Answer:
Step-by-step explanation:
(10 points) Find the height y and length of a side of its base x of a square pyramid with congruent isosceles triangle sides whose volume is cubic meters and whose lateral surface area is as small as possible. (The lateral surface area includes the sides but excludes the base of the pyramid.) Justify that the dimensions you found give minimum lateral surface area.
The minimum lateral surface area of the prism is approximately 1.194 square units.
The given base and height of the prism is y and x respectively.
Hence volume of the prism
V = 1/3 x²y
again 1/3 x²y = 1/6
or, y = 1/2x²
The lateral surface area of the prism is given by :
F = √(4y²+x²)
By the equation 1 we get :
F = x √ (1/x⁴ + x²)
Now we will use differentiation:
[tex]\frac{df}{dx} = \frac{2x^6-1}{x^4(x^2+\frac{1}{x^2} )}[/tex]
Now for the critical points we have to take df/dx = 0
hence solving the equation for x we get :
[tex]x = (\frac{1}{2} )^{\frac{1}{6}}[/tex]
Hence the values of x is [tex](\frac{1}{2} )^{\frac{1}{6}}[/tex] and the value of y will be [tex]\frac{1}{2^\frac{2}{3}}[/tex] units,
And the lateral surface are will be :
F (min ) = √(4y²+x²)
= √ (0.795 + 0.633)
= 1.194 square units
The approximate values of x and y are
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A box contains 2 red marbles and 3 black marbles. Two marbles are drawn in succession without replacement. Find the following: a. Find the probability the second marble is red? b. Find the probability that both marbles are the same color? c. Find the probability that the second marble is black given the first marble is red? d. Find the probability that first marble red given that the second marble is red?
a. The probability that the second marble is red is 2/5, since there are 2 red marbles and a total of 5 marbles.
b. The probability that both marbles are the same color is 4/15, since there are two ways that this could happen (both red or both black) and there are 15 possible outcomes in total.
c. The probability that the second marble is black given the first marble is red is 3/4, because out of the 4 possible outcomes (RR, RB, BR, BB) the only way to get a black marble on the second draw is if it is BR.
d. The probability that the first marble is red given that the second marble is red is 2/3, because out of the 3 possible outcomes (RR, RB, BR) the only way to get a red marble on the first draw is if it is RR or RB.
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4.) BLACK
Calculate the volume
of 500 g of salt
Density of Salt is 2.16
Answer: 2 170 kilograms [kg] of Salt fit into 1 cubic meter. 135.46867 pounds [lbs] of Salt fit into 1 cubic foot. Salt weighs 2.17 gram per cubic centimeter or 2 170 kilogram per cubic meter, i.e. density of salt is equal to 2 170 kg/m³; at 20°C (68°F or 293.15K) at standard atmospheric pressure . In Imperial or US customary measurement system, the density is equal to 135.469 pound per cubic foot [lb/ft³], or 1.254 ounce per cubic inch [oz/inch³] .
Step-by-step explanation:
The length of four rivers in Africa is shown in the table below.
How is the length of the Zambezi river written in scientific notation?
Move the correct answer to each box. Not all answers will be used.
The length of the Zambezi river is 838 × 10⁵ or 83.8 × 10⁶ or 8.38 × 10
What is scientific notation?
Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation.
For example, 750,000,000 can be written in scientific notation as 7.5 ✕ 10⁸.
The length of the Zambezi river 83,800,000 feet.
Rewrite 83,800,000:
83,800,000 = 838 × 100000
83,800,000 = 838 × 10⁵ [Since the number of zeros is 5]
Multiply and divide 10:
83,800,000 = 838 × 10⁵ × (10/10)
83,800,000 = (838/10) × 10⁵ × 10
83,800,000 = 83.8 × 10⁵ × 10
83,800,000 = 83.8 × 10⁶
Multiply and divide 10:
83,800,000 = 83.8 × 10⁶ × (10/10)
83,800,000 = (83.8/10) × 10⁶ × 10
83,800,000 = 8.38 × 10⁷
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Create a table showing all the tasks you and your family do around the house that use water and how often those tasks happen. Leave space for one more column.
Fully simplify.
(3x^2y^2)^3
(3x
2
y
2
)
3
Answer:
[tex]27x^6y^6[/tex]
Step-by-step explanation:
The formatting of the question is a bit confusing, but if the expression is [tex](3x^2y^2)^3[/tex], use the power of a product exponent rule [tex](ab)^m=(a)^m(b)^m[/tex]. So,
[tex](3x^2y^2)^3=(3)^3(x^2)^3(y^2)^3[/tex].
Next, use the power of a power exponent rule [tex](a^m)^n=a^{m*n}[/tex]. So,
[tex](3)^3(x^2)^3(y^2)^3=27(x^{2*3})(y^{2*3})=27x^6y^6[/tex]
AXY is similar to ABC
Which of the following expressions could be used to determine the length of segment AB?
The expression that could be used to determine the length of segment AB in the triangles given is: A. AB = AX * AC/AY.
What are Similar Triangles?When two triangles are stated to be similar to one another, it means both triangles have equal corresponding angles, but their corresponding sides have proportional lengths or have ratios that are equal.
This means similar triangles have the same shape but different sizes, since their corresponding side lengths have proportional length.
Given that triangle AXY is similar to triangle ABC, it means that:
m<A = m<A
m<X = m<B
m<Y = m<C
AX/AB = AY/AC = XY/BC
To find the length of AB, we could use the following expression derived from the ratios stated above:
AX/AB = AY/AC
Cross multiply:
(AB) * (AY) = (AX) * (AC)
Divide both sides by AY
(AB) * (AY) / AY = (AX) * (AC) / AY
AB = AX * AC/AY
The expression to use is: A. AB = AX * AC/AY
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Write the relation as a set of ordered pairs. A relation. An arrow goes from negative 2 to 4, 0 to 0, 2 to 4. a. ordered pairs: {(4, –2), (0, 0), (2, 4)} b. ordered pairs: {(–2, 4), (0, 0), (4, 2)} c. ordered pairs: {(–2, 4), (0, 0), (2, 4)} d. ordered pairs: {(4, –2), (0, 0), (4, 2)} Please select the best answer from the choices provided A B C D Mark this and return
The required relation as a set of ordered pairs is (C) {(–2,4), (0,0), (2,4)}.
What are the Ordered pairs in the set?A set of ordered pairs is any pair of components that appear in a specific sequence and are wrapped in brackets.
If there are two elements, "a" and "b," then the two distinct pairings are "(a, b)" (b, a).
A is referred to as the first element and B is referred to as the second element in an ordered pair (a, b).
A pair of numbers in a particular order is known as an ordered pair.
The ordered pairings (1, 2) and (-4, 12) are two examples.
It matters which of the two numbers comes first: (2, 1) and (1, 2) are not the same thing (2, 1).
So, an arrow in a relationship travels from -2 to 4, 0 to 0, and 2 to 4.
Consequently, by virtue of ordered pairs.
The ordered pairings are obtained:
(-2, 4)
(0, 0)
(2, 4)
Hence, the pairs are (-2, 4), (0, 0), and (-2). (2, 4)
Therefore, the required relation as a set of ordered pairs is (C) {(–2, 4), (0, 0), (2, 4)}.
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Correct question:
Write the relation as a set of ordered pairs.
A relation. An arrow goes from negative 2 to 4, 0 to 0, 2 to 4.
a. ordered pairs: {(4, –2), (0, 0), (2, 4)}
b. ordered pairs: {(–2, 4), (0, 0), (4, 2)}
c. ordered pairs: {(–2, 4), (0, 0), (2, 4)}
d. ordered pairs: {(4, –2), (0, 0), (4, 2)}
Please select the best answer from the choices provided
A
B
C
D
Instructor Celsius looked at her class data from Quiz 3. She recorded the students' amount of study time (in minutes) and quiz score (out of 100) She made scatterplot of her data and saw that it had linear pattern. She computed that r = 0.80.After telling the class about these results one student figures this means that if they study _ very long time they will make very high quiz score: What Is the wrong with this conclusion? The teacher is using the wrong type of plot; thc efore the results are invalid. Since 8 you know the slope will be negative 50 studying long time will give vou a lower score The student is assuming that correlation implics causation and are correct
For the given scatter plot of the data, the wrong with the conclusion was shown by option B. Since r = 0.80 slope will be negative 50 studying long time will give you lower score is incorrect.
As given in the question,
Based on the class data of quiz3,
Teacher made scatterplot to represent the linear relation between amount of study time and quiz score
Pattern form was linear.
Using which correlation coefficient was computed to r = 0.8.
From the data scatterplot as it was linear the more time students study the good will the score.
Therefore, from the information of scatterplot option B. Since r = 0.80 slope will be negative 50 studying long time will give you lower score is incorrect answer.
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Which type of set square has two sides with equal length?
Answer:
Step-by-step explanation:
1. What value of X makes this equation true?
1/2X +7=2X - 5
Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.
The value of x is +0008.00 that make true for the equation (1/2)x + 7 = 2x - 5.
What is solution of a linear equation?
An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.
Given equation is
(1/2)x + 7 = 2x - 5
Subtract (1/2)x from both sides:
(1/2)x + 7- (1/2)x = 2x - 5 - (1/2)x
7 = 2x - (1/2)x - 5
Add the like terms:
7 = 3/2 x - 5
Add 5 on both sides:
7 + 5 = 3/2 x - 5 + 5
12 = 3/2 x
Multiply both sides by 2/3
12 × (2/3) = x
8 = x
x = 8
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over the past 30 years, the sample standard deviations of the rates of return for stock x and stock y were 0.20 and 0.12, respectively. the sample covariance between the returns of x and y is 0.0096. the correlation of the rates of return between x and y is the closest to .
The correlation of the rates of return between x and y is the closest to = 0.4
What is Correlation?Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate). It's a common tool for describing simple relationships without making a statement about cause and effect.
Calculation for the correlation of the returns,
Using this formula,
Covariance of the returns = Correlation coefficient between the returns*Stock returns standard deviation*Mod T Stock returns standard deviation
The sample standard deviations of the rates of return for stock x and stock y were 0.20 and 0.12
The sample covariance between the returns of x and y is 0.0096.
Let plug in the formula
Covariance of the returns = Correlation * (0.20) * (0.12)
0.0096 = Correlation * (0.20) * (0.12)
0.0096 = Correlation * 0.024
0.0096 / 0.024 = Correlation
0.4 = Correlation
Correlation = 0.4
Therefore,
The correlation of the rates of return between x and y is the closest = 0.4
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Given the conditional statement ~p → q, which statement is logically equivalent?
p → ~q
~p → ~q
~q → ~p
~q → p
Answer:
~q → pStep-by-step explanation:
Given the conditional statement ~p → q, the statement logically equivalent is ~q → p.
the temperature of city changed by total of -12 degrees Celsius over 2 weeks period. the temperature changed by the same amount each week. Part A write an expression to show the average change in the temperature of the city each week. Part B simply the expression and explain, using words, what your answer mean
Answer:
The number of degrees Celsius goes down 6 every week. (-6)
Step-by-step explanation:
If the city's temperature changed the same every week, and over the period of 2 weeks it changed -12 degrees Celsius, we need to figure out how much it changed every week (c). We can do this by dividing the number of weeks (w), by the total number of Celsius it changed (t).
The equation will look something like this:
w ÷ t = c
Fitting the numbers into this equation will look something like this:
2 ÷ -12 = -6
Every week, it changed -6 degrees Celsius.
Simplifying the expression, every week it changed -6 degrees Celsius. We know this because the temperature changes the same amount every week. So if the total amount is -12, we have to divide that by 2 to get -6.
write down in trems of n an expression for the nth term in the following sequences 1 8 15 22 29
The expression which represents the nth term of the given sequence, in terms of n as required in the task content is; T (n) = 1 + 7(n - 1).
Which expression represents the nth term of the expression in terms of n?It follows from the task content that the expression which represents the nth term of the given sequence, in terms of variable, n be determined.
According to the task content, the first term, a of the sequence is; 1.
Also, since; 8 - 1 = 15 - 8 = 22 - 15 = 29 - 22 = Common difference, d = 7.
Consequently, the required expression is an arithmetic sequence which can be modelled by;
T (n) = a + d (n - 1)
Since the constant common difference of consecutive terms in the sequence is; 7,
Therefore, the expression for the nth term of the expression is;
nth = 1 + 7(n -1)
On this note, the required expression which represents the nth term of the arithmetic sequence in discuss is; T (n) = 1 + 7 (n -1).
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One number is twelve less than another. If their sum is increased by seven, the result is 83
please help me
Answer:
x=44
y=32
Step-by-step explanation:
Given numbers x and y:
y=x-12
x+y+7=83
x+x-12+7=83
2x=88
x=44
y=32
Need Help with this question.
Answer:
x=5
Step-by-step explanation:
If p and q are parallel, then the two angles in question should be equal to one another.
So,
(3x+15)°=(8x-10)°
(3x+15)°+10°=(8x-10)°+10°
(3x+25)°=(8x)°
(3x+25)°-(3x)°=(8x)°-(3x)°
25°=5x°
5=x
So, the two angles should be (8(5)-10)° and (3(5)+15)°. Both of these expressions equal 30°. This makes sense, as the illustration shows that the two angles are acute.
What are the prime factors that 27 and 36 share?
_______ and _______
Answer:
The prime factors are 3 and 3
what is the width of 1 book, if the bookshelf is 3 feet 9 inches wide?
Answer:
2.5
Step-by-step explanation:
Step-by-step explanation:
Given
Shelf Width = 3ft 9in
Copies = 18
Required
Determine the width of each book
This is calculated by dividing the shelf width by the number of copies.
Width = Shelf Width ÷ Copies
Width = (3 ft 9in) ÷ (18)
[Convert with to inches]
Width = (3 * 12 + 9) ÷ (18)
Width = (36 + 9) ÷ (18)
Width = 45 ÷ 18
Width = 2.5 inches
record the angular velocity w. calculate the total moment of inertia of the cylinder-person system. (hint: treat the person as a single particle.) calculate the total angular momentum of the system.
For recording the angular velocity we will use
angular velocity, ω = dθ /dt
Angular velocity:
Angular velocity is a vector quantity, expressed as the angular velocity or rotational speed of an object and the rate of change of angular displacement that specifies the axis about which the object rotates. The amount of change in a particle's angular displacement over time is called its angular velocity. The trajectory of the angular velocity vector is usually perpendicular to the plane of rotation in the direction given by the right-hand rule.
Total Moment of Inertia:
The total moment of inertia is the sum of the moments of inertia of the mass elements in the body.
Unlike mass, which is a constant for a given body, the moment of inertia depends on the location of the center of rotation. In general, the moment of inertia is calculated by using integral calculus.
Thin cylindrical shell open at both ends, radius r, mass m.
This formula assumes that the thickness of the shell is negligible. This is a special case of a thick-walled cylindrical tube with r1=r2. A point mass m at the end of a rod of length r has the same moment of inertia and the value r is called the radius of gyration.
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1-2t=2(1-t) what is the value of t
Step-by-step explanation:
1 - 2t = 2(1 - t)
1 - 2t = 2 - 2t
there is no value for t.
Find the value of csc for the angle 0 in standard position having 5,-12) on its terminal side
The cosecant of the angle is 0.2
How to determine the cosecant of the angle?From the question, we have the following parameters that can be used in our computation:
(5,-12)
This means that
(x, y) = (5,-12)
The csc(θ) is calculated as
csc(θ) = 1/x
Substitute the known values in the above equation, so, we have the following representation
csc(θ) = 1/5
Evaluate
csc(θ) = 0.2
Hence, the value of csc(θ) is 0.2
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A random sample of 30 male college students was selected, and their heights were
measured. The heights (in inches) are given below
(a) Complete the frequency distribution for the data. Make sure to enter your answers for
the relative frequency as decimals, rounded to the nearest tenth.
Height Frequency Relative Frequency
68
69
70
71
73
1244
70 7368
66 73 70 23 23 64
74
The decimal equivalent of the relative frequency, rounded to the closest tenth, is 1.
How does relative frequency work?The proportion of outcomes when a certain event occurs to all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.
Thirty male college students at random were chosen.
The following table lists their heights in inches. These heights are 12 44 70 73 68 66 73 70 23 23 64 74 and 68 69 70 71 73.
Therefore, the frequency of any height value in the data set is just its count. A value's relative frequency is simply the ratio of its corresponding frequency to the total frequency.
So, the frequency table is
Height(xi) Frequency(fi) Relative frequency
66 3 3/30=0.1
67 3 3/30=0.1
68 4 4/30=0.13
69 3 3/30=0.1
70 2 2/30=0.06
71 4 4/30=0.13
72 2 2/30=0.06
73 6 6/30=0.2
74 3 3/30=0.1
Total 30 1
the frequency distribution for the data is given above.
The relative frequency as decimals, rounded to the nearest tenth is 1
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Suppose that DEF is isosceles with base DE.
Suppose also that mZD=(5x+26)° and mZF = (3x+63)°.
Find the degree measure of each angle in the triangle.
k
D
(5x + 26)
-(3x + 63)°
E
mZD=
mZE=
mZF =
X
O
The degree measure of each angle in the triangle would be
m∠D = 56°
m∠F = 81°
m∠E = 43°
What is an isosceles triangle?
In an isosceles triangle, the two base angles are congruent, or equal in measure.
In addition, the sum of the measures of the angles in any triangle is always 180 degrees. Therefore, we can set up an equation to find the measure of each angle in the triangle:
m∠D + m∠F + m∠E = 180 degrees
Substituting the given values for the measures of angles D and F, we get:
(5x+26) + (3x+63) + m∠E = 180
Combining like terms and solving for m∠E, we find that:
m∠E = 180 - (5x+26) - (3x+63)
= 180 - 8x - 89
= 91 - 8x
Therefore, the measure of angle E is 91 - 8x degrees.
To find the measure of angles D and F, we can substitute this value back into the equation:
m∠D + m∠F + m∠E = 180
(5x+26) + (3x+63) + (91-8x) = 180
Solving for x, we find that x = 6.
m∠D =5(6) + 26 = 30 + 25 = 56°
m∠F = 3(6) + 63 = 18 + 63 = 81°
m∠E = 91 - 8(6) = 91 - 48= 43°
Therefore, the degree measure of each angle in the triangle would be
m∠D = 56°
m∠F = 81°
m∠E = 43°
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The degree measure of each angle in the triangle would be
m∠D = 56°
m∠F = 81°
m∠E = 43°
What is an isosceles triangle?
In an isosceles triangle, the two base angles are congruent, or equal in measure.
In addition, the sum of the measures of the angles in any triangle is always 180 degrees. Therefore, we can set up an equation to find the measure of each angle in the triangle:
m∠D + m∠F + m∠E = 180 degrees
Substituting the given values for the measures of angles D and F, we get:
(5x+26) + (3x+63) + m∠E = 180
Combining like terms and solving for m∠E, we find that:
m∠E = 180 - (5x+26) - (3x+63)
= 180 - 8x - 89
= 91 - 8x
Therefore, the measure of angle E is 91 - 8x degrees.
To find the measure of angles D and F, we can substitute this value back into the equation:
m∠D + m∠F + m∠E = 180
(5x+26) + (3x+63) + (91-8x) = 180
Solving for x, we find that x = 6.
m∠D =5(6) + 26 = 30 + 25 = 56°
m∠F = 3(6) + 63 = 18 + 63 = 81°
m∠E = 91 - 8(6) = 91 - 48= 43°
Therefore, the degree measure of each angle in the triangle would be
m∠D = 56°
m∠F = 81°
m∠E = 43°
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random samples of size 100 are drawn. from the population to generate a sampling distribution of sample means
The mean of the sample means from all feasible samples is less than the population means for random samples of size 100 from a population.
The population propose will match the pattern mean's proposal. The population trendy deviation divided by the rectangle root of the sample length yields the same results as the standard deviation of the distribution of the sample means, also known as the same old mistakes of the proposed (n).
The general sample recommends factors to be included in the pattern mean calculation.
The population suggest is calculated using the sum of all values within the population denoted with the aid of the summation of X divided by the number of values in the population that is denoted with the aid of N. The population suggest is the mean or average of all values within the given population.
Therefore,
The mean of the sample means from all feasible samples is less than the population means for random samples of size 100 from a population.
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Help me please just 5-8
Answer:
listed below
Step-by-step explanation:
5.) x=77 and y=63
6.)y=60 and x= 1230
7.)y=65 and x=92
8.)y=69 and x=175
I company sells concrete in batches of 5 yd.³ the probability distribution of X the number of cubic yard sold in the single order for concrete from this company shown in the table below the expected value of the probability distribution of X is 19.25 and the center deviation is 5.76 there's a fixed cost to deliver the concrete The Profit why in dollars for to particular order can be described by Y equals 70 5X -100 what is the standard deviation of why
432
The standard deviation of Y is 432.
A company sells concrete in batches of 5 yd³.The probability distribution of X, the number of cubic yards sold in a single order for concrete in batches from this company, is shown in the table below.The expected value of the distribution of X is 19.25 and the standard deviation is 5.76.There is a fixed cost to deliver the concrete in batches. The profit Y, in dollars, for a particular order in a company can be described by(Y = 75X - 100)
The formula of the standard deviation is :
SD(Y) = SD(75X - 100)
Substituting the value of SD(X) and SD(100) in the above expression.
SD(Y) = 75SD(X) - SD(100)
SD(Y) = 75 SD(X) - 0
SD(Y) = 75 × 5.76
SD(Y) = 432
Hence, the standard deviation of Y is 432.
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I've gotten stuck on this problem: "Let f(z) be the branch to z13+z14, which is defined on the entire complex plane except on the negative imaginary axis, for which f(1)=0. Find f(-1)."
I started by writing z13+z14 as e13(ln|z|+iθ(z)+i2nπ)+e14(ln|z|+iθ(z)+i2mπ) but when I try to solve f(1)=0 I just get the relationship between n and m, which means I won't get a specific branch. I am also not sure how to use the condition "not defined on the negative imaginary axis"
In order to find the value of f(-1), you can start by finding the value of f(1) and then proceed for the next step.
As you have already noted, writing z13+z14 as e13(ln|z|+iθ(z)+i2nπ)+e14(ln|z|+iθ(z)+i2mπ) will not give you a specific branch. Instead, you can write z13+z14 as follows:
(z-1)(z12+z11+z10+...+1)
Then, you can use the fact that f(1)=0 to solve for the value of z12+z11+z10+...+1. This will give you a specific value for f(1).
To find the value of f(-1), you can use the following relationship:
f(-1) = f(1) * (-1)13 * (-1)14
Substituting the value you found for f(1) and evaluating the expression will give you the value of f(-1).
As for the condition "not defined on the negative imaginary axis", this means that the branch of f(z) is not defined for any complex number with a negative imaginary part. This is because the 13th and 14th roots of a complex number are not unique when the imaginary part is negative, so the function is not defined for these values.
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Help please!!
Diana and Teri have a collection of books.
The number of books in Diana's collection can be represented with x.
Teri has four times as many books as DIana.
The total number of books is 200.
How many books does Diana have?
Answer:
Diana has 40 books in her collection.
Step-by-step explanation:
We can set up the equation 4x + x = 200 to represent the total number of books in the collection, where x is the number of books in Diana's collection and 4x is the number of books in Teri's collection. Solving for x, we get 5x = 200, so x = 40. This means that Diana has 40 books in her collection.
Answer:
Teri has 160 books
Step-by-step explanation:
7. Evaluate the expression below if a = 64,
b = 9, and c = 5
A. 19
B. 19/2
C. 49/4
D.49/2
The given expression can be simplified to get the value as 19. The correct option is (A).
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The given expression is as below,
[tex](12b - 2^{c}) /\sqrt[3]{a}[/tex]
Substitute a = 64, b = 9 and c = 5 to obtain the value as below,
⇒ (12 × 9 - 2⁵)/∛64
⇒ (108 - 32)/4
⇒ 76/4
⇒ 19
Hence, the value of the given expression is obtained as 19.
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The image of the complete problem is attached here.
