When the product of a fraction and a factor is greater than the factor, it means that the fraction is greater than 1.
Why is this true of fractions ?Due to the principles of multiplication, when multiplying a value greater than 1 with a given amount, the product will be larger than the original number. To provide an example, if we multiply 5 by 2, the result will be 10, which is greater than 5.
By extension, if we multiply a fraction with a factor that's greater than 1, the resulting product will be greater in size as compared to the initial quantity. For instance, when we calculate 1/2 multiplied by 3, the outcome is 3/2, which surpasses the worth of 1/2. Hence, it can be deduced that any result which exceeds its own source was obtained through multiplication by value greater than 1.
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There are 8 blue marbles, 6 red marbles, 2 green marbles and 4 black marbles in a box. What is the probability that the marble is not green?
A) 92
B) 10
C) 85
D)20
We have 20 marbles in the bag. The probability of a marble that is not green is 20/20.
So the probability of the randomly that the marble is not green is 20/20 or just 20.
Jerome buys 4 pints of milk for the baby goats and has pint of milk left from yesterday. If each baby goat gets pint of milk, how many goats can Jerome
feed?
Jerome can feed (blank) baby goats.
Answer:
5 baby goats
Step-by-step explanation:
4 + 1 = 5 pints total
each baby goat gets 1 pint
Find the length of the third side. if necessary, round to the nearest tenth of 1 and 3
Using the Pythagorean theorem we know that the third side is 15 units.
What is the Pythagorean theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.
The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a² + b², are equal to the squares on the legs.
To determine c, use the Pythagorean Theorem as follows:
a² + b² = c²
9² + 12² = c²
81 + 144 = c²
225 = c
c² = 225
c = √(225)
c = 15
Therefore, using the Pythagorean theorem we know that the third side is 15 units.
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Correct question:
Find the length of the third side. If necessary, round to the nearest tenth.
12 and 9
If someone wants to call Havana, Cuba from the United States (US) begins with US three-digit exit code 011 followed the two-digit country code for Cuba is 53, followed by the county code of Havana is 7 and finally by seven-digit local telephone numbers. But this seven-digit local telephone numbers cannot begin with 0. How many different telephone numbers are possible?
Answer:
9000000 different numbers---------------------------
The number is basically a combination in the form of:
abcdefg, where a can't be zero but the rest of the digits have no restrictionsHence the possible digits:
a = 9, b,c,d,e,f,g = 10So possible telephone number combinations:
9*10⁶ = 9000000Help please
Expand the logarithm as much as possible
logy^10
Answer: 2.303
Explanation: In image
Line n is perpendicular to the x-axis and passes through the point (–3,–7).
Write the equation for line n.
What is the slope of line n?
The equation for line n that is perpendicular to the x-axis and passes through the point (–3,–7) is x = -3, and its slope is undefined.
Since line n is perpendicular to the x-axis, it is parallel to the y-axis. Therefore, its slope is undefined since the y-axis is a vertical line with no defined slope.
To write the equation for line n, we know that the y-coordinate of every point on the line will be constant since the line is parallel to the y-axis. We also know that the line passes through the point (-3,-7), so we can write the equation as:
x = -3
This means that for any value of y, the x-coordinate will always be -3. Graphically, this represents a vertical line passing through the point (-3,-7) and parallel to the y-axis.
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please hurry thats all i ask
The value of A, B, C,D are 33, 36,25 and 16 respectively
What is word problem?A word problem is a math problem written out as a short story or scenario. We use this word problem to solve the unknowns.
The total number of students is 60 and 24 students prefer volley ball. therefore the number of students that prefer basketball = 60-24 = 36 students
Since 11 student are girls that prefer basketball, therefore the number of boys that prefers basketball = 36-11 = 25
C = 25
and B = 36
55% of the students are boys, therefore the number of boys = 55/100 × 60 = 33
A = 33
therefore the number of boys that prefer volley ball= 33-25 = 8
Number of girls = 60-33 = 27
therefore number of girls that prefer volley ball = 27-11 = 16
D= 16
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factor the expression
7x^2+12x+5
Hi again
I did it wrong
I'm here to redeem
When you have to factor these types of equations, you have to use a method called slide divide and bottoms up.
First you have to slide the a value to the end and mutiply with the c value so it is easily factorable
x^2+12x+35
Then you solve it like always
(x+7)(x+5)
Now, don't forget our buddy 7
7 is coming back
we divide 7 by 7 and 5 by 7
so
(x+1)(x+5/7)
7 has to move
So we move the 7 to the front
Therefore the answer is
(x+1)(7x+5)
If you have questions please ask me
Answer:
(7x + 5) (x + 1)
Step-by-step explanation:
7x² + 12x + 5
general form ax² + bx + c
a = 7
b = 12
c = 5
we have to find number that, if
... × ... = a . c = 7 . 5 = 35
... + ... = b = 12
and it would be
7 × 5 = a . c = 7 . 5 = 35
7 + 5 = b = 12
7x² + 7x + 5x + 5
= 7x (x + 1) + 5 (x + 1)
= (7x + 5) (x + 1)
#CMIIWFind the slope of the tangent to f(x)=x^2 at the point (3,9).
Answer:
f'(x) = 2x, so f'(x) = f'(3) = 2(3) = 6.
A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The four walls and one additional vertical segment (to separate the regions) are made up of fencing, as shown below. A rectangular area consisting of two separated regions. A rectangular area consisting of two separated regions. If the farmer has 162 feet of fencing, what are the dimensions of the region which enclose the maximal area?
The dimensions of the region which enclose the maximal area will be 40.5 feet in length by width 27 feet.
How to find the dimensions of the areaGiven that the farmer has 162 feet of fencing, we will have:
2L + 3W = 162 feet
2L = 162 - 3W
L = 162 - 3W\2
L = 81 -3/2W Eqn 1
Given that the area of a rectangle is A = L × W we will call this equation 2
Now we substitute the first equation in the second one to give
A = (81 -3/2W) × W
A = 81W -3/2W²
When we take the derivative W will equal
81/3 = 27
Now we substitute in the second equation, we will have:
= 81 - 3/2(27)
= 81 - 40.5
= 40.5.
So the length will be 40.5 feet while the width will be 27 feet.
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Graph the linear equation y=-3x-1
Answer:
Step-by-step explanation:
y=-3x-1
format for formula:
y=mx+b
b=1 that is your y-intercept. where it hits the y-axis
m= -3 this is your slope [tex]\frac{rise}{run} =\frac{-3}{1}[/tex]
from a point you have, the y-intercept, you go down 3 (because of the negative in front of it), this is your rise,
and to the right 1, this is your run
solve all four parts
The rocket will hit the ground after 19.09 seconds.
How to calculate projectilea) The height of the rocket can be describe as:
h(t) = -16t² + 210t + 75
where
t = time in seconds
h(t) = height of the rocket in feet
b) To find the time at which the rocket reaches its maximum height, we need to find the vertex of the parabolic function. The vertex is given by the formula:
t = -b/(2a)
where
a = -16
b = 210
Substituting these values, we get:
t = -210/(2(-16)) = 6.5625 seconds
To find the maximum height, we substitute this value of t back into the equation for h(t):
h(6.5625) = -16(6.5625)² + 210(6.5625) + 75 = 690.625 feet
This means that the rocket reaches its maximum height of 690.625 feet after 6.5625 seconds.
c) We need to find the time interval during which the height of the rocket is greater than 721 feet. We set the height function h(t) greater than 721 and solve for t:
-16t² + 210t + 75 > 721
-16t² + 210t - 646 > 0
Solving for t using the quadratic formula, we get:
t < 2.975 or t > 14.038
Therefore, the rocket will be more than 721 feet above ground level between 0 and 2.975 seconds, and between 14.038 and infinity seconds.
d) To find the time at which the rocket hits the ground, we set h(t) equal to 0 and solve for t:
-16t² + 210t + 75 = 0
Solving for t using the quadratic formula, we get:
t = [tex]\frac{-b \± \sqrt{b^{2} - 4ac } }{2a}[/tex]
a = -16, b = 210, c = 75
t = [tex]\frac{-210 \± \sqrt{210^{2} - 4(16)(75) } }{2(-16)}[/tex]
t = [tex]\frac{-210 \± \sqrt{22225} }{-32}[/tex]
t = [tex]\frac{-210 \± 149}{-32}[/tex]
t = 2.53125 or t = 13.53125
Since the rocket was launched from the top of a 75-foot building, it will hit the ground after an additional time of:
t + 2.53125 = 5.09375 seconds or t + 13.53125 = 19.09375 seconds
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In congress, each of the 50 states is represented by 2 senators. If you choose a senator randomly, what is the probability that you will choose a senator that represents Georgia, South Carolina, and Florida?
The probability of picking a senator from at least one out of Georgia, South Carolina, or Florida is equal to 3/50 or 0.06.
How to find the probabilityDetermining the probability of selecting a senator from either Georgia, South Carolina, or Florida is merely a summation of the individual probabilities of drawing one from each state.
There are 100 senators in all and two representatives from each region, thus resulting in an addition of 2 x 50 which equals to 100 senators altogether.
Subsequently, selecting a senator from Georgia has a chance of 1/50,
1/50 + 1/50 + 1/50 = 3/50
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I need help please
here is the picture is about Row Ops
The given operation of the matrix is expressed as: -9y + 2z = 12
How to use Matrix to solve simultaneous Equations?Matrices can be used to solve simultaneous linear equations, by first writing them in matrix form and then pre-multiplying by the inverse. Note firstly that these simultaneous equations can be written as the following matrix equation. If you need convincing, multiply out the matrices.
The simultaneous equations formed by the matrix are:
x + 2y + z = -5
4y - 2 = 3
4x - y + 6 = -8
We are told to Multiply row 1 by -4 and this gives us:
-4x - 8y - 4z = 20
Adding it to row 3 gives us:
-9y + 2z = 12
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-(9-6)+(-1-2)-(3+4)+(5-6)=
Answer:
Step-by-step explanation:
-9+6-1-2-3-4+5-6
-3-3-7-1
-6-8
-14
Answer:
The answer is -14.
Step-by-step explanation:
-(9 - 6) + (-1 -2) - (3 + 4) + (5 - 6)
Subtract 6 from 9 to get 3.
-3 -1 -2 - (3 + 4) + 5 - 6
Subtract 1 from -3 to get -4.
-4 - 2 - (3 + 4) + 5 - 6
Subtract 2 from -4 to get -6.
-6 - (3 + 4) + 5 - 6
Add 3 and 4 to get 7.
-6 - 7 + 5 - 6
Subtract 7 from -6 to get -13.
-13 + 5 - 6
Add -13 and 5 to get -8.
-8 - 6
Subtract 6 from -8 to get -14.
-14.
The National Academy of Science reported in a 1997 study that 40% of research in mathematics is published by U.S. authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 40%. He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 130 recent articles published by reputable mathematics research journals and finds that 62 of these articles have U.S. authors. Does this evidence support the mathematics chairperson's claim that the percentage is no longer 40%? Use a 0.05 level of significance.
There is evidence to suggest that the percentage of mathematics research published by U.S. authors is no longer 40%.
How to test for the evidenceTo test the claim that the percentage of research in mathematics published by U.S. authors is no longer 40%, we can use a hypothesis test with a 0.05 level of significance.
Let p be the true proportion of mathematics research published by U.S. authors.
The null hypothesis is that p = 0.4, and the alternative hypothesis is that p ≠ 0.4 (two-tailed test).
sample proportion, x/n = 62/130 = 0.477
The test statistic for a two-tailed test is given by:
z = (0.477 - 0.4) / √(0.4 * 0.6 / 130)
= 2.41
Using a z-table, we find that the p-value for a two-tailed test with z = 2.41 is approximately 0.016.
Since 0.016 < 0.05
, we reject the null hypothesis and conclude that there is evidence to suggest that the percentage of mathematics research published by U.S. authors is no longer 40%.
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Fully factorise 27t² + 15t
Answer: 3t(9t + 5)
Step-by-step explanation:
Sure! Factoring involves breaking down an expression into simpler factors that, when multiplied together, give the original expression.
To factor 27t² + 15t, we can look for the greatest common factor (GCF) of the two terms. The GCF of 27t² and 15t is 3t, because both terms can be divided by 3t.
So we start by factoring out the 3t:
27t² + 15t = 3t(9t + 5)
Notice that we can check if the factorization is correct by using the distributive property to multiply the factor 3t by the expression inside the parentheses:
3t(9t + 5) = 3t(9t) + 3t(5) = 27t² + 15t
Therefore, 27t² + 15t can be fully factorized as 3t(9t + 5).
Suppose that the function h is defined as follows.
The graph of the piecewise function is given by the image presented at the end of the answer.
What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
All the five definitions of the function in this problem are constant, hence the graph will be composed by horizontal lines.
The definitions are given as follows:
y = -3 between x = -2.5 and x = -1.5.y = -2 between x = -1.5 and x = -0.5.y = -1 between x = -0.5 and x = 0.5.y = 0 between x = 0.5 and x = 1.5.y = 1 between x = 1.5 and x = 2.5.More can be learned about piece-wise functions at brainly.com/question/19358926
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Which of the following represents vector w = ❬–27, 35❭ in linear form?
w = –27i + 35j
w = 27i – 35j
w = –35i + 27j
w = 35i – 27j
Answer: w = –27i + 35j
Step-by-step explanation:
Element X decays radioactivity with a half-life in 10 minutes if there are 660 g of element X how long to the nearest 10th of a minute would it take for the element to decay to 58 g
Step-by-step explanation:
58 g = 660 g * ( 1/2)^n
58 / 660 = (1/2) ^n LOG both sides
-1.056 = n log 1/2
n = 3.508 half lives
3. 508 x 10 min = ~ 35.1 min
[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\dotfill & 58\\ P=\textit{initial amount}\dotfill &660\\ t=minutes\dotfill &t\\ h=\textit{half-life}\dotfill &10 \end{cases} \\\\\\ 58 = 660\left( \cfrac{1}{2} \right)^{\frac{t}{10}} \implies \cfrac{58}{660}=\left( \cfrac{1}{2} \right)^{\frac{t}{10}}\implies \cfrac{29}{330}=\left( \cfrac{1}{2} \right)^{\frac{1}{10}\cdot t}[/tex]
[tex]\log\left( \cfrac{29}{330} \right)=\log\left[ \left( \cfrac{1}{2} \right)^{\frac{1}{10}\cdot t} \right]\implies \log\left( \cfrac{29}{330} \right)=t\log\left[ \left( \cfrac{1}{2} \right)^{\frac{1}{10}} \right] \\\\\\ \cfrac{ ~~ \log\left( \frac{29}{330} \right) ~~ }{\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{10}} \right]}=t\implies 35.1\approx t[/tex]
Law if sines math question
Question: What are the two possible angles of a triangle with sides of 100 and 75 with a 40° as marked in the triangles above? Solution: Use the law of sines formula where the 75 length is opposite of 40°, and 100 is opposite of θ. Answer: The two possible angles for this triangle is 58.97° and 121.03°.
In the diagram, AB, BC and CD are three sides of a regular polygon F
A
a) Work out the size of angle y.
square polygon P
B
D
square
regular 12-sided polygon
y z
b) Work out the size of angle z.
c) What is the name of polygon P?
Answer:
Step-by-step explanation:
The size of each interior angle of the polygon is 4x+28 °
The value of x is 34 degree and y is 56 degree.
What is a Tangent?Tangents to circles are lines that cross the circle at a single point. Point of tangency refers to the location where a tangent and a circle converge. The circle's radius, where the tangent intersects it, is perpendicular to the tangent. Any curved form can be considered a tangent.
here, we have,
We have, BOA is an isosceles triangle.
< CBO = 90°
So, < DBO = 90 - 56
<DBO = 34
and, <ODB = 34°
Now, let the angle ODB be x
As, from the figure < EBD is also 90°
So, <y = 180 - (90+34) (Angle sum property)
<y = 56
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complete question:
Work out the size of angle x and work out the size of angle y
A movie theater considers upgrading to offer luxury seating. The manager randomly surveys 1,200 resident who live within 10 miles of the theater. What is the sample in the situation
Please it’s due in 2min
In this circumstance, the sample consists of 1,200 inhabitants living within a ten-mile radius of the movie theater that were selected for random deliberation by the overseer.
What is a sample?Samples are frequently utilized to gain information concerning a larger population through the study of a single set of individuals or objects. The aim of selecting a sample is to inspect the populace by delving into a representative, relatively small group.
Surveys, polls, and experiments often utilize samples to make evidence-based inferences regarding the target population. For exact and dependable results, an instance should be randomly chosen, accurately mirroring those present in the whole population so as to reduce prejudice and fully optimize the evaluation.
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Which fraction is a multiple of 1/9?
Unit fractions are the fraction in which the value of numerator is 1. The multiple of the given fraction are,
1/9 = 2/9, 3/9, 4/9,5/9 ......so on.
Here, we have,
To find the multiple of the fraction 1/9 we need to know about the multiple of fraction.
We have,
Multiple of fraction is the number which is n times of the original function. Here can be any whole or fraction number.
The given number in the problem is the fraction number which is,
The above number is the unit fraction.
Unit fraction-
Unit fractions are the fraction in which the value of numerator is 1.
The multiple of unit fraction is in times the original function. For the given fraction the multiple fraction can be given as,
1/9 = 2/9, 3/9, 4/9,5/9 .......so on.
Hence the multiple of the given fraction are,
1/9 = 2/9, 3/9, 4/9,5/9 ......so on.
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Please help me i dont get this. PLEASE I GIVE 20 points. And I give BRAINLIEST
Answer:
A B
Step-by-step explanation:
Is between A or B
Answer: A yes
Step-by-step explanation:
The answer is A because they divided both sides by 5
Not by variable and they didn't add/sub
This equations are equivalent
Water flows from the bottom of a storage tank. After t minutes, the water is flowing at a rate of r(t)=200-4t liters per
minute, where 0≤t<50. Find the amount of water (in liters) that flows from the tank between the 7 minute mark and the
37 minute mark.
The total amount of water that flows from the storage tank between the 7 minute mark and the 37 minute mark is 720 liters.
What is rate of flow?The amount of fluid that moves through a pipe or other container over a given amount of time.
The amount of water that flows from the storage tank between the 7 minute mark and the 37 minute mark can be calculated using the equation for the rate at which the water is flowing.
Given that the rate at which the water is flowing at time t is r(t)=200-4t liters per minute and that 0≤t<50, the total amount of water that flows from the storage tank between the 7 minute mark and the 37 minute mark can be calculated as follows:
Total amount of water = ∫r(t)dt
= ∫(200 - 4t)dt
= (200t - 4t²)
= (200(37) - 4(37²)) - (200(7) - 4(7²))
= 1924 - 1204
= 720 liters
The rate of flow decreases linearly with time, which means that the total amount of water flowing from the tank at any given time is equal to the area under the graph of the rate of flow.
This means that the total amount of water that flows from the tank between the 7 minute mark and the 37 minute mark can be calculated by integrating the rate of flow function over the given time interval.
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Electronics store reduced price of tv From $900 to $837
The percentage decrease of the TV from $900 to $837 is 7%
Percentage decreaseOriginal price of TV = $900New price of TV = $837Percentage decrease = Difference in price / original price × 100
[tex]=\dfrac{(900-837)}{900} \times 100[/tex]
[tex]=\dfrac{63}{900} \times 100[/tex]
[tex]= 0.07 \times 100[/tex]
[tex]= 7\%[/tex]
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Complete question-
An electronics store reduced the price of a TV from $900 to $837. What was the percent of decrease?
helpppp helppppp helppppp
Answer:
No, i do not believe i have learned this yet so good luck bestiee
Evaluate this limit without using L'Hopital's Rules
The limit [tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}}[/tex] without using L'Hopital's Rules has a value of 1
Evaluate this limit without using L'Hopital's RulesFrom the question, we have the following parameters that can be used in our computation:
[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}}[/tex]
By substitution, we have
[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = \frac{1}{3^{}\infty}+3^{\frac{1}{\infty}}[/tex]
So, we have
[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = 0+3^0[/tex]
Evaluate the exponents
[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = 0+1[/tex]
Evaluate the sum
[tex]\lim _{x\to \infty \:}\frac{1}{3^x}+3^{\frac{1}{x}} = 1[/tex]
Hence, the solution is 1
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Given: mzA+m/B=m/B + mzC
Prove: m₂C=m/A
Write a paragraph proof to prove the statement.
We have proven that m∠C = m∠A.
We have,
We are given that m∠A + m∠B = m∠B + m∠C.
We want to prove that m∠C = m∠A.
Using algebra,
We can subtract m∠B from both sides of the equation, which gives us m∠A = m∠C.
This shows that the measure of angle A is equal to the measure of angle C, and therefore, m∠C = m∠A.
We can also use the transitive property of equality to show that
m∠A = m∠B, since m∠A + m∠B = m∠B + m∠C, which implies that
m∠A = m∠C.
Therefore,
We have proven that m∠C = m∠A.
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