The probability of selecting a number from the interval [10,23] is 3/32256 × (23^2 - 10^2) = 0.7122. Probability of selecting number [10,23] is 0.7122, integrating density function.
The probability of selecting a number from the interval [8,32] is given by the density function f(x)= 3/32256⋅x^2, where 8 ≤ x ≤ 32. We can calculate the probability of the event E=[10,23] by integrating the density function over the interval, i.e. P(E)=∫1023f(x)dx. This can be simplified to P(E)=3/32256 × (23^2 - 10^2), which equals 0.7122. Therefore, the probability of selecting a number from the interval [10,23] is 0.7122. To calculate this, we first determined the probability density function f(x) by noting that the probability of selecting a number between 8 and 32 is 1. We then divided this probability by the size of the interval, giving us the probability density f(x)= 3/32256⋅x^2. This was used to calculate the probability of the event E=[10,23] by integrating the density function over the interval. The integral was simplified to P(E)=3/32256 × (23^2 - 10^2), which equals 0.7122. This is the probability of selecting a number from the interval [10,23].
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a heavy rope, 30 ft long, weighs 0.8 lb/ft and hangs over the edge of a building 100 ft high. how much work w is done in pulling the rope to the top of the building? (a) how much work w is done in pulling the rope to the top of the building? show how to approximate the required work by a riemann sum, then express the work as an integral and evaluate it. (b) a heavy rope, 30 ft long, weighs 0.8 lb/ft and hangs over the edge of a building 100 ft high. how much work w is done in pulling half the rope to the top of the building?
(a) The work done in pulling the rope to the top of the building is approximately 4800 ft-lb.
(b) The work done in pulling half the rope to the top of the building is approximately 2400 ft-lb.
The work done in pulling the rope to the top of the building can be calculated using a Riemann sum:
W = Σ (0.8 lb/ft) x (g) x (Δx)Where Δx is a small change in the length of the rope, g is the acceleration due to gravity (32 [tex]ft/s^2[/tex]), and the sum is taken over the entire length of the rope (from 0 to 100 ft).
Expressing the work as an integral, we have:
W=∫ [tex]0^{100} (0.8 lb/ft) x (g) x (x) dx[/tex]
Evaluating this integral gives us the work done in pulling the rope to the top of the building:
[tex]W = (0.8 lb/ft) x (g) x (x^2/2)[/tex] evaluated from x=0 to x=100
W = 4800 ft-lb
(b)To find the work done in pulling half the rope to the top of the building, we simply evaluate the integral from x=0 to x=50 (the length of half the rope).
W = [tex](0.8 lb/ft) x (g) x (x^2/2)[/tex] evaluated from x=0 to x=50
W = 2400 ft-lb.
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what are the next three terms of the arithmetic sequence the first term is 3 common difference is 11
Answer:
second term=14
third=25
fourth=36
Step-by-step explanation:
n= the first term in the sequence+(n-1) times the common difference between terms
here n=3, because you asking for third term, so is 25
second term=14
third=25
fourth=36
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At the baseball game, nachos are $6.00 and hotdogs are $3.00. A group of 8 friends orders one item each and pays a total of $36.00.
Write an equation for the total amount of money spent. Let nachos be denoted by x and hotdogs by y.
Write an equation for the total number of items purchased. Let nachos be denoted by x and hotdogs by y.
Rewrite the equation for the total amount of money spent in slope-intercept form.
Rewrite the equation for the total number of items purchased in slope-intercept form.
Find the total of hotdogs and nachos sold
1. The equation for the total amount of money spent is: 6x + 3y = 36.
2. The equation for the total number of items purchased is: x + y = 8.
3. The slope-intercept equation is: y = -2x + 12
4. The equation is y = -x + 8
5. Total number is 8.
How to Write an Equation?The slope-intercept equation is expressed as y = mx + b.
1. The total amount of money spent can be represented by the equation: 6x + 3y = 36, where x represents the number of nachos and y represents the number of hotdogs.
2. The total number of items purchased can be represented by the equation: x + y = 8, where x represents the number of nachos and y represents the number of hotdogs.
3. To write the equation for the total amount of money spent in slope-intercept form, we need to solve for y:
6x + 3y = 36
3y = -6x + 36
y = -2x + 12
4. To write the equation for the total number of items purchased in slope-intercept form, we need to solve for y:
x + y = 8
y = -x + 8
5. The total number of hotdogs and nachos sold is 8, which is the sum of x and y.
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2. The Math Club is selling t-shirts as a fund-raiser. The function rule C = 9n +45 represents
their cost, with Crepresenting the total cost of the order, and n representing the
number of shirts. What could the numbers in the function represent? Select all that
apply.
C= the total cost
9= the cost of each shirt
45= could be some other variable (donation, how much they have so far, etc.)
Which expression is equivalent to 3x² - 10x - 8?
O
(3x-2)(x-4)
(3x - 4)(x + 2)
(x - 4)(3x + 2)
(3x-4)(x-2)
(x - 4)(3x + 2) is an expression that is equivalent to 3x² - 10x - 8.
What do you mean by quadratic equation?A quadratic equation is one in which the variable is squared in just one term and not in any other term where the variable is raised to a power greater than 2.
Lets take the quadratic equation: 3x² - 10x - 8
First we will multiply 3[tex]x^{2}[/tex] and -8, therefore we will get -24[tex]x^{2}[/tex].
Then we will break -10 x in a way that its terms give a product of -24[tex]x^{2}[/tex] when multiplied, i.e., -10x = 12x - 2x
Thus, 3x² - 10x - 8 = 3x² + 12x - 2x - 8
= 3x(x + 4) -2(x + 4)
= (3x - 2)(x + 4)
Hence, (3x - 2)(x + 4) is the correct answer.
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in a poker game with a standard 52 card deck, what is the probability of drawing a five-card hand without any queens?
Out of 52 cards, there is only one Queen of Hearts. Hence, then, the probability = 47/52
5 cards can be chosen from a deck of 52 cards in ⁵²C₅
In order to avoid choosing a queen of hearts, we must choose 5 cards. There is only one queen of hearts in a deck of 52 cards. There are still 51 cards left, and 5 of them can be chosen in ⁵²C₅.
Therefore, the likelihood that a five-card poker hand does not include the queen of hearts is equal to ⁵¹C₅/⁵²C₅
47/52
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The full question
What is the probability that a five-card poker hand does not contain the queen of hearts?
Three requirements for a lifeguard training course are shown in the sign below.
Swim a least 300 feet.
Tread water for at least 5 minutes.
And swim 30 feet or more under water while holding breathe.
Write three inequalities that represent the requirements shown
on the sign?
Alonzo can swim 250 feet, tread water for 6 minutes, and swim
35 feet underwater while holding his breath. Does he satisfy the
requirements of the course?
On solving the provided question, we can say that the inequality equation is swim ≥ 100 yards, tread ≥ 5 min and under ≥ 10 yards
What is inequality?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
the inequality equation is
swim ≥ 100 yards
tread ≥ 5 min
under ≥ 10 yards
swim is not satisfied because lifeguard only swam 250 ft. (83 1/3 yards)
under not satisfied because less than 10 yards.
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in a survey one fourth young girl like sour taste only and one third like chilly taste. if 50 of them do not like both the taste, find the total number of young girl
There are 120 young girls in the survey.
What is the Principle of Inclusion-Exclusion?
The Principle of Inclusion-Exclusion is a combinatorial principle used to find the number of elements in the union of two or more finite sets. It states that the total number of elements in the union of two sets is equal to the sum of the number of elements in each set minus the number of elements in their intersection.
To find the total number of young girls, we can use the Principle of Inclusion-Exclusion. This principle states that if A and B are two events, then the number of elements in the union of A and B is equal to the sum of the number of elements in A and B, minus the number of elements in their intersection.
In this problem, let's call the number of young girls who like sour taste only "A", the number of young girls who like chilly taste only "B", and the number of young girls who like both tastes "C". Then, the total number of young girls is equal to the number of girls in A, plus the number of girls in B, minus the number of girls in C.
Since one fourth of the girls like sour taste only, the number of girls in A is 1/4 of the total number of girls. Similarly, since one third of the girls like chilly taste only, the number of girls in B is 1/3 of the total number of girls. And since 50 of the girls do not like both tastes, the number of girls in C is 50.
So, the total number of young girls is equal to (1/4) * total + (1/3) * total - 50. We can solve for the total by rearranging the equation and using the given information:
total = (50 + (1/4) * total + (1/3) * total) / (1 - (1/4) - (1/3))
total = (50 + 3/12 * total) / (5/12)
total = (50 * 12/5) / (7/5)
total = 120
Therefore, there are 120 young girls in the survey.
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What mistake did Dennis make?
The mistake which Dennis made include the following: B. he didn't exclude x = 3, which makes the denominator in the original expression equal to zero.
What is a rational expression?In Mathematics, a rational expression simply refers to a type of expression which is expressed as a fraction. This ultimately implies that, a rational expression is composed of two (2) main parts and these include the following:
NumeratorDenominatorGenerally speaking, the excluded values of any rational expression simply refers to the values for which the expression is undefined, which is typically obtained when the denominator is equal to zero (0).
Rational expression = (x² - 6x + 0)/(x² + x - 12)
When x = 3, we have the following expression:
Rational expression = (x² - 6x + 0)/(3² + 3 - 12)
Rational expression = (x² - 6x + 0)/(9 + 3 - 12)
Rational expression = (x² - 6x + 0)/0
Rational expression = undefined.
Therefore, excluded values are x ≠ 3 and 4.
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In the figure below, mLABD=63°, and m/1 is 17° more than m2. Find m2.
L
B
D
m22=0.
X
The measure of angle 2 is 23 degrees.
What is an angle?An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. It is not necessary for the angle to be in Euclidean space if it lies in the plane. Angles are referred to as dihedral angles if they are created by the intersection of two planes in a space other than Euclidean.
Let the measure of angle 2 be x.
Then the measure of angle 1 = x + 17
The measure of angle ABD = 63.
From the figure we can observe that:
ABD = angle 1 + angle 2
Substitute the values:
63 = x + 17 + x
63 - 17 = 2x
46 = 2x
x = 23
Hence, the measure of angle 2 is 23 degrees.
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Which of the following sentences is written the passive voice?
1. Charlie ran down the street
2. The delicious bread is baked by Mr. Jilin
3. The plane will fly at five o clock
4. Kristin played with her dolls
The sentence written in the passive voice is - The delicious bread is baked by Mr. Jilin
Which of the following sentences is written the passive voice?This sentence is written in the passive voice because it follows the passive voice structure of: Object + Past Participle Verb (baked) + by Agent (Mr. Jilin).
In the passive voice, the object of the sentence (delicious bread) is the focus of the sentence, rather than the agent (Mr. Jilin).
Passive voice is a grammatical construction in which the subject of a sentence is not the one performing the action.
Instead, the action is done to the subject. For example, instead of saying "I ate the apple," one might say "The apple was eaten by me."
In passive voice, the subject of the sentence is often omitted and the verb is usually conjugated with a form of "to be" and the past participle of the verb.
This grammatical construction is used to emphasize the object of the action, rather than the subject, and can also be used when the subject is unknown or unimportant.
Passive voice can also be used in scientific and technical writing to create sentences that are clear and concise.
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what is the number of ways to order the 26 letters of the alphabet so that no two of the vowels a, e, i, o, and u occur consecutively?
There probability are 17,576,000 different ways to arrange the 26 letters of the alphabet so that the vowels a, e, I o, and u never appear back-to-back.
There are 21 consonants and 5 vowels (a,e,i,o,u) (all other letters).
The vowels can be arranged in 5! = 120 different ways.
The consonants can be arranged in 21! = 5,109,400,800 different ways.
The product of the two integers is 17,576,000, which is the total number of possible arrangements for all letters.
26 letters make up the alphabet, and 5 of them are vowels (a,e,i,o,u). We must determine how many ways there are to organize the vowels and consonants before we can determine how many ways there are to arrange the letters so that no two vowels appear consecutively.
There are 5! = 120 different ways to order the vowels. This is due to the fact that there are 5 vowels that must be grouped in various ways. Since there are 21 consonants that can be arranged, there are 21! = 5,109,400,800 different combinations that can be made. The product of the two integers is 17,576,000, which is the total number of possible arrangements for all letters.
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If we wish to accumulate $3,641 after 6 years at a 5% interest rate, how much must be set aside at the end of each of the 6 periods?
If we wish to accumulate $3,641 after 6 years at a 5% interest rate, then $2,717.16 must be set aside at the end of each of the 6 periods
The Amount = $3,641
Time = 6 years
Interest Rate = 5% = 0.05
Compounded at the end of each of the 6 periods.
So n = 6 × 6 = 36
Periodic interest rate;
i = r/m
i = 0.05/6
i = 0.00833
Compound Formula
A = P(1 + i)^n
3,641 = P(1 + 0.00833)^36
3,641 = P(1.00833)^36
3,641 = 1.35P
Divide by 1.35 on both side, we get
P = $2,717.16
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URGENT URGE T
Which of the following is the graph of 2x + y ≥ 4?
The graph of the inequality, 2x + y ≥ 4, is: option 1.
How to Find the Graph of Inequality?Given the inequality, 2x + y ≥ 4, rewrite in slope-intercept form:
2x + y ≥ 4
y ≥ -2x + 4
Thus, this means that the slope of the graph will be a declining slope of -2, and it will intercept the y-axis at 4.
Also, since the inequality sign is ≥, the shaded region will be above a solid line.
Option 1 has a slope of -2 and is also a solid line having the shaded part above it.
Therefore, the correct graph is option 1.
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According to the nutrition facts for these potato chips, a serving has 170
mg of sodium, or 7% of the daily recommended value for an average adult.
Based on this information, how many milligrams of sodium should an
average adult consume in a day?
O2428.57 or about 2400 mg
2 1500 mg
amin B6 10%
247.2 or about 300 mg
Answer:
2428.57mg
Step-by-step explanation:
170 mg of sodium =7%
170/7% = 2428.57mg
<
Find the surface area of the cube shown below.
units2
NIT
Check the picture below.
so we really have 6 faces, each one with an area of 2½ x 2½
[tex]\stackrel{mixed}{2\frac{1}{2}}\implies \cfrac{2\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{5}{2}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the 6 faces }}{6\left( \cfrac{5}{2}\cdot \cfrac{5}{2} \right)}\implies 6\cdot \cfrac{25}{4}\implies \cfrac{75}{2}\implies 37\frac{1}{2}[/tex]
Select from the drop-down menus to correctly complete each statement.
−25 is 25 units to the
Choose...
of zero on a number line. The opposite of −25 is 25 units to the
Choose...
of zero on a number line.
On a number line, -25 is 25 units to the left of zero, while the opposite of 25 is 25 units to the right of zero.
What is Number Line?In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.
On both sides, the magnitude of the numbers will increase from 0 to 1.
So, based on the graph in the attached, 25 is 25 units to the left of zero on a number line.
On a number line, the opposite of 25 is 25 units to the right of zero.
Here, the opposite of -25 refers to +25, which will be 25 units to the right of zero on a number line.
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8x - 2y = 16
- 4x + y = 8
Answer: i think its B the slope is 8 and the y-intercept is -3/2 the candle starts at a height of 3/2 of an inch and decreases 8 inches every hour
i said i think so srry if you get it wrong :)
Step-by-step explanation:
Write a number entence uing multiplication to how what fraction repreented on the number line i equivelent to 3/4
After multiplying by 2 in the numerator and denominator both, we can write 3/4 in an equivalent fraction as 6/8.
The equivalent form is the process in which we write the same expression in simple numbers or modified form.
To find the equivalent fraction, divide or multiply by the same number to both the denominator and numerator that is equal to one
For example, Equivalent to 1/2 is 1/2 × 2/2 = 2/4
The fraction number, 3/4
Now, further multiplying and dividing number 2 in the given fraction number 3/4
⇒ 2 × 3/2 × 4
⇒ 6/8
Hence, the equivalent form is 6/8.
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HELP⁉️
What is the least integer value in the solution set to 7(3x-1)<4x
Answer:
x = 3
Step-by-step explanation:
x = -1
7(3^(‐1 - 1)) <= 4^-1
7(3^-2) <= 1/4
7/9 <= 1/4
no, wrong.
x = 2
7(3^(2 ‐ 1)) <= 4²
7(3¹) <= 16
21 <= 16
no, wrong.
x = 3
7(3^(3 - 1)) <= 4³
7(3²) <= 64
7×9 <= 64
63 <= 64 correct
so, 3 is the correct answer.
Linear Equation
X
Linear Inequality
What's the same with the two functions?
What's different with the two functions?
Q
S
Submitt
Answer:
Step-by-step explanation:
the this it the r po ggr
. the second hand on a clock is 5 inches long. how far (to the nearest tenth of an inch) does the tip move in 10 seconds?
The tip of the second hand of the clock moves a distance as far as 5.2 inches in 10 seconds.
The distance traveled by the tip of the second hand on a clock can be calculated by using the formula for circumference of a circle, which is:
C = 2πr
where C is the circumference, π is approximately equal to 3.14159, and r is the radius.
If the length of the second hand is 5 inches, then the radius of the circle is 5 inches.
Therefore, the circumference of the circle traced by the tip of the second hand is C = 2πr = 2π(5 inches) = 10π = 31.4159
If we assume that the second hand moves at a constant speed, then the distance traveled by the tip in 10 seconds is equal to the circumference of the circle multiplied by the fraction of the circumference covered in 10 seconds.
Since the second hand completes one full revolution in 60 seconds, then in 10 seconds it covers 1/6 of the circumference. Therefore, the distance traveled by the tip in 10 seconds is:
1/6 C = 1/6(31.4159 inches) = 5.23598 inches
Round off to the nearest tenth of an inch.
5.23598 inches = 5.2 inches
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You design a tree house using a coordinate plane in which the coordinates are measured in meters ( m ). The vertices of the rectangular floor are (0,5), (4,3) ,(4,13) and (8,11).
Part A: What is the perimeter of the tree house floor?
Part B: What is the area of the tree house floor?
The area of the rectangle is 36.83 m² and perimeter is 25.42 m
What is rectangle?A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°). The opposite sides of a rectangle are equal and parallel.
Given that, you design a tree house using a coordinate plane in which the coordinates are measured in meters. The vertices of the rectangular floor are (0,5), (4,3), (4,13) and (8,11).
We know that, distance between two points is = [tex]\sqrt{(x_{2}-x_{1} )^2+(y_{2} -y_1)^2}[/tex]
Distance between (0,5) and (4,3) = [tex]\sqrt{(4-0)^2+(3-5)^2}[/tex]
= [tex]\sqrt{16+4}[/tex]
= 4.47 m
Distance between (4, 3) and (8, 11) = [tex]\sqrt{(8-4)^2+(11-3)^2}[/tex]
= [tex]\sqrt{4+64}[/tex]
= 8.24 m
Therefore, in reference to the rectangle given, the length = 8.24 m and width = 4.47 m
Area of the rectangle = 4.47 x 8.24 = 36.83 m²
Perimeter = 2(4.47+8.24) = 2 x 12.71 = 25.42 m
Hence, the area of the rectangle is 36.83 m² and perimeter is 25.42 m
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if a is any rectangular matrix prove that a*a and aa* are both hermitian
A matrix A is said to be hermitian if it satisfies the property A = A*
A* Means the conjugate transpose of A
Here
Given that A is a rectangular matrix.
we can prove that AA and AA are both hermitian by showing that AA = (AA)* and AA* = (AA*)*
we will prove that A*A is hermitian:
(AA) = (A*)A = A*A
AA = (AA)
so we can see that it is "AA" indeed hermitian,
Now we will prove that AA* is hermitian
(AA*)* = A*(A*)* = A*A
AA* = (AA*)
AA is indeed hermitian.
given any rectangular matrix A, we have shown that AA and AA are both hermitian, as they both satisfy the property of A = A*.
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A matrix A is said to be hermitian if it satisfies the property A = A*
A* Means the conjugate transpose of A
Given that A is a rectangular matrix.
we can prove that AA and AA are both hermitian by showing that AA = (AA)* and AA* = (AA*)*
we will prove that A*A is hermitian:
(AA) = (A*)A = A*A
AA = (AA)
so we can see that it is "AA" indeed hermitian,
Now we will prove that AA* is hermitian
(AA*)* = A*(A*)* = A*A
AA* = (AA*)
AA is indeed hermitian.
given any rectangular matrix A, we have shown that AA and AA are both hermitian, as they both satisfy the property of A = A*.
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given the matrix a=⎡⎣⎢aa39−6−259a⎤⎦⎥, find all values of a that make |a|=0. give your answer as a comma-separated list.
The values of a that make |a| = 0 are the roots of the cubic polynomial equation -6a^3 + 27a^2 + 81 = 0.
What is polynomial ?
A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
To find the values of a that make the determinant of the matrix |a| equal to 0, we need to evaluate the determinant of the matrix:
|a| = a * (-6a + 9) - (3a^2 - 9) * 9
= -6a^3 + 27a^2 + 9a * 9 = 0
We can then solve for a using polynomial roots:
-6a^3 + 27a^2 + 81 = 0
The values of a that make |a| = 0 are the roots of the cubic polynomial equation -6a^3 + 27a^2 + 81 = 0.
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Anita purchaed a new building for her buine. Being in the prime location, he decided to
make ome more money by putting up an advertiement ign for a rental ad income on the roof
of the buildin
Anita has acquired a new building, which is located in a prime location. She aims to generate additional income by putting up an advertisement sign for rental purposes on the roof of the building.
By placing an advertisement sign on the roof, Anita is making use of the building's prime location and visibility to attract potential tenants. The sign is a cost-effective way of advertising her building and helps to reach a large audience, who may be interested in renting a space in the building.
Additionally, the rental income generated from the advertisement sign will help to offset the costs of owning the building, making it a profitable investment for Anita in the long run. By utilizing all the resources at her disposal, she is making smart business decisions that will help her achieve her financial goals.
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The complete question is-
What is the plan of Anita for the new building that she purchased for her business?
You are given the equation 13 = 2x + 5 with no solution set.
Part A: Determine two values that make the equation false. (2 points)
Part B: Explain why your integer solutions are false. Show all work. (2 points)
Answer:Determine two values that make the equation false. (2 points)
Step-by-step explanation:
Answer: You are only giving 4 point!
Step-by-step explanation:
i need to get this right, help
(im not to sure on my answer)
Answer:
First choice
Step-by-step explanation:
The graph appears to show the time and the distance a motorcycle is from a house.
By inspection of the graph we can say that the first two hours the position of the motorcycle steadily moves away from the house. Then for the duration of 1 hour(hour2-hour3) the motorcycle moves closer to the house. Finally the motorcycle's position for an hour does not change meaning that the motorcyle has not moved for the duration of another hour.
So the motorcycle moves away from the house for two hours. Then it moves back towards the house for an hour. Finally it parks for an hour. This corresponds to the first answer choice.
The probability a certain spinner will land on 1 is 15%, 2 - 20%, 3 - 30%, 4 - 35%/ What is the expected value (mean) the spinner will land on?
A. 2.15
B. 2,5
C. 2,75
D. 2.85
Which math expreion mean the um of an unknown number and 15
A. 15. X
B. X 15
C. X - 15
D. 15 divided x
Answer:
i think x+15 would be the correct answer
