750$ in 4 days unit rate
Evaluate (2 minus 5 i) (p + q) (i) when p = 2 and q = 5 i.
29 i
29 i minus 20
Negative 21 i
29
The value of the expression is 29
How to evaluate the expression?The expression is given as
(2 - 5i)(p + q)
Where
p = 2
q = 5i
Substitute these values in (2 - 5i)(p + q)
So, we have
(2 - 5i)(p + q) = (2 - 5i)(2 + 5i)
Apply the difference of two squares
(2 - 5i)(p + q) = 4 - (-25)
Evaluate the difference
(2 - 5i)(p + q) = 29
Hence, the value of the expression is 29
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Could you please help me answer this step-by-step?
answer:
the solution is
A mountain biking park has 48 trails, 37.5% of which are beginner trails.
The rest are divided evenly between intermediate and expert trails.
How many expert trails are in the park?
The number of expert trails in the park is 15.
How many expert trails are in the park?Percentage can be described as the fraction of an amount expressed as a number out of hundred. The sign :used to represent percentages is %.
The first step is to determine the total number of intermediate and expert trails
Intermediate and expert trails = (1 - percentage of beginner trails) x total number of trails
(1 - 0.375) x 48
0.625 x 48= 30
The second step is to divide the total number of intermediate and expert trails by 2 since they are an equal number.
30 / 2 = 15
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find the volume of the cylinder with 2 meters squared and height 10 meters
Simplify: (39x^5z^4)^0 • 18x^2y
The simplification of (39x⁵z⁴)⁰ • 18x²y is 18x²y.
What is Simplification?Making anything simpler is known as simplification. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler.
To simplify an equation:
By eliminating all common components from the numerator and the denominator and putting the fraction in its simplest/lowest form, we can simplify fractions. Mathematical expressions can be made simpler by grouping and combining related terms.Rewrite the given equation using the commutative property of multiplication.
18(39x⁵z⁴)⁰x²y
Use the power rule (xy)ⁿ=xⁿyⁿ for distributing the exponent.
18(39⁰(x⁵)⁰(z⁴)⁰)x²y
Anything raised to 0 is 1.
18(1(x⁵)⁰(z⁴)⁰x²y
Multiply (x⁵)⁰(x⁵)⁰ by 11.
18((x⁵)⁰(z⁴)⁰)x²y
Multiply the exponents in (x⁵)⁰.
18(x⁰(z⁴)⁰)x²y
Multiply x⁰ by x² by adding the exponents.
18(x²(z⁴)⁰)y
Simplify 18(x²(z⁴)⁰)y
18x²y
Therefore, simplification of given equation is 18x²y.
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Solve the compound inequality and give your answer in interval notation.
7x - 3 < - 52 OR-5x - 2 < 28
Hence , on solving 7x - 3 < - 52 the value of x lies in interval (-∞ , 7) and on solving -5x - 2 < 28 the value of x lies in interval (-6 , ∞) .
Intervals are written with rectangular brackets or parentheses, and 2 numbers delimited with a comma. The 2 numbers are referred to as the endpoints of the interval. The amount on the left denotes the smallest amount part or boundary.We have given two inequalities 7x - 3 < - 52 and -5x - 2 < 28
On solving 7x - 3 < - 52 , we get
7x < 3 - 52
7x < 49
x < 7
Therefore, x could be any number less than 7.
In interval notation , it is given by (-∞ , 7) .
On solving -5x - 2 < 28 , we get
-5x < 2 + 28
-5x < 30
-x < 6
Multiplying by negative sign , inequality changes
x > -6
Therefore, x could be any greater than -6.
In interval notation , it is given by (-6 , ∞) .
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Find the average rate of change on the interval [-3,3] for the given function
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
so let's use those two points off the curve in order to get it, check the picture below.
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-3)}}} \implies \cfrac{1}{3 +3}\implies {\LARGE \begin{array}{llll} \cfrac{1}{6} \end{array}}[/tex]
Proxima Centauri, the star nearest to our solar system, is 4.3 light-years away. Use the information below to express this distance in miles.
(a) A light-year, the distance that light travels in one year, is about 5,900,000,000,000 mi.
(b) The diameter of an electron is about 0.0000000000004 cm.
(c) A drop of water contains more than 33 billion billion molecules.
The distance of Proxima Centauri, which is 4.3 light years away can also be expressed in miles is equivalent to 253.7 x 10¹¹ miles from solar system.
What is Star?A star is an astronomical object comprising a luminous spheroid of plasma held together by its gravity. The nearest star to Earth is the Sun
Given that a star named Proxima Centauri is 4.3 light-years away. Therefore, we can write that -
Distance [D] = 4.3 light years
The Proxima Centauri is 4.3 light - years away. As given in the question that light-year is the distance that light travels in one year and 1 light year is equal to 5,900,000,000,000 miles. Therefore in 4.3 light years, there will be -
D [miles] = 4.3 x 59x 100,000,000,000 = 253.7 x 10¹¹ miles
Therefore, the Proxima Centauri is 253.7 x 10¹¹ miles away.
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i need an explanation how to solve it
f(1) = -2
Step-by-step explanation:The relationship between x and y-values can be represented through a function.
Function Notation
Function notation is one way to write out an equation. In this notation, f(x) represents the y-value at a specified x-value. Thus, f(1) equals the y-value when x is 1. Many times f(x) will be replaced with variable y. So, another way to write the function above is y = -x - 1.
Solving For f(1)
To find f(1), plug 1 into the equation for x.
f(1) = -1 - 1Now, you can easily solve the equation.
f(1) = -2How many hours are in a week
Answer: 168
Step-by-step explanation:
f(x-2)=4x^2+5x-9.
Please explain thoroughly with work. Thank you!
Answer:
Hello,
If you want f(x) read this.
Step-by-step explanation:
I am going to use Horner's method.
[tex]\begin {array}{c|c|c|c}&x^2&x&1\\---&--&--&--\\&4&5&-9\\x=2&&8&26\\---&--&--&--\\&4&13&\boxed{17}\\x=2&&8&42\\---&--&--&--\\&4&\boxed{21}&59\\x=2&&8\\---&--&--&--\\&\boxed{4}&29\\\end {array}\\\\\\F(x-2)=4(x-2)^2+21(x-2)+17\\\\So\ \boxed{F(x)=4x^2+21x+17}\\\\Proof:\\\\F(x-2)=4(x-2)^2+21(x-2)+17\\\\\\=4x^2-16x+16+21x-42+17\\\\=4x^2+5x-9\\[/tex]
I hope this is what you want.
The demand for water use in Phoenix in 2003 hit a high of about 442 million gallons per day on June 27. Water use in the summer is normally distributed with a mean of 310 million gallons per day and a standard deviation of 45 million gallons per day. City reservoirs have a combined storage capacity of nearly 350 million gallons.
(a) What is the probability that a day requires more water than is stored in city reservoirs?
(b) What reservoir capacity is needed so that the probability that it is exceeded is 1%?
(c) What amount of water use is exceeded with 95% probability?
Using the normal distribution, it is found that:
a) There is a 0.1867 = 18.67% probability that a day requires more water than is stored in city reservoirs.
b) A capacity of 415 million gallons is needed.
c) An amount of 236 million gallons of water use is exceeded with 95% probability.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 310, \sigma = 45[/tex]
For item a, the probability is one subtracted by the p-value of Z when X = 350, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (350 - 310)/45
Z = 0.89
Z = 0.89 has a p-value of 0.8133.
1 - 0.8133 = 0.1867.
There is a 0.1867 = 18.67% probability that a day requires more water than is stored in city reservoirs.
For item b, the capacity should be the 99th percentile, which is X when Z = 2.327, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
2.327 = (X - 310)/45
X - 310 = 45 x 2.327
X = 415. (rounded)
A capacity of 415 million gallons is needed.
For item c, the amount of water use is the 5th percentile, which is X when Z = -1.645, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
-1.645 = (X - 310)/45
X - 310 = -1.645 x 45
X = 236.
An amount of 236 million gallons of water use is exceeded with 95% probability.
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the distribution of lengths of rainbow trout from a certain river are normally distributed with a standard deviation of 2.4 inches. it 15% of the rainbow trout are longer than 15 inches, which of the following is closest to the mean of the distribution?
Based on the calculations, the value which closest to the mean of the distribution is equal to: B. 18 inches.
What is a z-value?A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.
In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:
Z = (x - μ)/δ
Where:
x represents the sample mean or observed data.μ represents the mean.δ represents the standard deviation.If 15 percent of the rainbow trout are longer than 15 inches, then we have:
P(x > 15) = 0.15
From the z-table, the z-value which corresponds to a mean of 0.15 is given by:
z-value = -1.036
Substituting the given parameters into the formula, we have;
Z = (x - μ)/δ
-1.036 = (15 - μ)/2.4
-1.036 × 2.4 = 15 - μ
-2.4864 = 15 - μ
μ = 15 + 2.4864
Mean, μ = 17.4864
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Complete Question:
The distribution of lengths of rainbow trout from a certain river are normally distributed with a standard deviation of 2.4 inches. it 15% of the rainbow trout are longer than 15 inches, which of the following is closest to the mean of the distribution?
A. 26 inches
B. 18 inches
C. 30 inches
D. 33 inches
E. 34 inches
Find x. Sum of angle measures: 360
Answer:
126
Step-by-step explanation:
→ Find the sum of the angle
x + x - 35 + x - 46 + 0.5x = 3.5x - 81
→ Equate to 360
3.5x - 81 = 360
→ Add 81 to both sides
3.5x = 441
→ Divide both sides by 3.5
x = 126
What would happen if you divide by 2/5 instead of 4/5
Answer:
2/5= 0.4 and 4/5= 0.8
Step-by-step explanation:
log(x(x^2 + 3)^−1/2)
= [tex]logx-{\frac{1}{2} log(x^2 + 3 )[/tex]
Step-by-step explanation:
Given that
The logarithmic equation[tex]log(x.(x^2 + 3 )^{\frac{-1}{2} })[/tex]
To find
The solution of this given logarithmic equationSo, according to the question
we have,
The logarithmic equation[tex]log(x.(x^2 + 3 )^{\frac{-1}{2} })[/tex]
We know that,
∵ log(m.n) = logm + logn
Now using this property to solve that logarithmic equation
= [tex]log(x.(x^2 + 3 )^{\frac{-1}{2} })[/tex]
= [tex]logx+log(x^2 + 3 )^{\frac{-1}{2} }[/tex]
We know that,
∵ log(mⁿ) = nlogm
Now using this property to solve that logarithmic equation
= [tex]logx+log(x^2 + 3 )^{\frac{-1}{2} }[/tex]
= [tex]logx+({\frac{-1}{2} )log(x^2 + 3 )[/tex]
= [tex]logx-{\frac{1}{2} log(x^2 + 3 )[/tex]
This is the the solution of given logarithmic equation.
Logarithmic equation.
The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number. The logarithm, in its most basic form, counts the number of times the same factor appears when multiplied repeatedly; for instance, since 1000 = 10 x 10 x 10 = 103, its "logarithm base 10" is 3, or log10 (1000) = 3. When there is no possibility of confusion or when the base is irrelevant, as in big O notation, the logarithm of x to base a is written as logₐ (x), logₐ x, or even without the explicit base, log x.Answer:
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If 8/9 is multiplied by 3/7, will the product be greater than either of the 2 factors?
Answer:
No, it is less than both of the fractions.
Step-by-step explanation:
Multiply the two fractions
[tex]\frac{8}{9}[/tex] x [tex]\frac{3}{7}[/tex] = 0.380952381
Figure out the value of the two fractions
[tex]\frac{8}{9}[/tex] = 0.8888888889
[tex]\frac{3}{7}[/tex] = 0.4285714286
Reduce/Simplify:
0.380952381 = 0.38
0.8888888889 = 0.89
0.4285714286 = 0.43
h(y) = -3y³ - 6y + 9
a. h(4)
b. h(-2y)
c. h(5b + 3)
Answer:
a. h(4) = -207
b. h(-2y) = 24y³ +12y +9
c. h(5b+3) = -375b³ -675b² -435b -90
Step-by-step explanation:
You want the simplified form of h(y) = -3y³ -6y +9 for using 3 different values of y.
The expression is evaluated by putting the argument where y is, then simplifying the resulting expression.
a. h(4)[tex]h(4)=-3(4)^3 -6(4) +9 = -3(64) -24 +9\\\\\boxed{h(4) = -207}[/tex]
b. h(-2y)[tex]h(-2y)=-3(-2y)^3-6(-2y)+9=-3(-8y^3+12y+9\\\\\boxed{h(-2y)=24y^3+12y+9}[/tex]
c. h(5b+3)[tex]h(5b+3)=-3(5b+3)^3-6(5b+3)+9=-3(125b^3+225b^2+135b +27) -30b-18+9\\\\\boxed{h(5b+3)=-375b^3-675b^2-435b-90}[/tex]
__
Additional comment
It can be useful to remember that ...
(a +b)³ = a³ +3a²b +3ab² +b³
NEED HELP ASAP WILL GIVE BRAINLIST!
Question 2
? Question
Match the real-world descriptions with the features they represent within the context of Melissa's garden.
Not all tiles will be used.
Tiles
length of the tomato patch when
the area of the bell pepper patch
Is 0
area of the bell pepper patch when
the length of the tomato patch is 0
all possible areas of the tomato
patch
area of the tomato patch when the
length of the bell pepper patch is 0
all possible areas of the bell pepper
patch
all possible lengths of the tomato
patch
y intercept - area of the bell pepper patch when the length of the tomato patch is 0. because y intercept when the value of x is 0.
Range - all possible areas of the tomato patch. because range is the value of all possible outcomes based on the set of input.
x intercept - area of the tomato patch when the length of the bell pepper patch is 0. because x intercept when the value of y is 0.
we plot as
y = area of bell pepper.
x = area of tomato patch.
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Can someone please help me I’m doing ratios and proportions and I need it by 8 o’clock
Answer:
5 tomato and 14 pineapples
Select the best answer for the
7. What is the value of x in the diagram?
E
OA. 42°
OB. 64°
OC. 10°
OD. 20°
329 C
Answer:
10 degree will be the answer.. buddy..
Devon wants to write
an equation for a line that passes
through 2 of the data points he has collected. The points
are (8, 5) and (-12, -9). He writes the
equation
7x 10y = 3. Is this a good model? Explain your
reasoning.
Answer: The equation given is not in slope-intercept form, which is y=mx+b. The equation for the line which passes through the given points is y = 7/10x - 3/5.
Please answer and help thank you
Answer:
25
62.5
1.25
hope this helps
Answer:
Step-by-step explanation:
$12.50=10b
so 20$=(20)10/12.5=16
50$=(50)10/12.5=40
1$=(1)10/12.5=0.8
Which expression is equivalent to the quantity nine raised to the negative second power times three raised to the fifth power end quantity all raised to the negative second power?
A:negative three raised to the third power divided by nine raised to the fourth power
B:three raised to the third power divided by nine raised to the fourth power.
C:negative nine raised to the fourth power divided by three raised to the tenth power
D:nine raised to the fourth power divided by three raised to the tenth power
The simplification of the given indices is; D: nine raised to the fourth power divided by three raised to the tenth power
How to use the Law of Indices?We want to find the expression that is equivalent to the quantity nine raised to the negative second power times three raised to the fifth power end quantity all raised to the negative second power. This is written as;
(9⁻² * 3⁵)⁻²
According to laws of indices, we know that;
(a²)³ = a²*³ = a⁶
Thus;
(9⁻² * 3⁵)⁻² = (9⁻²)⁻² * (3⁵)⁻²
⇒ 9⁴ * 1/3¹⁰
⇒ 9⁴/3¹⁰
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The gravitational force (F ) felt by an object (m1) due to another object (m2) at a distance d is given by F = G m1m2/r2.
what is the value of r?
Based on the equation for gravitational force, the value of radius (r) is equal to r = √(GM₁M₂/F).
What is a gravitational force?A gravitational force can be defined as a universal force of attraction which acts between two (2) physical objects, especially by pulling them together.
How to calculate the gravitational force?Mathematically, the gravitational force between two (2) planetary objects is given by this formula:
F = GM₁M₂/r²
Where:
r represents the radius or mean distance.G represents the gravitational constant.M represents the mass.F represents the gravitational force.Making r the subject of formula, we have:
Fr² = GM₁M₂
Divide both sides by F, we have:
r² = GM₁M₂/F
Taking the square root of both sides, we have:
r = √(GM₁M₂/F)
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Given the following sets, find the set A' n (BUC')
U=(1, 2, 3,…,9}
A = {1, 5, 6, 7)
B={1, 2, 7)
C=(2, 3, 4, 6, 7}
From the given sets we get A’∩ (B∪C’) = {2,8,9}.
Given the universal set U= {1,2,3,4,5,6,7,8,9}
A = {1,5,6,7}
B = {1,2,7}
C= {2,3,4,6,7}
A’ (A not) means to remove all the elements of set A from the universal set U
A∪B (union of A and B) means to write all the elements of both the sets but to not repeat the single element
A∩B (intersection of A and B) means to write only the common elements of both the sets
A’ = {2,3,4,8,9}
C’ = {1,5,8,9}
First we need to find out B∪C’ which means the union of B and C’
B∪C’ = {1,2,5,7,8,9}
Now we need to find A’ (B∪C’) = {2,8,9}
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Please help me, I need it right now
You put $205 into an investment at 7% compounded annually for eight years. What will the balance be at the end of eight years?
Answer:
If there is no additional contribution during these 8 years your balance will be $352.23
Step-by-step explanation:
