x^2}[/tex]simplifying further
[tex]\sqrt{16\times2\times x^2}=\sqrt{16}\times\sqrt{x^2}\times\sqrt{2}[/tex]Hence, we have
[tex]\sqrt{16}\times\sqrt{x^2}\times\sqrt{2}=4\times x\times\sqrt{2}=4x\sqrt{2}[/tex]Finally, we will combine the simplified terms, so that we will have
[tex]\sqrt{50x^3}\div\sqrt{32x^2}=5x\sqrt{2x}\div4x\sqrt{2}[/tex]Hence, we will have
[tex]\frac{5x\sqrt{2x}}{4x\sqrt{2}}=\frac{5}{4}\times\frac{x}{x}\times\frac{\sqrt{2}}{\sqrt{2}}\times\frac{\sqrt{x}}{1}[/tex]By canceling out the common parts, we will have the answer to be
[tex]\frac{5}{4}\sqrt{x}[/tex]Can I please get help on this math problem always been bad at math.If X=-5 and y=-3 what is the value of x (y-10) i can't provide pictures
Given
[tex]x(y-10)[/tex][tex]\begin{gathered} x(y-10) \\ x=5,y=3 \\ 5(3-10) \\ 5(-7) \\ -35 \end{gathered}[/tex]Given the equation of a line
y = mx + 1, for what values of m will the line be increasing? Enter (<,>,=).
greater than 1. If its less than, it will be decreasing.
Given that f(x) = x² - 3 and g(x) = 3x + 5, find (g- f)(9), if it exists.
(3x+5)-([tex]x^{2} - 3[/tex])=9
[tex]x^{2}[/tex]-3x-8=-9
[tex]x^{2}[/tex]-3x=-1
[tex]x^{2}[/tex]-3x+1=0
Simplify -16.26-(-5.82)-(4.20) - (-6.85).
Answer:
Step-by-step explanation:
=−10.44−4.2−(−6.85)
=−14.64−(−6.85)
=−7.79
Answer:
-7.79
Step-by-step explanation:
Given problem,
→ -16.26 - (-5.82) - (4.20) - (-6.85)
Let's simplify the problem,
→ -16.26 - (-5.82) - (4.20) - (-6.85)
→ -16.26 + 5.82 - 4.20 + 6.85
→ -10.44 + 2.65 = -7.79
Hence, the answer is -7.79.
out of water park 243 out of 675 tickets were sold child tickets what percentage of the tickets were child tickets
Total ticket = 675
Child tickrt sold = 243
percentage of child tickets sold
[tex]\begin{gathered} =\text{ }\frac{243}{675}\text{ x 100\%} \\ \\ =\text{ }\frac{243\text{ x 100}}{675} \\ =\text{ }\frac{24300}{675} \\ =\text{ 36\%} \end{gathered}[/tex]Which expression is equivalent to −40+(−20)+(−60) ?
Responses
−40−(20−60)
negative 40 minus open parenthesis 20 minus 60 close parenthesis
−(40−20)+(−60)
negative open parenthesis 40 minus 20 close parenthesis plus open parenthesis negative 60 close parenthesis
40 + 20 + 60
40 + 20 + 60
−20+(−40)+(−60
PLEASE HELP!
The expression equivalent to [-40 + (-20) + (-60)] is [−20 + (−40) + (−60)]
As per the question statement, we are provided with a linear expression of [-40 + (-20) + (-60)], and four options.
We are supposed to determine the one expression from the given options, that is equivalent to the question mentioned expression of [-40 + (-20) + (-60)].
To solve this question, we will first calculate the value of the question mentioned equation, and then, calculate and compare the values of individual expressions provided in the options, to obtain our desired answer.
Therefore, [-40 + (-20) + (-60)] = [-40 - 20 -60]
or, [-40 + (-20) + (-60)] = -( 40 + 20 + 60)
or, [-40 + (-20) + (-60)] = -120.
Now, coming to the first option, expression [−40 − (20 − 60)] equates to
[-40 - (-40)] = (-40 + 40) = (40 - 40) = 0,
And [0 ≠ (-120),
Hence, [−40 − (20 − 60)] is not the equivalent expression to
[-40 + (-20) + (-60)].
Now, coming to the second option, expression [-(40 − 20) + (-60)] equates to [-(20) + (-60)] = (-20 - 60) = -(20 + 60) = (-80),
But again, [(-80) ≠ (-120)],
Hence, [-(40 − 20) + (-60)] is not the equivalent expression to
[-40 + (-20) + (-60)].
Coming to the third option, expression [40 + 20 + 60] equates to (120)
But again, [120 ≠ (-120)],
Hence, [40 + 20 + 60] is not the equivalent expression to
[-40 + (-20) + (-60)].
Finally, Coming to the last option, expression [−20 + (−40) + (−60)] equates to (-20 - 40 - 60) = -(20 + 40 + 60) = (-120).
And [(-120) = (-120)],
Hence, [−20 + (−40) + (−60)] is the required equivalent expression to
[-40 + (-20) + (-60)].
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Answer:
−20+(−40)+(−60)
Step-by-step explanation:
they add up to the same thing and the order doesn't matter I think.
Name the rule for this sequence.
27, 21, 15, 9, 3,…
A. divide the previous term by 0.06
B. divide the previous term by 0.6
C. add 6 from the previous term
D. subtract 6 from the previous term
C. add 6 from the previous term
To get the next term in the sequence, you subtract 6 from the previous term.
HELPP! Algebra 2
If the length of one side of a square is triple and the length of an adjacent side is increased by 10, the resulting rectangle has an area that is 6 times the area of the original square. Find the length of a side pf the original square.
Answer:
Side = 10 units
Step-by-step explanation:
Original square area = s x s =s^2
now change the sides and this equals 6s^2
3s * ( s+10) = 6 s^2
3s^2 -30s = 0
s ( 3s-30) = 0 so s = 0 or 10
If I eat pizza after midnight, then I'll
have a stomach ache.
Choose the equivalent statement.
A. If I don't have a stomach ache, then I didn't eat pizza after
midnight.
B. If I don't eat pizza after midnight, then I won't have a stomach
ache.
C. If I have a stomach ache, then I ate pizza after midnight.
Answer:
B. If I don't eat pizza after midnight, then I won't have a stomach ache.
Determine the values of m in the equation m2 = 16. m = ±4 m = 4 m = ±8 m = 8
The values of m that can fit into the equation m² = 16 will be m = ±4.
How to compute the value?It should be noted that a equation is simply used to illustrate the relationship between the variables that are given. From the information, it should be noted that the equation is illustrated as m² = 16.
Since m² = 16, we need to find the square root. This will be illustrated as:
m² = 16
m = ✓16
m = 4
It should be noted that (-4) × (-4) = 16 and 4 × 4 = 16.
Therefore, the correct option is m = ±4
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Decide whether there is enough information to prove mn.
m
O Yes
O No
You
An
If so, state the theorem you can use. If not, answer "cannot" for the blank below.
✓prove mn
Yes, there is enough information to prove m||n.
By using the Vertical Angles Theorem, Corresponding Angles Theorem, and Alternate Exterior Angles Theorem we can prove that line m is parallel to line n.
In the given figure,
Let the given angles formed by transversal r, adjacent to line m be angle 1, and to line n be angle 2.
Now, the vertically opposite angle to angle 1 will be equal to it as they both are congruent.
The vertically opposite angle equal to angle 1 would be corresponding to angle 2 and corresponding angles formed by a transversal are equal and congruent.
Moreover, angle 1 and angle 2 are alternate exterior angles and by Alternate Exterior Angles Theorem, they are congruent.
Hence, it is proved by the Vertical Angles Theorem, Corresponding Angles Theorem, and Alternate Exterior Angles Theorem that line m is parallel to line n (m||n).
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what is this equation rewritten in the form that reveals the minimum of the function
We are given the quadratic function c(p) = p^2 - 28p + 250 and we need to rewrite this in such a way that the minimum value is easy to find.
Remember that the vertex
[tex]f(x)=a(x-h)^2+k[/tex]where (h, k) is the vertex or the minimum point.
We use completing the squares method to do this. We divide the second term, -28p, by 2p, then square it.
[tex](\frac{-28p}{2p})^2=(-14)^2=196[/tex]We add 196 to p^2 - 28p to make it equal to (p - 14)^2, but since it will change the value of the equation, we need to subtract the same value from 250 so that the net effect is zero.
[tex]\begin{gathered} c(p)=p^2-28p+250 \\ c(p)=(p^2-28p+196)+250-196 \\ c(p)=(p-14)^2+54 \end{gathered}[/tex]The equation is c(p) = (p - 14)^2 + 54.
The area of a rectangle is solved by multiplying the length and width of a rectangle. A rectangular field has an area of 57,600 square feet. If its width is 160 feet, what is its length?
Answer:
360ft
Step-by-step explanation:
Here,
Given,
→Area=57600ft²
→Width=160ft
Now,
→Length=Area/Width
→Length=57600ft²/160ft=360ft
Write an equation for each line
The equation for each line will be y=-x+2.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that,
The coordinate of the points are (2,0) and (0,2)
The slope of the line is,
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1} \\\\ m = \frac{2-0}{0-2} \\\\ m = -1[/tex]
The standard equation of the line is,
y-y₁ = m(x-x₁)
y-0=-1(x-2)
y=-x+2
Thus, the equation for each line will be y=-x+2.
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$(x) = x2 – 25 and g(x) = x + 5Step 2 of 4 : Find (J - 8)(x), Simplify your answer,Answer( -8)(x) =
Solve for (f - g)(x)
[tex]\begin{gathered} (f-g)(x)=f(x)-g(x) \\ (f-g)(x)=(x^2-25)-(x+5) \\ (f-g)(x)=x^2-25-x-5 \\ \; \\ \text{Therefore,} \\ (f-g)(x)=x^2-x-30 \end{gathered}[/tex]
A plane traveled 3465 miles with the wind in 5.5 hours and 3245 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind.
The speed of the plane in still air is
The speed of the wind is
The most appropriate choice for speed will be given by-
Speed of plane in still air = 610 miles/hour
Speed of wind = 20 miles/hour
What is speed?
Distance travelled by a body in unit time is called speed.
Let the speed of plane in still air be x miles/hour
Speed of wind be y miles/hour
A plane traveled 3465 miles with the wind in 5.5 hours
So,
x + y = [tex]\frac{3465}{5.5}[/tex]
x + y = 630.......(1)
The plane travelled 3245 miles against the wind in the same amount of time
so,
x - y = [tex]\frac{3245}{5.5}[/tex]
x - y = 590.......(2)
Adding (1) and (2),
2x = 1220
x = [tex]\frac{1220}{2}[/tex]
x = 610 miles/hour
Putting the value of x in (1),
610 + y = 630
y = 630 - 610
y = 20 miles/hour
Speed of plane in still air = 610 miles/hour
Speed of wind = 20 miles/hour
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The width of a rectangle is fixed at 5 cm. Determine (in terms of an inequality) those lengths for which the area will be less than 125 cm2.
The lengths of the rectangle for which the area will be less than 125 cm² is 5 < m < 25
In this question, we have been given the width of a rectangle is fixed at 5 cm.
We need to determine (in terms of an inequality) those lengths for which the area will be less than 125 cm²
Let 'm' be the length of the rectangle.
The area of the rectangle is:
A = length × width
The area of the rectangle should be less than 125 cm²
5 × m < 125
Divide both the sides of the inequality by 5
m < 25
This means, the length of rectangle should be less than 25 cm
But length is always greater than the width of the rectangle.
So, we get an inequality 5 < m < 25
Therefore, the lengths of the rectangle for which the area will be less than 125 cm² is 5 < m < 25
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What is the direction and strength of the association between the variables?
How many positive odd integers less than 10,000 can be written using the digits 3, 4, 6, 8, and 0 if repeating the digits are allowed? A.100 B. 125 C. 150
olution:
Recall the Fundamental Counting principle; if there are m ways to make a selection and n ways to make a second selection, then there are m x n number of ways in which two selection can be made.
ut of the provided digits, if the number ends with 3
ase 1: Tnumber of one digit numbers.
ut of the digits provided, only one way to fil;l the box that is with one.
Thus, there is one digit odd integer here.
Case 2: The number of two digits.
Out of the digits provided, only one way to fill the last box is with digit 3, and any one of the 4 digits can filled in it as 0 cannot filled in either of the box.
Thus, number of ways are;
[tex]4\times1=4[/tex]Aase 3: The number of three digit numbers.
ut of the digits provided, only one way to flll the last box is with digit 3, and any one of the 5 digits can be filled in second box, and thus any one of the 4 digits can be filled in first box as 0 cannot be fixed in the box.
Thus, number of ways are;
[tex]4\times5\times1=20[/tex]Lastly;
: The numbver of four digit numbers.
he number of ways are;
[tex]4\times5\times5\times1=100[/tex]Thus, the total number of ways to select are;
[tex]100+20+4+1=125[/tex]INAL ANSWER: 125