Answer:
Step-by-step explanation:
We need to find the number of teenagers in the group, given that the product of their ages is 18,727,200.
To solve this problem, we need to factorize the given number into its prime factors and then determine how many distinct factors there are.
18,727,200 can be factorized as:
18,727,200 = 2^6 × 3^2 × 5^2 × 13^2
To find the number of distinct factors, we add 1 to each exponent and then multiply them together:
(6+1) × (2+1) × (2+1) × (2+1) = 7 × 3 × 3 × 3 = 189
Therefore, there are 189 factors of 18,727,200, which means that there are 189 ways to multiply whole numbers together to get this number.
Since we want to find the number of teenagers in the group, we need to look for combinations of factors that result in whole numbers for the ages. We can start by dividing the total number of factors by 2 (since we are looking for pairs of factors) and then slowly increase the divisor until we find the smallest number that results in a whole number.
189 ÷ 2 = 94.5 (not a whole number)
189 ÷ 3 = 63 (not a whole number)
189 ÷ 4 = 47.25 (not a whole number)
189 ÷ 5 = 37.8 (not a whole number)
189 ÷ 6 = 31.5 (not a whole number)
189 ÷ 7 = 27 (a whole number)
Therefore, there are 27 pairs of factors that result in whole numbers for the ages. Each pair corresponds to a group of teenagers, and since each group has the same number of teenagers, there are 27 teenagers in the group.
Steps for solving t|u prove mt=mu
We may conclude after answering the presented question that As a equation result, we have demonstrated that mt = mu when t | u.
How to solve the problem?Make a note of the definition of t | u. It denotes the existence of an integer k such that u = tk.
To get mt = m, substitute u = tk into mt = mu (tk).
Rewrite m(tk) as (mt)k using the associative property of multiplication.
To get mt = (mt)k, substitute (mt)k for m(tk) in the equation mt = mu.
Multiply both sides by mt. If mt is greater than zero, we obtain 1 = k. If mt is zero, we must also have mu = 0, hence the equation holds.
Since 1 Equals k, we get u = tk = t(1) = t.
We get mt = mt by substituting u = t into the original equation mt = mu.
As a result, we have demonstrated that mt = mu when t | u.
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SEE ATTACHED IMAGE
1) 12x^3+8x
2) 18a^2+2a
3) 25b^4+30b^3
1. Factor each term and mark the common factors.
2. Multiply the common factors to find the GCF.
3. Rewrite each term as the product of the GCF and other factors.
4. Rewrite the expression using the factors from the previous step.
5. Use the distributive property: ab ac + = a b( ) +c .
Step-by-step explanation:
remember the GCF (greatest common factor) ?
every number or term is the product of certain prime numbers (prime factors).
the product of factors that the discussed numbers or terms have in common is the GCF.
1)
12x³ + 8x
12x³ :
12 / 2 = 6
6 / 2 = 3
3 / 2 no
3 / 3 = 1 finished
12 = 2×2×3
x³ = x×x×x
so,
12x³ = 2×2×3×x×x×x
8x :
8 / 2 = 4
4 / 2 = 2
2 / 2 = 1 finished
8 = 2×2×2
x = x
so,
8x = 2×2×2×x
what factors do they have in common ?
2×2×x = 4x
so, the GCF = 4x
that means
12x³ + 8x = 4x×3x² + 4x×2 = 4x(3x² + 2)
2)
18a² + 2a
18a² :
18 / 2 = 9
9 / 2 no
9 / 3 = 3
3 / 3 = 1 finished
18a² = 2×3×3×a×a
2a :
2 / 2 = 1 finished
2a = 2×a
so, they have 2×a = 2a in common.
the GCF = 2a.
that means
18a² + 2a = 2a×9a + 2a×1 = 2a(9a + 1)
3)
25b⁴ + 30b³
25b⁴ :
25 / 2 no
25 / 3 no
25 / 5 = 5
5 / 5 = 1 finished
25b⁴ = 5×5×b×b×b×b
30b³ :
30 / 2 = 15
15 / 2 no
15 / 3 = 5
5 / 3 no
5 / 5 = 1 finished
30b³ = 2×3×5×b×b×b
so, they have 5×b×b×b = 5b³ in common.
the GCF = 5b³
that means
25b⁴ + 30b³ = 5b³×5b + 5b³×6 = 5b³(5b + 6)
You move up 7 units and down 4 units. You end at (-2, -2). Where did you start?
Answer:-2,-5
Step-by-step explanation:
7-4=3
You move 3 units up
You land on -2, -2
the higher units you move up, the higher the number gets to.
what are the different types of graphs; i know there’s constant speed, things like that. looking for a quick answer!!
A graph is made up of vertices, or points, and edges, or lines connecting those vertices.
Explain about the graphs and its types?Graphs come in a wide variety of forms in discrete mathematics.
These are a few of them:
A graph with no edges connecting all of its vertices is referred to as a null graph, sometimes known as an empty graph.A graph that has assigned weights, essentially numerical values, to each of its edges is referred to as a weighted graph.A disconnected graph is one in which not every vertex is always connected by the path of the edges.Simple graph: Any undirected graph where there is just one edge, or an edge from one vertex to itself, among each pair of vertices and there are no loops.Know more about the graph
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The correct question is-
what are the different types of graph.
What is the distance between the two points?
A. 4 units
B. 5 units
C. 6 units
D. 7 units
Answer:
6 units the answer is C. just see it
A car is traveling at a speed of 80 miles per hour. What is the car's speed in kilometers per hour? How many kilometers will the car travel in 4 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
answer is
512
Step-by-step explanation:
1.6x80=128
128x4=512
Which of the following sets of numbers could not represent the three sides of
a triangle?
{14, 24, 37}
{15, 30, 43}
{9, 21, 32}
{10, 19, 26}
The triangle that would not represent the three sides of a triangles is: {9, 21, 32}
How do determine this triangleWe can determine this through the use of the triangle rule. The rule tells us that the sum of the two sides of the triangle have to be greater than that of the other side.
With this in mind, we have that for each of this
14 + 24 > 37
15 + 30 > 43
9 + 21 < 32
10 + 19 > 26
Hence the third option does not fulfill the rule
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please help! the question is in the picture ! PLEEAASSEE
If the circle is dilated by a factor of 2, the equation of the circle is: C. (x + 3)² + (y - 2)² = 18.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.By critically observing the graph of this circle, we have the following parameters:
Radius, r = 3 units.Center, (h, k) = (-3, 2).By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - (-3))² + (y - 2)² = 3²
(x + 3)² + (y - 2)² = 9.
By dilating with a scale factor of 2, we have:
(x + 3)² + (y - 2)² = (9 × 2)
(x + 3)² + (y - 2)² = 18
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In which quadrant does the terminal ray fall with an angle of rotation of 6 radians?
The angle is in the fourth quadrant.
What do you mean by quadrant?
The coordinate system's two axes (the x-axis and y-axis) constitute a region called a quadrant. The quadrants are the four areas generated when the x- and y-axes cross at a 90-degree angle.
Coordinate values, also known as x- and y-values, are present in both positive and negative directions in these locations.
What is a quadrant circle?
Any one of the four regions is a quadrant when a circle is uniformly divided into two perpendicular parts. In fact, anything that can be divided into four equal halves is said to be made up of quadrants. Hence, a quadrant of a circle is one-fourth of the entire circle.
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The terminal ray strikes the fourth quadrant at a rotational angle of 6 radians.
What are quadrants?Two-dimensional Cartesian axes separate the plane into four infinite regions known as quadrants, each of which is bordered by two half-axes.
The coordinate system's two axes, the x-axis, and the y-axis constitute a region called a quadrant.
The quadrants are generated when the two axes, the x-axis, and the y-axis, cross at a 90-degree angle.
These areas include coordinates or positive and negative values of the x- and y-axes.
The terminal ray falls at a rotational angle of 6 radians in the fourth quadrant.
Therefore, the terminal ray strikes the fourth quadrant at a rotational angle of 6 radians.
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Rose has made this scale drawing of her house. If her house actually 56 feet wide, then scale of her drawing is
If her hοuse actually 56 feet wide, then scale οf her drawing is scale = 56 feet / (drawing width)
What is the slοpe?The slοpe is a mathematical cοncept that refers tο the steepness οf a line. It is cοmmοnly denοted by the letter "m" and can be calculated using the fοrmula:
slοpe (m) = (change in y) / (change in x)
Withοut having the actual measurements οf the drawing, we cannοt determine the scale.
Tο find the scale οf a drawing, yοu need tο knοw the actual measurements οf the οbject being drawn as well as the cοrrespοnding measurements in the drawing. Fοr example, if yοu knοw that the actual width οf Rοse's hοuse is 56 feet and the width οf the hοuse in the drawing is 8 inches, yοu can determine the scale by using the fοllοwing fοrmula:
scale = actual width/drawing width
Using this fοrmula with the given infοrmatiοn, we get:
scale = 56 feet / (drawing width)
Therefοre, we dο nοt have the drawing width, we cannοt calculate the scale.
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John can mow a lawn in 90 minutes. Bullwinkle can mow the same lawn in 60 minutes. How long does it take for both John and Bullwinkle to mow the lawn if they are working together? Express your answer as a reduced fraction.
Answer:
32
Step-by-step explanation:
On bonfire night at sleepaway camp, Lily's counselor puts marshmallows, graham crackers, and several chocolate bars on the snack table. Lily uses
3/4
of a chocolate bar to make herself a s'more. Now 3 1/4
chocolate bars remain on the table.
Which equation can you use to find the number of chocolate bars b the counselor puts on the table?
3/4b = 3 1/4
b - 3/4 = 3 1/4
b + 3 1/4 = 3/4
b + 3/4 = 3 1/4
Answer:
The correct equation is:
b - 3/4 = 3 1/4
Explanation:
Lily used 3/4 of a chocolate bar, so the remaining chocolate bars can be found by subtracting 3/4 from the total number of chocolate bars b:
b - 3/4 = remaining chocolate bars
The problem tells us that there are 3 1/4 remaining chocolate bars, so we can substitute this value in the equation and solve for b:
b - 3/4 = 3 1/4
b = 3 1/4 + 3/4
b = 4
Therefore, the counselor put 4 chocolate bars on the table.
Integers descending order
1.) +8,-4,-6,-2,+3
2.)+10,-11,-13,+8,+9
3.)-15,+5,+8,-11,-10
4.)+6,+9-14,-12,+1
5.)-10,+3,-4,+4,-3
Jenna's Tea Shop has caffeinated tea and decaffeinated tea. The tea shop served 36 caffeinated teas and 39 decaffeinated teas. What percentage of the teas served were caffeinated?
According to the solution we have come to find that, 48% of the teas served were caffeinated.
What is percentage?A percentage is a way of expressing a proportion or a fraction as a number out of 100. The symbol used for percentage is the "%" sign. For example, if you have 10 apples and you want to express how many of them are red, you can say that 20% (or 2 out of 10) of the apples are red.
To find the percentage of caffeinated teas served, we need to divide the number of caffeinated teas by the total number of teas served, and then multiply by 100 to get the answer as a percentage.
Total number of teas served = 36 + 39 = 75
Percentage of caffeinated teas served = (36/75) x 100%
= 48%
Therefore, 48% of the teas served were caffeinated.
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A local doctor wants to test the effects of a new diet she decided to lower triglycerides on 10 randomly selected patients. The triglyceride level of each patient is checked twice, once before they start the diet, and again at three weeks after that time. The results are in the table below, (the photo). All data is in milligrams per deciliter (mg/dL).
The Null and alternative hypothesis for the study are (in the photo)
! Thank you , 100 points!!
A) test statistic T equals -1.952; P value, 0.0414. There is sufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.
B) test statistic, T equals 0.3619. P value, 0.6392. There is insufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.
C) test statistic, T = -1.952; p value, 0.0509. There is sufficient evidence to reject the no hypothesis of no difference between a triglyceride test levels.
D) test statistic T equals 0.3651. P value, 0.6425. There is insufficient evidence to reject the null hypothesis of no difference between the triglyceride test levels.
The correct answer is A) test statistic T equals -1.952; P value, 0.0414.
How would you define hypothesis?An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true. In the scientific process, the hypothesis is developed before any pertinent research—aside from a basic background review—has been conducted.
The null hypothesis that there is no difference between the triglyceride test levels is sufficiently refuted by the available data.
With 9 degrees of freedom and a significance threshold of 0.05, this can be ascertained by comparing the derived test statistic (T) with the critical value of t from the t-distribution table. We reject the null hypothesis if the estimated T value is in the rejection zone (i.e., T value is smaller than the critical value of t).
The computed T value in this instance is -1.952, which is in the rejection region (i.e., less than the critical value of t of -1.833). Hence, we get to the conclusion that there is enough data to imply that the new diet has an effect on lowering triglyceride levels and reject the null hypothesis that there is no difference between the triglyceride test levels.
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From his tent, Mario can see a tree 120m away on a bearing of 056°. He can also see a rock that is due east of his tent and due south of the tree.
a) Sketch and label a diagram showing this information.
b) Hence find the distance from the rock to the tree.
The distance from rock to tree is approximate 99.48 m.
What is bearing in navigation?The bearing in navigatiοn refers tο the path between twο pοints, calculated in clοckwise rοtatiοns arοund nοrth. It is frequently emplοyed tο indicate the directiοn οf travel between twο places οr the οrientatiοn οf a landmark with respect tο a ship οr aircraft.
The azimuth, which is the angle between a reference directiοn (οften nοrth) and the directiοn tο an οbject οr pοint, is distinct frοm the bearing.
A. check the attachment given.
B. Let the distance from rock to tree be = H meter
Now, [tex]$ \rm \frac{Sin(056^{\circ})}{1} = \frac{H}{120}[/tex]
H = Sin(056°) × 120
H = 99.48 m
Thus, The distance from rock to tree is 99.48 m.
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What is the perimeter of the decks?
The perimeter of the decks is 120 feet
What is perimeter :
Perimeter is a mathematical term that refers to the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.
Property of circles:The property of circles states that "the tangents drawn from the same point on a circle are equal in length". It means that if two tangent lines are drawn from an external point to a circle, the length of both tangents will be equal.
Here we have
Tangents QR and QV from point Q
Tangents RS and ST from point S
Tangents VU and UT from point U
As we know,
The tangents drawn from the same point on a circle are equal in length
=> Tangent QR = QV --- (1) from point Q
=> Tangent RS = ST ----- (2) from point S
=> Tangent VU = UT ----- (3) from point U
From the figure,
The perimeter of decks = QR + RS + ST + TU + UV + VQ
From (1) (2) and (3)
=> QR + ST + ST + UV + UV + QR
=> 2QR + 2UV + 2RS
From the figure,
=> 2(24 ft) + 2(26 ft) + 2 (36 - 26) [ ∵ ST = US - TU ]
=> 48 ft + 52 ft + 20 ft
=> 120 ft
Therefore,
The perimeter of the decks is 120 feet
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Which ones would equal to less than 300 square centimeters
The circles having an area less than 300 square centimeters are;
Option A: A circle with a radius of 9. 5 centimeters
Option D: A circle with a diameter of 15 centimeters
How to determine the circlesIt is important to note the formula for calculating the area of a circle is expressed as;
A = πr²
Such that the parameters are;
A is the area of the circle.π takes the constant value of 3.14 or 22/7r is the radius of the circleFrom the information given, we have that;
radius = 9.5 centimeters
Substitute the value
Area = 3.14 × (9. 5)²
Area = 283. 4 cm²
For diameter of 15 centimeters
Radius = 7.5 centimeters
Substitute the values
Area = 3.14 × (7.5)²
Area = 176. 6 cm²
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I need help with my homework
Therefore , the solution of the given problem of function comes out to be y grows by 19/4 units for every unit increase in x.
Describe function.There will be questions on design, mathematics, each subject, and both real expression and imagined locations on the midterm exam. a list of the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input. Every mailbox also has a specific address, which may be an enclave, a neighborhood.
Here,
The slope of the equation
=> y = 19/4x - 19 is 19/4.
This implies that y grows by 19/4 units for every unit increase in x.
You would need to be familiar with the expression or
graph of the other function in order to compare the rate of change with it.
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Cuántos meses son 44 semanas
Answer:
Step-by-step explanation:
Para convertir 44 semanas a meses, debemos saber cuántas semanas hay en un mes. El número de semanas en un mes no es exacto, pero generalmente se considera que hay alrededor de 4.33 semanas en un mes (ya que el año tiene aproximadamente 52 semanas y 12 meses).
Entonces, para calcular cuántos meses hay en 44 semanas, podemos dividir 44 por 4.33:
44 semanas / 4.33 semanas por mes = 10.16 meses (aproximadamente)
Por lo tanto, 44 semanas equivalen aproximadamente a 10.16 meses.
1 is subtracted from the square of a number.
Represent the following sentence as an algebraic expression. Where “ a number” is the letter X. You don’t need to simplify. Please help.
The sentence represented as an algebraic expression is x² - 1
What are algebraic expression?Algebraic expressions can be defined as a mathematical expression that consists of terms, variables, constants, coefficients and fractions.
Also, these algebraic expressions are identified with arithmetic or mathematical operations. These operations are;
AdditionMultiplicationSubtractionBracketParenthesesDivisionFrom the information given, we have that;
Let the number be x
If 1 is then subtracted from the square of a number.
Fiirst, the square of the number is x²
This is represented as;
x² - 1
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If triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6) and you perform the following transformations, where will B' be?
Reflection over the y-axis, rotation 90° clockwise, and translation (x + 2, y - 1)
The coordinates of B' after the sequence of transformations are given as follows:
B'(3,-4).
How to obtain the coordinates of B'?The coordinates of B are given as follows:
B(-3,1).
After a reflection over the y-axis, the x-coordinate of B is exchanged, hence:
B'(3, 1).
The rule for a 90º clockwise rotation is that (x,y) becomes (y,-x), hence the coordinates of B' after the 90º clockwise rotation are given as follows:
B'(1, -3).
The translation (x + 2, y - 1) means that 2 is added to the x-coordinate while 1 is subtracted from the y-coordinate, hence the final coordinates of B' are given as follows:
B'(3,-4).
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If triangle ABC has points A(2, -4), B(-3, 1), and C(-2, -6) and you perform the following transformations, B' would be at B' (3, -4).
What is a rotation?In Geometry, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).
By applying a reflection over the y-axis to the coordinate of the given point B (-3, 1), we have the following coordinates:
Coordinate B = (-3, 1) → Coordinate B' = (-(-3), 1) = (-3, 1).
Next, we would apply a rotation of 90° clockwise as follows;
(x, y) → (y, -x)
Coordinate B' = (-3, 1) → Coordinate B' = (1, (-3)) = (1, 3)
Finally, we would apply a translation (x + 2, y - 1) as follows:
Coordinate B' = (1, 3) → (1 + 2, 3 - 1) = B' (3, 2).
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In this unit, you learn about linear functions and graphing lines in the coordinate plane. Linear functions are used in businesses, construction, and planning cities. The slope of a line determines its steepness. Why do you think a horizontal line (flat) has zero slopes, but a vertical line (straight up and down) is considered to have no slope. What's the difference between zero slope and no slope?
Answer:
Step-by-step explanation:
In math, slope is used to describe the steepness and direction of lines. ... You can determine the slope of a line from its graph
ABCD Is a rectangle that represents a park.
The lines show all the paths in the park.
The circular path is in the centre of the rectangle and has a diameter of 15m.
Calculate the shortest distance from A to C across the park,using only the lines shown.
The circumference's shortest distance between points A and C is 102.91m.
What is a rectangle?A rectangle is a quadrilateral with four right angles in the Euclidean plane.
It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal.
A square is a rectangle with four equally long sides.
As a result, a square is a particular form of rectangle since it has rectangles with equal-length sides.
So, we know that:
AC = 80 m
CD = 50 m
Apply the Pythagorean theorem to the right triangle using ADC.
AC = √AD² + CD²
AC = √80² + 50²
AC = 94.34m
The shortest path through the park from point A to point C must only follow the lines depicted in the diagram.
Hence, we must deduct AC by 15 meters in diameter.
94.34m - 15m = 79.34m
The shortest distance is 79.34 miles plus one-half a circle's circumference.
As the circle's diameter is 15 meters, the radius is 15/2 = 7.5m.
The circumference would be:
2*π*r = 47.14m
The half circumference would be:
47.14/2 = 23.57m
Then,
79.34m + 23.57m = 102.91m
Therefore, the circumference's shortest distance between points A and C is 102.91m.
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Evaluate the following expressions.
Accοrding the given expressiοns this is the right answer (1/2)⁵ = 1/2 × 1/2 × 1/2 × 1/2 × 1/2 = 1/32
(1/5)³= 1/5 × 1/5 × 1/5 = 1/125
What is an expressiοn?In mathematics, an expressiοn is a cοmbinatiοn οf numbers, variables, and οperatοrs that represents a mathematical relatiοnship οr fοrmula. It can include numbers, variables, and mathematical οperatοrs such as additiοn, subtractiοn, multiplicatiοn, divisiοn, expοnents, and rοοts. Fοr example, 2x + 3y is an expressiοn that includes the variables x and y, and the οperatοrs additiοn and multiplicatiοn. Expressiοns can be simplified, evaluated, οr used tο represent mathematical relatiοnships.
a) (1/2)⁵ = 1/2 × 1/2 × 1/2 × 1/2 × 1/2 = 1/32
b) (1/5)³ = 1/5 × 1/5 × 1/5 = 1/125
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maria scored points 92 in 4 games how many points will it be in 17 games
Answer:
The answer to this question is 391 points will be scored in 17 games. to find this answer you divide 94 by 4 to find the total points per single game, then multiply that by 17. in this case is is 92 divided by 4 = 23 then 23 X 17 = 391
find the area of this shape (4.5 ft 3 ft 3ft)
Answer:assuming its a rectangle its 13.5
Step-by-step explanation: L x H = Area
Find the surface area obtained by rotating the curve [tex]y=4e^2^x[/tex] on the interval x=0 to x=2 about the x-axis
Farrah borrowed $155 from her brother. She has already paid back $15. She plans to pay back $35 each month until the debt is paid off. Which describes the number of months it will take to pay off the debt? Select three options. x + 15 + 35 = 155 35 x + 15 = 155 35 x = 155 minus 15 It will take 8 months to pay off the debt. It will take 4 months to pay off the debt.
Answer: 3. 35x + 15 = 155
Step-by-step explanation:
35 x 4 = 140
140 + 15 = 155
You deposit $1000 each year into an account earning 8% compounded annually.How much will you have in the account in 10 years?
Answer:
If you deposit $1000 each year into an account earning 8% compounded annually, you will have $13,366.37 in the account in 10 years. Using the compound interest formula A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years, we can calculate the amount. Plugging in the values, we get A = 1000(1 + 0.08/1)^(1*10) = $2,159.15. Therefore, the total amount after 10 years will be $13,366.37, which is the sum of the principal and the interest earned.
Given,
Annual deposit = $1000
Rate = 8% compounded annually
Time(n) = 10 year
Amount = ?
As we know the formula ,
Amount = P(1+r/100)ⁿ
Amount = 1000(1+8/100)¹⁰
Amount = 1000(1+0.08)¹⁰
Amount =1000(1.08)¹⁰
Amount = 1000 × 2.15892
Amount = $2158.92
Hence, amount in 10year will be $2158.92