52 tiles are there in the 25th figure in this pattern.
What is a pattern?A pattern is described as a series of recurring symbols, figures, or numbers. Any form of event or object can be related to a pattern.
A pattern has a rule that specifies which items fall within the pattern's umbrella and which do not.
A pattern in mathematics is a recurring arrangement of numbers, forms, colors, and other elements.
Any kind of event or object can be connected to the Pattern.
A pattern is referred to as a rule or a way in which a group of numbers is related to one another.
Sometimes a pattern is also referred to as a sequence.
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Under a microscope, a single celled organism 200 microns in length appears to be 50 millimeters long. If 1 millimeter =1000 microns, what magnification setting (scale factor) was used? Explain your reasoning.
The length of the organism in millimeters is 200 ч 1000 or 0.2 mm.
What is a microscope?A microscope is a laboratory tool used to examine objects that are too small to see with the eye. Microscopy is the science of using a microscope to examine small objects and structures. Microscopic means invisible to the eye unless magnified.There are numerous types of microscopes, and they can be classified in various ways. One method is to describe the method a device uses to interact with a sample and produce images, such as sending a beam of light or electrons through a sample in its optical path, detecting photon emissions from a sample, or scanning across a short distance from a sample.In the given situation, the organism's length in millimeters is 200 ч 1000 or 0.2 mm.
Therefore, the length of the organism in millimeters is 200 ч 1000 or 0.2 mm.
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Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms. y=x-2(x+5)
The given function y = x- 2(x+5), is a linear function.
It has no quadratic termIts linear term is -xIts constant term is -10What is a function?A function is a mathematical expression or equation that allows us to visualize graphically the behavior of a function. A function is not real when it cuts the vertical axis at the same point of x.
A function can be linear or quadratic, this is evidenced by the higher exponential degree.
We rewrite the function and reduce it to its minimum expression:
y = x- 2(x+5)
y = x + (-2x - 10)
y = x - 2x - 10
y = -x - 10 , linear function.
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A beverage company makes 100% cranapple juice, which makes up of 3 1/4 parts of cranberry juice to 5 3/4 parts of apple juice, with no other ingredients. how much apple juice is there in a 64 fluid ounce bottle of cranapple juice?
The amount of apple juice needed in a 64 fluid ounce bottle of cranapple juice is 40.8 fluid ounce.
The beverage company makes 100% cranapple juice which is made up of 3 1/4 cranberry juice to 5 3/4 apple juice. Converting to decimal, it is made up of 3.25 cranberry juice to 5.75 apple juice. The ratio of cranberry juice to apple juice in the cranapple juice would be
=3.25/5.75
=> Total ratio = 3.25 + 5.75 = 9
The amount of apple juice needed in a 64 fluid ounce cranapple juice would be
5.75/9 × 64 = 40.8 fluid ounce
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An equation of he line through the points (-2,5) and (3,-4)
The equation of the line passing through points (-2,5) and (3,-4) is 9x + 5y = 7.
Hence, option C) 9x + 5y = 7 is the correct answer.
What is the equation of line that passes through the points (-2,5) and (3,-4)?Given the data in the question;
Point1 (-2,5)
x₁ = -2y₁ = 5Point2 (3,-4)
x₂ = 3y₂ = -4First, we determine the slope of the of the line,
m = (y₂-y₁)/(x₂-x₁)
m = ( -4-5 )/( 3-(-2) )
m = -9/5
Using the formula for equation, we determine the y-intercept
y = mx + b
Plug in the first point (-2,5) and the slope and then solve for the y-intercept b.
5 = -9/5(-2) + b
5 = 18/5 + b
b = 5 - 18/5
b = ( 25 - 18 )/5
b = 7/5
Now, plug the slope and y-intercept into y = mx + b to determine the equation of the line.
y = mx + b
y = -(9/5)x + 7/5
Convert to standard form
y = -(9/5)x + 7/5
Multiply each term by 5
5y = -9x + 7
5y + 9x = 7
9x + 5y = 7
The equation of the line passing through points (-2,5) and (3,-4) is 9x + 5y = 7.
Hence, option C) 9x + 5y = 7 is the correct answer.
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Write an equation of the line satisfying the given conditions. the line passes through (25,24) and is perpendicular to y=6.
The equation of the line satisfies the given conditions. the line passes through (25,24) and is perpendicular to y=6 is x = 25.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The line passes through the point (25, 24)
y - 24 = m(x - 25)
y = 6
The slope of the line perpendicular to the line y = 6
m = not defined
m = 1/0
y - 24 = [1/0](x - 25)
x - 25 = 0
x = 25
Thus, the equation of the line satisfies the given conditions. the line passes through (25,24) and is perpendicular to y=6 is x = 25.
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If a = -2 then evaluate 2a^2 - 5a + 6
After evaluating the given expression at a = -2, we get 24.
We have the following expression -
[tex]2a^{2} -5a +6[/tex]
We have to evaluate it for a = -2.
How a expression in mathematics is evaluated ?To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.
According to the question, we have -
[tex]2a^{2} -5a +6[/tex]
Evaluating the expression for a = -2, we get -
2(-2)(-2) - 5(-2) + 6 = 8 + 10 + 6 =24
Hence, after evaluating the given expression at a = -2, we get 24.
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Suppose that e and f are two events and that p(e)=0.6 and p(f|e)=0.4. what is p(e and f)?
The required value of p(e and f) is 0.24, which is calculated using the conditional probability formula.
What is conditional probability?
Conditional probability is the measure in probability theory that depicts the probability of occurrence of an event given that another event has already occurred. Its mathematical formulation is given by:
P(A/B) = P(A∩B) / P(B)
Here, A is the event and B has already occurred
The calculation for the value of p(e and f)
The assigned value of p(e) = 0.6
Conditional probability, p(f/e) is given as 0.4
We know, that conditional probability = p(e∩f) / p(e)
W need to calculate p(e∩f) which is equal to p(f/e) × p(e)
p(e∩f) = 0.4 × 0.6
= 0.24
Hence, the value of p(e and f) is 0.24.
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Solve each inequality. Check your solution. 3n < -4(2+n)
The inequality given by 3n < -4(2 + n) has the solution n < -8/7 or (-∞ , -8/7).
Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.
To solve an inequality is to find the values of x such that when we substitute that number for x we have a true statement.
Given the inequality 3n < -4(2 + n), expand the right term by distributing -4 inside the parenthesis.
3n < -4(2 + n)
3n < -8 - 4n
Add 4n to both sides.
3n + 4n < -8 - 4n + 4n
7n < -8
Divide both sides by 7
7n < -8
n < -8/7
To check, let n = -9/7
n = -9/7 < -8/7
Substitute this value to the inequality.
3n < -4(2 + n)
3(-9/7) < -4(2 + -9/7)
-27/7 < -20/7
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Select the reason that best supports Statement 6 in the given proof.
URGENTTTT!!!
Answer:
B) distributive propertyStep-by-step explanation:
The statements 6 covers the operation:
3(x + 7) = 3x + 21This is the reflection of the distributive property of multiplication.
The matching answer choice is B.
These cards can be sorted into three pairs,
where each pair adds to the same number.
What is this number?
-3-8-53-20
Applying addition of integers, it is found that this number is of -5.
Why is the number -5?The addition of these following three pairs is given as follows:
-5 + 0 = -5.-3 - 2 = -5.-8 + 3 = -5.Hence, we got three pairs of values from these cards, all cards are used, and all the additions result in -5, hence, this number is of -5.
The addition of integers used in this problem is as follows:
Two negatives: keep the signal and add the numbers, hence -3 - 2 = -5.Positive and negative: signal of bigger absolute value, find the difference, hence: -8 + 3 = -(8 - 3) = -5.More can be learned about addition of integers at https://brainly.com/question/17695139
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CARD #2:
A figure on a
coordinate plane is
dilated. Point A(3, 9)
is dilated to A'(1, 3).
Bobby says the
dilation can be
represented by
(x, y).
Betty says the
dilation can be
represented by
(3x, 3y).
Answer:
(3x,3y) if you're representing the dilation from A' -> A
Step-by-step explanation:
I think that it would be (3x, 3y) bc the original point was dilated by 1/3 (3 x 1/3 = 1, 9 x 1/3= 3), so I'm wondering which dilation it specifies for exactly, b/c if its for A', then the answer would be Betty. Hope this helps somewhat tho
points A(-1.5) and b(6) are marked on a number line. find the coordinate of point m if it is know that AM:md = 1:2
The coordinates of point m if it is known that am : md = 1 : 2 is (4/3, 5)
How to find the coordinates of point m?The given parameters are
A = (-1, 5)
B = (6, 5)
Ratio, m : n = 1 : 2
The coordinates of point m are calculated using
M = 1/(m + n) * (mx2 + nx1, my2 + ny1)
So, we have
M = 1/(1 + 2) * (1 * 6 + 2 * -1, 1 * 5 + 2 * 5)
Evaluate the sum of products
So, we have
M = 1/3 * (4, 15)
Evaluate the product
M = (4/3, 5)
Hence, the coordinates of point m if it is known that am : md = 1 : 2 is (4/3, 5)
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Compare and contrast inscribed angles and central angles of a circle. If they intercept the same arc, how are they related?
If a central angle and an inscribed angle intersect the same arc, the central angle is twice the inscribed angle and half the central angle.
What is the relation between the central and inscribed angle on the same arc?According to the inscribed angle theorem, an angle inscribed in a circle is half the central angle 2 that subtends the same arc on the circle.
The central angle has the same length as the intercepted arc. As can be seen, if a central angle and an inscribed angle intersect the same arc, the central angle is twice as large as the inscribed angles. Similarly, the inscribed angle equals half of the central angle.
An inscribed angle is one that has its vertex on a circle and its sides are chords. The intercepted arc is the arc that is contained within the inscribed angle and has its endpoints on the angle.
If a central angle and an inscribed angle intersect the same arc, the central angle is twice the inscribed angle and half the central angle.
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Identify a pattern and find the next three numbers in the pattern.
6,12,18,24, . . .
The answer is 6, 12, 18, 24, 30, 36, 42.
The pattern is in increasing order i.e., +6.
How to find the pattern in the numbers?Given,
6,12,18,24, . . .
Solution:
Note the difference in the given number series 6,12,18,24, . . .
12 - 6 = 6
18 - 12 = 6
24 - 18 = 6
The difference is common and is 6.
The sequence is in increasing order.
So, add 6 to 24 and the consecutive numbers to get the answer.
24 +6 = 30
30 +6 = 36
36 + 6 = 42
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What are the next three terms in the sequence, 500, 100, 20?
Answer: –1, 9, 19, 29, … (1 point)
38, 37, 32
40, 51, 62
39, 49, 59
38, 47, 56.
Step-by-step explanation: tried
(x−4)(x−6)
Cómo lo hago?
Ayuda!! me confunden mucho los signos!! :((
hj2 ÷ 5; use h = 5, and j = 5
The hj and the 2 after it is supposed to be squared so it’s 2 squared.
Answer:
25
Step-by-step explanation:
Work shown in the attached screenshot!! Please let me know if you have any questions! :)
The Atlanta Falcons scored 13 more points than twice the number of points that the Miami Dolphins scored. Altogether, the teams scored 43 points. How many points did the Dolphins score? Is 21 a viable solution to this problem?
Yes, because 21 points is less than the total number of points scored
No, because 2(21) + 13 ≠ 43
Yes, because 21 points is less than the number of points Atlanta scored
No, because 2(21) ≠ 43
Answer:
No, because 2(21) + 13 is not equal to 43.
The Dolphins scored 10 points.
Step-by-step explanation:
A = 13 + 2D
43 = 13 + A + D
43 = 13 + 3D
43 - 13 = 30
30 = 3D
30/3 = 10
D = 10
A = 13 + 2(10)
A = 33
D + A = 43
33 + 10 = 43
Therefore, the Atlanta Falcons scored 33 points which is 13 points more than twice what the Dolphins scored.
There is one bus driver, two coaches, and three teams, each with four dancers going to a competition. Nia writes the expression 1 + 2 + 3 ∙ 4 to represent everyone that will be on the bus and solves it using the following steps:
1 + 2 + 3 ∙ 4
= 3 + 3 ∙ 4
= 6 ∙ 4
=24
A. Nia concludes that 24 people will be on the bus going to the competition. Describe the mistake Nia made when solving her expression. Then write an explanation and draw a picture to help Nia understand how to solve her expression correctly.
B. How would you write this expression if n represents the number of teams?
C. How would this expression be different if there were two coaches for each team? Write an expression and draw a picture to support your expression.
A. The mistake that Nia made when solving her expression is that she added all the numbers before multiplying by 4.
B. The expression, if n represents the number of teams, will be 3 + 4n.
C. The expression be different if there were two coaches for each team will be 1 + 6n 4.
How to illustrate the information?It should be noted that the mistake that Nia made when solving her expression is that she added all the numbers before multiplying by 4.
Therefore, the correct answer will be:
= 1 + 2 + 3 × 4
= 1 + 2 + (3 × 4)
= 3 + 12
= 15
B When the number of teams is n, with four dancers in each, then the expression is:
1 + 2 + 4n = 3 + 4n
C When the number of teams is n and each team consists of two coaches and 4 dancers then the expression is:
1 + (2 + 4)n = 1 + 6n
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Correct way of calculation, using PEMDAS
1 + 2 + 3 · 4 = Multiply first1 + 2 + 12 = Add all together15 Correct answerThe mistake was incorrect order of operations. Addition (A) comes after multiplication (M) or division (D) if no parenthesis (P) or exponents (E) present.
Part BIf the number of teams is n, with four dancers in each, then the expression is:
1 + 2 + 4n or3 + 4nHere 4n is the number of dancers in n teams.
Part CIf the number of teams is n and each team consists of two coaches and 4 dancers then the expression is:
1 + (2 + 4)n or1 + 6nHere 6n is the number of coaches and dancers in n teams.
What are multiples of 5/4?
For example; Kendal is doing math problems to study for an exam, and she has completed 5/4of the number of assigned problems. What multiple of the number of assigned problems has Kendal completed?
I need help
Also, I'm in 6th grade and its a lot harder whenever you are in SEARCH/GT(Smart people classes basically)
pls I'm failing my class and I need to do this grade and get them all right to get my grade up
The multiples of 5/4 will be 2 1/2, 3 3/4, 5, etc.
How to illustrate the information?It should be noted that multiples simply mean the answer that one gets when the number of multiplied by any whole number.
Therefore, the multiples will be:
= 5/4 × 2 = 2 1/2
= 5/4 × 3 = 3 3/4
= 5/4 × 4 = 5
Therefore, the multiples of 5/4 will be 2 1/2, 3 3/4, 5, etc.
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Arrange the population of the seven countries from least to greatest. your answer should have the numbers in scientific notation. 1.37 x 101, 2.75 x 100, 8.56 x 101, 6.37 x 107, 1.44 x 10-3, 1.83 x 104, 6.53 x 100
The population of the seven countries, arranged from least to greatest in scientific notation is: 1.38 x 10², 1.48 x 10², 1.9 x 10², 2.75 x 10², 6.53 x 10², 6.81 x 10² and 8.64 x 10².
To arrange from least to the greatest means to arrange from the smallest number to the largest number. Before we can arrange the population of the seven countries from the least to the greatest, we would need to resolve the numbers and convert to scientific notation, hence:
Population of first country = 1.37 x 101 = 138.37 = 1.38 x 10²Population of second country = 2.75 x 100 = 275 = 2.75 x 10²Population of third country = 8.56 x 101 = 864.56 = 8.64 x 10²Population of forth country = 6.37 x 107 = 681.59 = 6.81 x 10²Population of fifth country = 1.44 x 103 = 148.32 = 1.48 x 10²Population of sixth country = 1.83 x 104 = 190.32 = 1.9 x 10²Population of seventh country = 6.53 x 100 = 653 = 6.53 x 10²Therefore, if we are to arrange the population of the seven countries, starting with the smallest number and ending with the largest number in scientific notation, we will have: 1.38 x 10², 1.48 x 10², 1.9 x 10², 2.75 x 10², 6.53 x 10², 6.81 x 10² and 8.64 x 10².
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What is the expected number of times Clarence will roll doubles with two number cubes in 90 trials? (Doubles occur when both number cubes show the same number in a trial.)
F. 6
G. 9
H. 10
J. 15
For 90 trials , expected no. of times of rolling doubles will be 15 times.
It is given that Clarence roll doubles with two cubes.
We have to find out the expected number of times of rolling doubles in 90 trials.
What do you mean by probability ?
Probability is the ratio of the number of favorable outcomes to the total number of outcomes of an event.
As per the question ;
Clarence roll doubles in 90 trials with two cubes.
We know that ;
There are 36 outcomes for a pair of dice.
So ;
In a pair , there are 6 possible doubles.
i.e.,
1-1 , 2-2 , 3-3 , 4-4 , 5-5 and 6-6
So ;
Probability will be ;
= 6 / 36
or
= 1 / 6
And
For 90 trials , expected no. of times of rolling doubles will be ;
= [tex]\frac{1}{6}[/tex] × 90
= 15 times
Thus , for 90 trials , expected no. of times of rolling doubles will be 15 times.
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Solve each equation. Check your answer. 43-3 d=d+9
d= 17/2 is the solution of the given equation 43-3 d=d+9.
According to the given question.
We have a linear equation in one variable 43 -3d = d + 9.
Since, we have to solve the above linear equation in one varible 43 -3d = d + 9, which means we have to solve the above equation for d.
As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Thereofore, the solution of the given linear equation in one variable 43 -3d = d + 9 is given by
43 -3d = d + 9
⇒ 43 - 9 -3d = d (subtracting 9 from both the sides)
⇒ 34 = d + 3d (adding 3d both the sides)
⇒ 34 = 4d
⇒ d = 34/4
⇒ d = 17/2
Now, we will check whether d = 17/2 is the solution of the given equation or not.
Thereofore,
LHS
= 43 - 3(17/2)
= 43 - 51/2
= 86 - 51/2
= 35/2
RHS
= 17/2 + 9
= 17 + 18/2
=35/2
Here, LHS = RHS for d = 17/2
Hence, d= 17/2 is the solution of the given equation 43-3 d=d+9.
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The “communication revolution” has given us prepaid phone calling cards. These cards are used to make long distance phone calls from any phone. In a recent year the industry posted sales of $500.000. Three years later the sales figure had risen to $200,000,000. What is the increase in sales over the three-year period
The sales increased exponentially at the rate of $6,65,00,000/year for the next three consecutive years.
We have sales record of communication industry.
We have to determine the increase in sales over the three-year period.
What is the advantages of prepaid phone plans?The advantage of using prepaid phone plans is you only pay for the data you use, and you're not tied into a lengthy service contract.
According to the question -
Initial Sales - $500,000
Sales after 3 years - $200,000,000
Therefore, the rate at which the sales increased is -
r = [tex]$\frac{2\times 10^{8}- 5\times 10^{5} }{3}[/tex] = $6,65,00,000
Hence, the sales increased exponentially at the rate of $6,65,00,000/year for the next three consecutive years.
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Laci and Leon are saving money to go to an amusement park. Laci has $1 more than 4 times the amount of money Leon has. Together, they have $76. Write an equation to determine how much money they have together
Answer:
Step-by-step explanation:
x+4x+1=76 is the answer
Find the missing term(s) of each geometric sequence. -20 ~, □,□,□,-1.25, l . . . l . . .
Missing terms of the geometric sequence = -10, -5, -2.5
For the geometric sequence to the nth term, the formula is
[tex]t_{n}[/tex] = a [tex]r^{n-1}[/tex]
Here the sequence is -20, __ , __, __, -1.25...
So we have to find the 2nd, 3rd and 4th terms of the sequence.
We know the 5th term of the series by which we can find out the common ratio.
[tex]t_{5}[/tex] = -20 [tex]r^{5-1}[/tex]
-1.25 = -20 [tex]r^{4}[/tex]
[tex]r^{4}[/tex] = 1.25/20
= 1/16
r = 1/2
The common ratio is 1/2
[tex]t_{2}[/tex] = -20 [tex](\frac{1}{2})[/tex]
= -10
[tex]t_{3}[/tex] = -20 [tex](\frac{1}{2} )^{2}[/tex]
= -20 [tex]\frac{1}{4}[/tex]
= -5
[tex]t_{4}[/tex] = -20 [tex](\frac{1}{2} )^{3}[/tex]
= -20[tex]\frac{1}{8}[/tex]
= -2.5
Therefore the missing terms are -10, -5 and -2.5.
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The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of n objects where order of selection is not important is called the rule for?.
Combination is the counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects, where order of selection is not important.
The formula for combination is given by:
C = N! / n!(N - n)!
where N is the set of objects
and n is the number of objects to be selected from N
example: If the order doesn't matter, how many ways can 3 girls be selected from a group of 5 girls?
C = N! / n!(N - n)!
where N = 5 and n = 3
C = 5! / 3!(5 - 3)!
C = 120/(6)(2)
C = 10
Hence, there are 10 ways to select 3 girls from a group of 5 girls.
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The mathematical relationship between the total cost for a person to bowl at the local bowling alley and the number of games played is represented by
y = 3.50x + 6.00
Explain how you can use this linear function to find out how many games you can bowl for $34.
Pls don't send links or wrong answers I WILL REPORT YOU
The number of games that will be played will be 8 games.
How to illustrate the information?It should be noted that the mathematical relationship between the total cost for a person to bowl at the local bowling alley and the number of games played is represented by
y = 3.50x + 6.00.
The games that you can bowl for $34 will be:
y = 3.50x + 6.00.
34 = 3.50x + 6.00.
Collect like terms
3.50x = 34 - 6
3.50x = 28
Divide
x = 28 / 3.50
x = 8
Therefore, the number of games will be 8 games.
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help me pls pls pls pls pls pls pls pls
Answer:
15, 10, 6
Step-by-step explanation:
Gavin: 2.52 + 6.25 + 6.25 =15.02 = 15
Jason: 6.25 = 6
Evan: 6.25 + 3.72 = 9.97 = 10
i hope this helped if did pls mark brainliest
f(x)= -x-5 g(x)=x^2-6x+13 find f(g(x))
Answer:
f(g(x)) = x² - 6x + 8
Step-by-step explanation:
to evaluate f(g(x)) , substitute x = g(x) into f(x)
f(x² - 6x + 13)
= x² - 6x + 13 - 5 ← collect like terms
= x² - 6x + 8
