The statement that is logically equivalent to the following conditional statement is " If it is a hexagon, then it does not have exactly four sides."
What is a regular hexagon?
It is a regular hexagon when the lengths of all the sides and the measures of all the angles are equal. In a regular hexagon, each inside angle is 120 degrees. The characteristics of a regular hexagon. The lengths of each side are equal.
Here, we let
P = it has exactly four sides.
Q = it is not an hexagon.
The negation is like this;
If it is a hexagon, then it does not have exactly four sides.
Thus, we concluded that “it is a hexagon” is your hypothesis (p) and “it has exactly 6 congruent sides” is your conclusion (q).
Hence, the statement that is logically equivalent to the following conditional statement is " If it is a hexagon, then it does not have exactly four sides."
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Which of the following expressions is equivalent to 2y (3y^2 + 4y^4)
The expression that is equivalent to the given expression is 6y³ + 8y⁵
Evaluating an expression and determining an equivalent expressionFrom the question, we are to determine the expression that is equivalent to the given expression
The given expression is
2y (3y^2 + 4y^4)
This can be properly written as
2y (3y² + 4y⁴)
Now, to determine the expression that is equivalent to this expression, we will expand the expression by applying the distributive property.
2y(3y² + 4y⁴)
2y(3y²) + 2y(4y⁴)
Multiplying
6y³ + 8y⁵
Hence,
The expression is 6y³ + 8y⁵
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Evaluate the expression when g = 0.6.
400g2−0.9÷g
d) The rent of a room for 4 months is Rs 20,000. (i) What is the rent for 7 months? (ii) How long would a tenant hire the room for Rs 55,000 at the same rate of rent?
The rent for seven months is 35000 and a tenant hire the room for Rs 55,000 at the same rate of rent for 11 months
The rent of a room for 4 months is Rs 20,000.
The rent of a room for 1 month is Rs 20,000./4
The rent of a room for 1 month is Rs 5000
The rent of a room for 7 months is Rs 5000 x 7
The rent of a room for 7 months is Rs 35000
Now we need to calculate the number of month a tenant hire the room for Rs 55,000 at the same rate of rent
The rent is 5000 for 1 month
The rent will be 55000 for 1/5000 x 55000 = 11 months
Therefore, the rent for seven months is 35000 and a tenant hire the room for Rs 55,000 at the same rate of rent for 11 months
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Find the equation of the linear function represented by the table below in slope-
intercept form.
The equation of the linear function is represented by the table given in the slope-intercept form is y = x -1.
What is an equation of a line?
A line's equation is a single representation of all of the line's points. The general form of a line equation is ax + by + c = 0, and each point on the line satisfies this equation. The slope of the line and a point on the line are the two necessary components to create the equation of a line.
The equation of a line, in the slope-intercept formula:
y = mx + b
In which,
m is the slope, that is, how much y changes when x changes by 1.
b is the y-intercept, that is, the value of y when x = 0.
Given two points (x,y), the slope is the change in y divided by the change in x.
We have points (-1, -2) and (1, -4).
[tex]m = \frac{(-2 - (-4))}{1 - (-1)}[/tex]
m = 1;
Then,
y = 1x + b
Point (-1,-2) means that when x = -1 and y = -2, we use this to find b.
y = 1x + b
-2 = 1(-1) + b
b = -2 + 1
b = -1
Thus,
y = x -1.
Hence, the equation of the linear function is represented by the table given in the slope-intercept form is y = x -1.
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At school, 40% of the sixth grade students said that hip hop was their favorite kind of music. If 100 sixth grade students prefer hip hop music how many sixth graders are at the school
If 100 sixth grade students prefer hip hop music, the number of sixth graders at the school is 250.
How many sixth graders are at the school?Percentage is a measure of frequency that is used to express a number as as a fraction of 100. In order to change a value to percentage, multiply the number by 100. The sign that represents percentage is %.
In order to determine the number of sixth graders, divide the number of sixth graders that prefer hip hop music by the percentage.
Number of sixth graders = number that prefer hip hop / percentage
100 / 40%
100 / 0.4 = 250
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the measure of the middle ordinate of a yaw mark is 6 ft. the radius of the arc is 70 ft. what was the length of the chord used in this situation? round the answer to the nearest tenth of a foot.
The length of the chord used in this situation is approximately 40.54 ft.
To find the length of the chord used in the situation, we can use the formula for the chord length in a circular arc:
Chord length = 2√(r² - (r - h)²)
where r is the radius of the arc and h is the measure of the middle ordinate.
Given that the radius of the arc is 70 ft and the measure of the middle ordinate is 6 ft, we can substitute these values into the formula:
Chord length = 2√(70² - (70 - 6)²)
Chord length = 2√(4900 - 4489)
Chord length = 2√(411)
Chord length ≈ 2 * 20.27
Chord length ≈ 40.54 ft
Therefore, the length of the chord used in this situation is approximately 40.54 ft.
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Can anyone write the equation of the graph?
The equation of the graph represented by the figure is f(x) = |x - 3| + 5
How to find the equation of the graph line?From the question, we have the following graph that can be used in our computation:
The graph is an absolute value graph
As a general rule, an absolute value is expressed as
y = |x - h| + k
In this case, the vertex is
Vertex = (h, k)
As a general rule, the vertex of a function is the minimum point on the graph
On the given graph, the minimum point is (3, 5)
This means that
(h, k) = (3, 5)
Substitute the values (h, k) = (3, 5) in the equation y = |x - h| + k
So, we have the following representation
y = |x - 3| + 5
Rewrite the equation as a function
f(x) = |x - 3| + 5
Hence, the equation is f(x) = |x - 3| + 5
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A person invested $440 in an account growing at a rate allowing the money to double every 8 years. How long, to the nearest tenth of a year would it take for the value of the account to reach $2,860?
The time that It would take for the value of the account to reach $2,860 is; 21.6 years
How to solve compound interest problems?We are told that a person invested $440 in an account growing at a rate allowing the money to double every 8 years. Thus, the account balance can be modeled by the equation;
A = 440(2)^(t/8)
where;
A is final amount
t is in years
We want to find t when A = 2860. Thus;
2860 = 440(2^(t/8))
divide both sides by 440 to get;
6.5 = 2^(t/8)
log(6.5) = (t/8)log(2)
t = 8 * log(6.5)/log(2)
t ≈ 21.604
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Rachel used 12 centimeters of tape to wrap 3 presents. How many presents did Rachel wrap if she used 20 centimeters of tape?
The number of wrapped present with 20 centimeters of tape is given as 5 presents.
How to solve for the wrapped presentsIn this question, we have the following values
12 centimeters of tape was used to wrap 3 presents
hence we would have
12 = 3 presents - - - - 1
Then we are to know the presents that would be wrapped with the use of 20 centimeters of tape.
we would have
20 = ? presents - - - 2
We have to bring the equations together
12 = 3 presents
20 = ? presents
? is the presents that is to be wrapped with 20 centimeters of tape. It is our unknown.
We would have to cross multiply
12 x ? = 3 x 20
12? = 60
We would have to divide through by 12 in order to get the unknown
? = 60 / 12
? = 5
Hence the number of presents that she wrapped is given as 5
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"14 more than twice a number" translate expression
Answer: 14=2x
Step-by-step explanation:
the answer is 14=2x7=14
a=4 b=2, find value of a) 3ab
b) a+5b
Answer:a. 24
b. 14
Step-by-step explanation:
a. 3ab=
3*a*b=
3*4*2=
12*2=24
b. a+5b=
a+5*b=
4+5*2=
4+10=14
Answer: a) 24
b) 14
Step-by-step explanation:
step1: We have to substitute the numbers.
step2: Then finish the answer.
a) 3ab = 3 x 4 x 2 = 24
b) a+5b = 4 + 5 x 2 = 4 + 10 = 14
How many solutions can be found for the linear equation?
3(x + 4) = 3x + 4
Responses
A infinitely many solutionsinfinitely many solutions
B no solutionno solution
C two solutionstwo solutions
D one solution
Answer:
B No solution
Step-by-step explanation:
3(x+ 4) = 3x + 4 Distribute the 3
3(x) + 3( 12) = 3x + 4
3x + 12 = 3x + 4 There is not number that I can multiply by 3 and then add to 12 on one side and add to 4 on the other side of the equal sign to make a true statement, so the answer is no solution.
3x + 12 = 3x +4 Subtract 3x from both sides
12≠4. A false statement means no solution.
When the equation is simplified and the coefficient of the variable (the number before the letter) is the same on both sides of the equation and the constraints (the numbers without letters) are different, this will result in no solution.
let 0 < a < b < 1,
a) is a^x < b^x, for x>0
b) is a^x < b^x, for x<0
For 0 < a < b < 1, a^x < b^x, for x < 0.
What are inequalities and their types?
Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, 0 < a < b < 1.
Assuming a = 0.25 and b = 0.5.
∴ (0.25)^x < (0.5)^x for x > 0, again assuming x to be 2.
∴ (0.25)^2 = 0.625 and (0.5)^2 = 0.25.
Now, 0.625 > 0.25 which is not satisfying a^x < b^x, for x > 0.
Therefore, if 0 < a < b < 1, then a^x < b^x, for x < 0.
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y=3x−15 in standard form please answer MY GRADES DEPEND ON IT
The equation, y = 3x - 15, written in standard form is 3x - y = 15
Writing an equation is standard formFrom the question, we are to write the given equation is standard form.
The given equation is
y = 3x - 15
The standard form of a linear equation is
Ax + By = C
Where A, B, and C are constants
x and y are variables
Now, we will write the given equation is the standard form of a linear equation.
y = 3x - 15
Substract y from both sides
y - y = 3x - y - 15
0 = 3x - y - 15
That is,
3x - y - 15 = 0
Add 15 to both sides of the equation
3x - y -15 + 15 = 0 + 15
3x - y = 15
Hence, the standard form is 3x - y = 15
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what is 9/10 x (-1 1/4)
Answer:
-2.475
Step-by-step explanation:
its easy but i dont want to do it because im to lazy
The equation of the given line written in the slope-intercept form is: y = 21x + 10.25.
What is a slope?
The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.
Note that the general slope equation is:
y = mx + b
Where
m is the slope of the line and
b is the y-intercept.
In this specific instance, m is the change in the price of the ticket
b is the additional fee value that needs to be included for each ticket
Hence, the cost of the ticket (y) is given as:
y = (change rate of x) + added fee to every order
Where rate of change = 21; and
The fee added to each order is 10.25
Given the above, the general equation becomes:
y = 21x + 10.25
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please help will give brainliest
Step-by-step explanation:
2x - 27 + 3x + 27 = 180
5x = 180
x = 36
What is the value of the following numerical expression?
-23 +-15+|-17| + -35
A. -56
B.-26
C. 1-261
D. 56
The value of expression -23 +-15+|-17| + -35 is -56
In this question, we have been given a numerical expression.
-23 +-15+|-17| + -35
We need to find the value of given numerical expression.
Consider given numerical expression,
-23 +-15+|-17| + -35
= -23 + (-15) + |-17| + (-35)
= -23 - 15 + |-17| - 35
We know that for any real number a, |±a| = a
So, |-17| = 17
= -38 + 17 - 35
= -56
Therefore, the value of expression -23 +-15+|-17| + -35 is -56
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(3x-19)
what is the value of x
What does 3x-19 equal? You can find x without it being an equation
The solution is, the value of x is 6.33.
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
given that,
(3x-19) = 0,
here, we have to make the given expression simple, as we have to find the value of x.
so, we get, by isolating the variable & numbers,
adding 19 on both sides we get,
3x = 19
dividing both sides by 3, we get,
or, x = 19/3
or, x = 6.33
Hence, The solution is, the value of x is 6.33.
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a person must score in the upper 4% of the population on an iq test to qualify for membership in mensa, the international high iq society, if iq scores are normally distributed with a mean of 100 and a standard deviation of 15, what score must a person have to qualify for mensa. (2 decimals)
A person must have a score of 126.26 to qualify Mensa.
it is given that,
Mean [tex](\mu) = 100,[/tex]
Standard deviation [tex](\sigma) = 15[/tex].
A person must score in the upper 4% of the population,
100% - 4% = 96% = 0.96
P(X < Xo) = 96% = 0.96
P(X < 1.7507) = 0.96 ....................................using the Normal distribution table,
Or, when the Invnorm function is used, Invnorm(0.96) = 1.7507
Therefore, The required value of X is,
[tex]Z = \frac{(X - \mu )}{ \sigma }[/tex]
1.7507 = (X - 100) / 15
X - 100 = 26.26
X = 100 + 26.26
X = 126.26
thus, the score a person must have to qualify Mensa is 126.26.
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A rectangular athletic field has an area of 40x² + 190x-50. The width of the athletic field is 8x - 2. What is the length of the athletic field?
Answer:
The length = 5x + 25
Step-by-step explanation:
A = l x w
(x³-15)+(x-1) Divide using synthetic division
The quotient is x²+x+1 - 14/(x-1) after divide x³-15 by x-1.
What is synthetic division?
In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.
The divisor is x - 1.The dividend is (x³-15).
Step 1:Take the constant term of the divisor with the opposite sign and write it to the left.
Write the coefficients of the dividend to the right (missed terms are written with zero coefficients).
Step 2:Write down the first coefficient without changes:
Step 3:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
Step 4:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).Add the obtained result to the next coefficient of the dividend, and write down the sum
Step 5:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).Add the obtained result to the next coefficient of the dividend, and write down the sum.
We have completed the table and have obtained the following resulting coefficients: 1,1,1,−14.
All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.
The quotient is x²+x+1 and the remainder is -14.Therefore (x³-15)÷(x-1) = x²+x+1 - 14/(x-1)
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Graph the line with the equation y=− 6/1x +1
Answer:
The answer is (1, 6)
Step-by-step explanation:
In the diagram below, \overline{TU} TU is parallel to \overline{QR} QR . If TUTU is 55 less than TSTS, QS=45QS=45, and QR=36QR=36, find the length of \overline{TS} TS . Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
The length of TS, using similar triangles, is given as follows:
TS = x = 25.
What are similar triangles?Similar triangles are two triangles that share these two features:
Same angle measures.Proportional side lengths.In the context of this problem, the similar triangles are given as follows:
STU and SQR.
The proportional side lengths from these two similar triangles are given as follows:
TS = x and QS = 45.TU = x - 5 and QR = 36.Hence the proportional relationship that relates these lengths on the similar triangles is given as follows:
x/45 = x - 5/36
Applying cross multiplication, the length of TS, equals to x, is obtained as follows:
45(x - 5) = 36x
45x - 225 = 36x
9x = 225
x = 225/9
x = 25.
Missing InformationThe diagram is given by the image shown at the end of the answer.
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state how the 2 triangles are congruent?? SSS and SAS HELP ASAPPP??
The two triangles are congruent by SAS criterion.
What is SAS criterion?According to this standard, two triangles are said to be congruent if their two sides are equal to the sides of another triangle and their respective angles are also equal. The "Side-Angle-Side" triangle congruence theorem is referred to as the SAS Criterion.According to the Side-Angle-Side theorem of congruency, two sides and the angle they produce are congruent if they are equivalent to two sides and the included angle of another triangle.Verification:
Let's carry out an exercise to demonstrate SAS's validity. AB=PQ, BC=QR, and ∠B=∠Q are given. To demonstrate: ΔABC≅ΔPQRPlacing the triangle ABC over the triangle PQR will cause B to fall on Q and the AB side to coincide with the PQ side.Point A falls on point P because AB=PQ.The side BC will fall along the side QR since ∠B=∠Q.Point C is in line with point R since BC=QR. As a result, BC and QR coincide, while AC and PR coincide.ΔABC will therefore match ΔPQR. Consequently, ΔABC ≅ ΔPQR. This exemplifies the SAS congruence criterion.To learn more about SAS criterion, refer to https://brainly.com/question/22472034
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Dominique uses a car service company to travel to work and back home. She uses the same route each way. The company charges a ride fee of $3.00 and $1.25 per mile. Dominique pays $11.75 for transportation each way. Select all of the equations that model the total amount of money Dominique spends on travel each day if her route to work is x miles long.
The equation that model the total amount of money Dominique spends on travel each day if her route to work is x miles long is 3 + 1.25x = 11.75.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, Dominique uses a car service company to travel to work and back home.
The company charges a ride fee of $3.00 and $1.25 per mile. The appropriate equation will be:
3 + 1.25(x) = 11.75
where x = number of miles
3 + 1.25(x) = 11.75
3 + 1.25x = 11.75
This illustrates the equation.
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Epsilon3 is an exoplanet with a mass of 9.43x10^27g. It has a radius of 7.6x10^8cm. What is the density of the planet? What is it made of?
The density of the planet is 4.81 g/cm^3, and with this in mind, we assume that the planet is made of titanium or yttrium.
How to get the density of the planet?Density is defined as the quotient between mass and volume.
Here we know that the mass is:
9.43*10²⁷g
And the radius is 7.6x10^8cm, remember that the volume of a sphere of radius R is:
V = 3.14*(3/4)*R³
Then in this case the volume is:
V = 3.14*(3/4)*(9.43*10⁸ cm)³ = 1.96*10²⁷ cm³
Then the density is:
D = (9.43*10²⁷g)/(1.96*10²⁷ cm³) = 4.81 g/cm^3
For this density, we can assume that the planet is made of Titanium or Yttrium (or a combination of a lot of elements like most planets)
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help asap please. . . . .
(b)
Simplify
45e6f8
5ef²
an instructor gives a course grade of b to students who have total score on exams and homeworks between 800 and 900, where the maximum possible is 1000. if the total scores have approximately a normal distribution with mean 830 and standard deviation 50, about what proportion of the students receive a b?
Let x denote the score. Assuming x follows normal distribution with
mean m = 70 and SD = 5 ,
we first calculate P( x < or = 80)
The SNV is z = (x — m) /SD
When x = 80, Z = ( 80 — 70)/5 = 2
So, P( x < or= 80)
= P( z < or= 2)= Area under the standard normal curve on LHS of z = 2=0.5000 + 0.4772=0. 9772, which is the relative frequency of x < or = 80Given that total number of students is
N = 1000. Let f be the number of students who have scored < or equal to 80,Then f/N = relative frequency = 0.9772Hence f = 0.9772 X N = 0.9772 X 1000 = 977learn more about binomial distrubution click here:
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