The number of buttons on each card from Elaine's grandmother is given as follows:
7 buttons.
How to obtain the number of buttons on each card?The number of buttons on each card is obtained applying the proportions in the context of this problem.
Elaine sorted the buttons into 6 piles, putting 8 buttons in each pile, hence the total number is given as follows:
6 x 8 = 48.
Elaine had 6 buttons, hence the number donated is given as follows:
48 - 6 = 42.
6 cards were donated, hence the number of buttons in each card is given as follows:
42/6 = 7.
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A certain compound has a half-life of 5 days. Write and use an exponential decay function to find the amount
of compound remaining from a 84-ounce sample after seven weeks.
The amount of compound remaining from a 84-ounce sample after seven weeks is 4.32 ounces.
How to calculate the half life of the substanceGiven a half-life of 5 days and a sample of 84 ounces, the exponential decay function can be represented as:
A(t) = 84 * (1/2)^(t/5)
Where A(t) represents the amount of the compound remaining after t days.
To find the amount of compound remaining after 7 weeks
7 weeks * 7 days/week = 49 days,
we can substitute t = 49 into the function:
A(49) = 84 * (1/2)^(49/5)
A(49) = 84 * (1/2)^9.8
A(49) ≈ 4.32 ounces
So, the amount of the compound remaining after 7 weeks would be approximately 4.32 ounces.
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use a=8 and b=24 too work out these expressions.
The results of the expressions are;
1) 192
2) 3
3) 1024
How do we work out the expressions?
We have to note that when we say that there is an expression, the implication of that is that the equality sign is missing in the mathematical statement as it has been written.
We know that;
1) a*b
a=8
b=24
8*24
= 192
2) b/a
b/a
b=24
a=8
24/8
= 3
3) (a+b)^2
a=8
b=24
(8+24)^2
= 1024
This is the way that we can be able to obtain all the expressions that we have in the question that is shown here.
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Missing parts;
Use a = 8 and b = 24 to work out the value of these expressions. b) ab c) b/a d) (a + b)^2
Analyzing the Intervals of a Function A 2-column table with 7 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries 15, 0, 3, 0, negative 3, 0, 15. Predict which statements are true about the intervals of the continuous function. Check all that apply. f(x) > 0 over the interval (−, 3). f(x) ≤ 0 over the interval [0, 2]. f(x) < 0 over the interval (−1, 1). f(x) > 0 over the interval (–2, 0). f(x) ≥ 0 over the interval [2, )
The predicted interval for the given function is, f(x) ≥ 0 over the interval [-1,1]. So Option C is correct
What are functions?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
Vertical line test:-
Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.
If we get more images then it will not be a function.
For example, let us take, y² = 4ax
y = ±√4ax
For single value of x we get two values of y
Hence, it will not be a function.
Given that,
The ordered pairs of the given function
(-3,15), (-2,-5), (-1,0), (0,5), and (1,0).
It can be observed from the values of f(x) with respect to x, that the function reaches zero at x = -1, then then reach up to 5 at x = 0 and then again reaches zero at x = 1
Hence, the value of f(x) remains positive within the interval of [-1,1].
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The diagram shows the graph of y=2x+c. Where c is a constant find the value of K.
Answer:
Step-by-step explanation:
The graph of y = 2x + c is a straight line with a slope of 2 and a y-intercept of c. The value of k cannot be determined from the equation alone, as it depends on the value of the constant c. To find the value of k, you would need additional information such as the coordinates of a point on the line or the x and y values that correspond to a specific k.
Can someone help please?
Note that where Tom Harris is 24 years old and he wishes to purchase a $7,000 value 10-year term insurance, his annual premium will be: $290.5.
Gross premiums written in the insurance sector are the sum of direct and assumed premiums written before subtracting ceded reinsurance. Direct premiums written are the premiums on all policies issued by the company's insurance subsidiaries throughout the fiscal year.
To compute Tom's insurance premium we must use the information given as well as the table above:
Given:
Tom's Age = 24 years
Value of Insurance Cover Requested = $7,000
Type of Insurance cover requested = 10-Year Term
The rate for the Type of Insurance Cover requested: Since he 24 and wants a 10-year term, the rate applicable from the table is; 4.15%
Thus, his annual premium = 7000 * 4.15%
= 29050/ 100
= $290.5
Thus, Tom Harris' annual insurance premium is: $290.5
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identify the slope of and y-intercept of the line -2x +5y=-30
Choose the number (X) that should come next in this series (1 4 9 16 X)
Answer:
25 is X
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
1+3=4
4+5=9
9+7=16
16+9=25
3+2=5
5+2=7
7+2=9
On saturday, dylan earned $100 for cleaning a local business. He also walked dogs to earn money, charging $12.50 for each dog he walked. In total, Dylan earned more than $210 on saturday. How many dogs could he have walked on saturday? Write an in inequality
The correct inequality that represent the dogs could he have walked on Saturday is,
⇒ 100 + 12.50x > 210
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
On Saturday, Dylan earned $100 for cleaning a local business.
And, He also walked dogs to earn money, charging $12.50 for each dog he walked.
Now, Let number of dogs = x
Then, We get;
The correct inequality that represent the dogs could he have walked on Saturday is,
⇒ 100 + 12.50x > 210
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Find the smaller of two
consecutive integers, x, if the
sum of the smaller and the
larger is 15. Write an equation
and solve.
From 2008 through 2012, the function Y equals 0.3 5X +9.6 can be used to approximate the movie box office in billions of dollars in region A, while the function Y equals 0.9 X +6.5 approximates the box office in region B. For both regions, X represents the number of years since 2008. Hey. If he’s trying to continue, predict the year in which the region a box office and region Vbox office will be the same. Be. Use these equations to project the box office for originate and read and beer for the year 2018
Answer:
9.818 years after 2008
Step-by-step explanation:
Y_A = 0.35 * X + 9.6
Y_B = 0.9 * X + 6.5
Equal in year X = (Y_B - Y_A) / (0.35 - 0.9) = (6.5 - 9.6) / (-0.55) = 9.818 years after 2008
X = 9.818 + 2008 = 2018.818
Y_A = 0.35 * (2018 - 2008) + 9.6 = 14.3 billion
Y_B = 0.9 * (2018 - 2008) + 6.5 = 15.3 billion
Find the distance between the two points. Show your work.
Answer:
Below
Step-by-step explanation:
Points (-3,5) and ( 3,1)
distance d can be found using the distance formula ( modified Pyhtagorean theorem)
d^2 = ( x1-x2)^2 + ( y1-y2)^2
d^2 = ( -3 -3)^2 + ( 5-1)^2
d^2 = 36 + 16
d^2 = 52
d = sqrt(52) = 2 sqrt(13)
Use what you know about square roots to complete problems 7-10.
7. When does a quadratic equation in the form ax + b = c have only complex solutions?
8. The area of a square with sides of length s is given by s. The area of a square is 40 square
centimeters. What is the length of one side of the square?
9. The area of a circle with radius r is given by mr. The area of a circle is 60 square millimeters.
What is the radius of the circle?
10. The surface area of a cube with sides of length a is given by 6a². If the surface area of a cube
is 200 square inches, what is the length of one side of the cube?
X2 + 7x + 10 = 0 has roots -5 and -2, the answer.
How to Find the roots of the equation x2 + 7x + 10 = 0?x2 + 7x + 10 = 0 is a mathematical equation.
x2 + 5x + 2x + 10 = 0 [dividing the middle term] is another way to express the aforementioned equation.
After factoring 2 from the second term of the expression, 2x + 10, and x from the first term of the expression, (x2 + 5x), the expression may be broken down into its constituent parts.
We obtain the factorized equation as follows: x (x + 5) + 2 (x + 5) = 0.
Now we can calculate (x + 2) (x + 5) = 0 by utilizing the distributive property.
The result of separately equating both terms with 0 is,
The equation x2 + 7x + 10 = 0 has -5 and -2 as its roots.
The Complete Question is :
How to Find the roots of the equation x2 + 7x + 10 = 0?
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Evaluate uv+12 / w if u=3, v=4, and w=6.
Answer: 4
Step-by-step explanation:
3x4+12
------------ (over)
6
12+12
---------
6
24
----- = 4
6
I need to write an equivalent expression that is a product for:
[32]x^{2} + 48x
Step-by-step explanation:
The equivalent expression in the form of a product is:
(8x) * (4x + 6)
Elisa starts baking a pie at 11:25 a.m.
The pie needs to bake for 45 minutes.
What time will the pie be done?
Answer:
12.10 pm
Step-by-step explanation:
just take the 45 minutes she uses to bake and add to the time she starts
11.25 a.m+45
12.10 pm
Pls help explain how to do this I need help
[(4r²t)³]²
Answer:
To solve the expression [(4r²t)³]², you need to follow the order of operations (PEMDAS):
Calculate the expression inside the outermost parenthesis first: (4r²t)³ = (4 * r^2 * t)^3, where r and t are variables.
Raise the result to the power of 3: (4 * r^2 * t)^3 = 64 * r^6 * t^3.
Raise the result to the power of 2: (64 * r^6 * t^3)^2 = 4096 * r^12 * t^6.
So, [(4r²t)³]² = 4096 * r^12 * t^6.
Step-by-step explanation:
(Geometry) I need help fast on questions 4 and below!
The measure of angle 4 is 90 degrees
How to determine the measure of the angle 4?From the question, we have the following parameters that can be used in our computation:
The rectangle
Also, we have
<5 = 12x -3
<6 = 10x + 9
Angles 5 and 6 add up to 90
So, we have
12x - 3 + 10x + 9 = 90
Evaluate the like terms
22x = 84
So, we have
x = 3.82
The angles in a triangle add up to 180
So, we have
<4 + 12 * 3.82 - 3 + 10 * 3.82 + 9 = 180
Evaluate
<4 = 90
Hence, the measure o this angle is 90 degrees
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Why does it take 3 copies of 1/6 to show the same amount as 1 copy of 1/2? Explain your answer in works and pictures.
Answer:1/6 can be represented as a fraction of a whole unit, where the whole unit is divided into 6 equal parts. Each of these parts represents 1/6 of the whole.
1/2, on the other hand, represents half of the whole unit, so it is twice as much as 1/6.
To visualize this, you can think of a ruler divided into 6 equal parts. 1/6 would represent 1 mark on the ruler, while 1/2 would represent 3 marks. To have the same length as 1/2, you need to add up 3 marks, or 3 copies of 1/6.
You can also think of this as converting 1/6 to a common denominator, which in this case is 6. 3 copies of 1/6 is equal to 3/6 or 1/2.
Step-by-step explanation:
1/6 can be represented as a fraction of a whole unit, where the whole unit is divided into 6 equal parts. Each of these parts represents 1/6 of the whole.
1/2, on the other hand, represents half of the whole unit, so it is twice as much as 1/6.
To visualize this, you can think of a ruler divided into 6 equal parts. 1/6 would represent 1 mark on the ruler, while 1/2 would represent 3 marks. To have the same length as 1/2, you need to add up 3 marks, or 3 copies of 1/6.
You can also think of this as converting 1/6 to a common denominator, which in this case is 6. 3 copies of 1/6 is equal to 3/6 or 1/2.
Writing linear equations in slope-intercept form. Write the equation of each linear below:
Answer:1. y=2x+3
2. y=-1x-2
3. y=-3x+4
4= y=3x+0
Please help I need this
1 Find the measure of angle BOC. I
2 Find the measure of angle DOE.
3 Find the measure of angle AOE
1. [tex]m\angle BOC=45^{\circ}[/tex] since angles on a straight line add to [tex]180^{\circ}[/tex]
2. [tex]m\angle DOE=60^{\circ}[/tex] because vertical angles are congruent
3. [tex]m\angle AOE=120^{\circ}[/tex] because vertical angles are congruent
Find the maximum value of the function z=5x+3y subject to the following constraints.
x≥2
y22
6x+7y≤68
The function at its maximum value will be at point (9,2) and its value is 51 which can be derived keeping in mind the constraints that have been given.
What is Maximizing a function ?The maximum value of any kind of a function is the place where the said function reaches its highest point, or vertex, on a graph. If your kind of quadratic equation has something as a negative of a term, it will also have a maximum value.
There are a bit of three ways to find that maximum, depending on which form of a quadratic function you have got.
here, we have,
Herein we can find the closed region ABC from the three equations or constraints given
and can mark the points as
A = (2,2)
B = (5, 2)
C = (9, 2)
if we put up the values of the points, we get
at (9, 2) ,
z=5x+3y
=45+6
=51 that is the maximum value amongst the three.
Thus, the maximum point of the function can be calculated as (9,2)
How do you extract out the maximum or minimum value of a function?
We will at first set out the first derivative of the function to absolute zero and then solve for x to get the exact critical point.
If we then take the second derivative or f’’(x), there in we can find out whether this point will be a maximum or minimum. If the second derivative is seen as positive, it will be a minimum value
What is the maximum value of a function called?
The maximum or minimum value that is calculated over the entire function is called an “Absolute” or “Global” maximum or minimum of the function.
There is presence of only one global maximum (and only one global minimum) but there can be several that is more than one local maximum or minimum
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What is the value of 9 ÷ 0?
Answer: Undifined!
Step-by-step explanation: Division by zero is considered an invalid operation in mathematics because there is no number that can be multiplied by zero to produce the original number. In other words, there is no single valid answer to dividing by zero. Example: You have 0 cookies and you want to share them among 9 friends. There's no way to share, since you don't have cookies haha!
Answer:
UNDEFINED OR NO ANSWER.Step-by-step explanation:
An expression without a value is referred to as being undefined; it has an indeterminant form. When a number is divided by zero, it usually has no specified meaning. Mathematically, we can't divide by zero because the result is an equation we can't compute.
Hope it helps!What is the percent of increase from 70 to 84?
Answer:
16.7%
Step-by-step explanation:
84 - 70 = 14
14 divided by 84, times 100 = 16.7%
So, it increase by 16.7%
Comparing TVs
Clayton County Mathematics Curriculum
Jamon. Histon
Vehicle Viewing, Inc. and Traveling TV Co. have each designed new small HD flat-screen square-shaped televisions to be used
in automobiles. They feel that these will be very popular because of the desire for parents to entertain their children during the
many hours spent in traffic each day. Television size is measured along the diagonal. The diagonal in the Vehicle Viewing, Inc.
television is V75 inches and the Traveling TV Co. television has a diagonal of 8.5 inches.
You are the owner of a packaging company and both Vehicle Viewing, Inc. and Traveling TV Co. have hired you to package their
new televisions.
1. Who has the larger television? How do you know?
PLEASE HELP
The larger television is Vehicle Viewing, explanation is mentioned below,
What is diagonal ?The diagonal of a television refers to the length of a line segment connecting two opposite corners of the screen. It is a way of measuring the size of the television screen, rather than its width or height. The diagonal measurement gives a good indication of the overall screen size and is commonly used as a specification for television screens.
Given that,
Two television,
Vehicle Viewing having diagonal 75 inches
Traveling TV Co having diagonal 8.5 inches
larger television =?
Vehicle Viewing, Inc. has the larger television with a diagonal of 75 inches compared to Traveling TV Co.'s diagonal of 8.5 inches.
This can be determined by simply comparing the two diagonal measurements given.
Hence, the larger television is Vehicle Viewing.
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Beryllium-11 is a radioactive isotope of the alkaline metal Beryllium. It decays at a rate of 4.9% every second. Assuming you started with 100%, how much would be left after 35 seconds?
The quantity that will be left after 35 seconds would be =-71.5%
How to calculate the quantity of radioactive isotope left?The quantity of radioactive Beryllium-11 isotope that was used to start the experiment = 100%
The rate at which the isotope decays= 4.9%/second
The quantity that will remain after 35 seconds = ?
That is;
4.9% = 1 second
x% = 35 seconds
make X the subject of formula;
X = 4.9×35
X= 171.5
The quantity that will be left = 100-171.5 = -71.5%
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What are the coordinates of the point where y-4x=1 crosses the y-axis
Answer:
( 0,1)
Step-by-step explanation:
y-4x=1
We want to find the y-intercept ( where it crosses the y-axis).
Let x = 0
y-4*0=1
y = 1
The coordinates of the y-intercept are ( 0,1).
Write as an algebraic expression: The product of a a and b b increased by 5 5. Answer:
The expression can be written as: a * b + 5.
How to determine the algebraic expressionFrom the question, we have the following parameters that can be used in our computation:
The product of a and b increased by 5.
The product of a and b is represented as
a * b
Increased by 5 means
a * b + 5
So, the expression is a * b + 5
The expression "a * b + 5" represents the mathematical operation of first multiplying two values, 'a' and 'b', and then adding 5 to the result.
The '*' symbol is used for multiplication, and the '+' symbol is used for addition.
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In ΔHIJ, h = 97 cm, m m∠H=144° and m m∠I=24°. Find the length of i, to the nearest 10th of a centimeter.
Answer: 67.1 cm
Step-by-step explanation:
Using the Law of Sines:
[tex]\frac{i}{\sin I}=\frac{h}{\sin H}\\\\\frac{i}{\sin 24^{\circ}}=\frac{97}{\sin 144^{\circ}}\\\\i=\frac{97 \sin 24^{\circ}}{\sin 144^{\circ}}\\\\i \approx 67.1 \text{ cm}[/tex]
Answer: 67.1
Step-by-step explanation:
This rectangle of x's is 6/5 of another (original) rectangle of x's. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x a. (5 points) Show the original rectangle. Attach a picture of only your drawing. b. (5 points) Use our definition of fraction to help you solve this problem and explain your solution.
The fraction 6/5 represents the scale factor of one rectangle towards the other. The figure has been shown.
What is the scale factor?The scale factor is defined as the ratio of the modified change in length to the original length.
Here,
one rectangle = 6/5 [original rectangle]
one rectangle / original rectangle = 6 / 5
Scale factor [for the rectangle] = 6/5
Thus, the fraction 6/5 represents the scale factor of one rectangle towards the other. The figure has been shown.
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I need help with my math homework
To locate the fractions we must divide the unit in the number of the denominator (point A). According to the information, each shell symbol means 2 shells. Mark found 4 fewer shells than Tania. Mark and Carlos found 10 more shells than Mei Ling. Lastly, the numbers are rounded to the nearest number.
How to locate the fractions (Question A)?To locate the fractions we must divide the unit in the part number that says the denominator of the fraction and locate the fraction in the numerator position as shown in the graph. They all go in the first position.
How were the shells distributed (Question B)?Based on the information in the graph, it can be established that:
Each shell symbol means 2 shells.Mark found 4 fewer shells than Tania.Mark and Carlos found 10 more shells than Mei Ling.How to approximate the numbers in the graph (Question C)?To approximate the numbers we must identify which of the numbers in the graph is closest:
98 is almost 100.151 is almost 200.278 is almost 300.336 is almost 300.120 is almost 100.189 is almost 200.249 is almost 200.303 is almost 300.Learn more about numbers in: https://brainly.com/question/17429689
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