Answer:
d = 7n -4
Step-by-step explanation:
d is number of dimes, n is number of nickels.
7 X number of nickels = 7n.
4 less than that is 7n - 4.
so d = 7n -4.
Let sets A and B be defined as follows. A is the set of integers greater than or equal to -6 and less than or equal to -4 B={−29,20,28,29} (a) Find the cardinalities of A and B. n(A)=n(B)= (b) Select true or false.
The cardinality of set A (n(A)) is 3.
The cardinality of set B (n(B)) is 4.
To find the cardinality of a set, we count the number of elements in that set.
For set A, we need to count the number of integers between -6 and -4 (inclusive).
The integers in this range are -6, -5, and -4.
Therefore, the cardinality of set A (n(A)) is 3.
For set B, we simply count the number of elements given in the set. From the given set B = {-29, 20, 28, 29}, we have 4 elements.
Therefore, the cardinality of set B (n(B)) is 4.
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Which expression is equivalent to
3xy-3
15x2,10?
2,10? Assume X*0,y*0
The expression which is equivalent to the given expression is 1 / 5x⁸ y¹³.
Given expression is,
3 x⁻⁶y⁻³ / 15 x² y¹⁰
We have to find the equivalent expression for this, which means that the end value for both expressions will be same.
We can write the given expression as,
3/15 × (x⁻⁶ / x²) × (y⁻³ / y¹⁰)
1/5 × (x⁻⁶ ⁻ ²) × (y⁻³ ⁻ ¹⁰)
= x⁻⁸ y⁻¹³ / 5
When the variables goes in to the denominator sign changes to positive in the exponent.
= 1 / 5x⁸ y¹³
Hence the correct expression is 1 / 5x⁸ y¹³.
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What is the diameter of a sphere with a volume of 79cm^3, to the nearest tenth of a centimeter?
The diameter of the sphere to the nearest tenth is [tex]5.3\ cm[/tex].
According to the question:
[tex]Volume(V) = 79\ cm^3[/tex]
To find:
[tex]Radius(r)[/tex]
We know that:
[tex]V = \frac{4}{3}\pi r^3[/tex]
⇒ [tex]r = (\frac{3V}{4\pi})^{1/3}[/tex]
Take [tex]\pi[/tex] = [tex]3.1415[/tex] and substitute the given values in the above equation:
[tex]r = (\frac{3\times 79}{4\times 3.1415})^{1/3}[/tex] ...(∵ [tex]\pi = 3.1415[/tex])
[tex]r = 18.8604^{1/3}[/tex]
[tex]r = 2.661\ cm[/tex]
⇒[tex]diameter = 2\times 2.661\ cm[/tex]
⇒[tex]diameter = 5.322\ cm[/tex]
Rounded to the nearest tenth:
[tex]diameter = 5.3\ cm[/tex]
Therefore, the diameter of the sphere to the nearest tenth is [tex]5.3\ cm[/tex].
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Review the simple interest rate based on FICO scores to answer the question:
FICO Score Simple Interest Rate
800–850 4.295%
740–799 5.597%
670–739 8.132%
580–669 9.358%
300–579 12.413%
A consumer, with a credit score of 645, is planning to buy a used car and needs to borrow $3,500 with a simple interest rate loan. Determine the interest rate the consumer will qualify for if they raise their credit score 60 points. Is it?
A, 4.295%
B. 5.597%
C. 8.132%
D. 9.358%
If the consumer raises their credit score by 60 points to 705, they will qualify for interest rate of 8.132%. The Option C
What interest rate will the consumer qualify for if they raise their credit score by 60 points?To know new interest rate, we have to get new credit score range and corresponding interest rate. The consumer's current credit score is 645, which falls within the range of 580-669.
To calculate the new credit score, we add 60 points to the current credit score:
= 645 + 60
= 705
The new credit score of 705 falls within the range of 670-739. According to the given table, this range corresponds to a simple interest rate of 8.132%
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Help pls and thank you
By using the parallelogram method, the addition of the vectors [tex]\vec a + \vec b[/tex] is (3, 1).
How to add vectors by using the head to tail method or parallelogram method?In Mathematics, a vector typically comprises two (2) points. First, is the starting point which is commonly referred to as the "tail" and the second (ending) point that is commonly referred to the "head."
Furthermore, the head to tail method of adding two vectors requires drawing the first vector ([tex]\vec a[/tex]) on a graph and then placing the tail of the second vector ([tex]\vec b[/tex]) at the head of the first vector. Finally, the resultant vector would be drawn from the tail of the first vector ([tex]\vec a[/tex]) to the head of the second vector ([tex]\vec b[/tex]).
Furthermore, the head to tail method of adding two (2) vectors requires drawing the first vector ([tex]\vec a[/tex]) on a graph and then placing the tail of the second vector ([tex]\vec b[/tex]) at the head of the first vector. Finally, the resultant vector would be drawn from the tail of the first vector ([tex]\vec a[/tex]) to the head of the second vector ([tex]\vec b[/tex]).
By adding the given vectors algebraically, we have the following:
[tex]\vec a + \vec b[/tex] = (4, -3) + (-1, -2)
[tex]\vec a + \vec b[/tex] = [(4 + (-1)), (-3 + (-2))]
[tex]\vec a + \vec b[/tex] = [(4 - 1), (-3 - 2)]
[tex]\vec a + \vec b[/tex] = (3, -5).
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3. Net income is important because it is
a.
your total earnings over a specific time period.
b. how much you spend over a period of time.
your take-home pay after taxes.
C.
d.
how much you have left after paying your bills.
Answer:
The correct answer is C. Net income refers to your take-home pay after taxes and other deductions have been taken out of your gross income. It is an important financial measure because it represents the actual amount of money you have available to save, invest, or spend on your expenses and bills.
Step-by-step explanation:
If M is the set of all square numbers less than 80 and N is the set of all non-negative even numbers that are under 30, Write the lists of all elements of M and N.
Answer:
The set M of all square numbers less than 80 is:
M = {0, 1, 4, 9, 16, 25, 36, 49, 64}
The set N of all non-negative even numbers that are under 30 is:
N = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28}
Answer:
All elements of the set M in ascending order are:
1, 4, 9, 16, 25, 36, 49, 64All elements of the set N in ascending order are:
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28Step-by-step explanation:
A square number, also known as a perfect square, is a non-negative integer that is obtained by multiplying an integer by itself. In other words, it is the result of squaring an integer.
The square numbers less than 80 are:
1, 4, 9, 16, 25, 36, 49, and 64.An even number is an integer that is divisible by 2 without leaving a remainder.
The non-negative even numbers that are under 30 are:
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, and 28.Therefore:
All elements of the set M in ascending order are:
1, 4, 9, 16, 25, 36, 49, 64All elements of the set N in ascending order are:
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28Please help!
find the ending size or value for the tenth or tenth of a percent.
given percent change.
a. A $100 stock loses 20% of its value.
b. An $80 stock gains 20% of its value.
Answer: a. A $100 stock loses 20% of its value.
To find the ending value of the stock after a 20% decrease in value, we can multiply the initial value by (1 - 0.20) or 0.80.
Ending value = $100 x 0.80 = $80
Therefore, the ending value of the stock after a 20% decrease is $80.
b. An $80 stock gains 20% of its value.
To find the ending value of the stock after a 20% increase in value, we can multiply the initial value by (1 + 0.20) or 1.20.
Ending value = $80 x 1.20 = $96
Therefore, the ending value of the stock after a 20% increase is $96.
Step-by-step explanation: :)
Please solve and explain fully
1. We can see here that the initial flounder population will be = [tex]\frac{220}{0.6t + 1}[/tex].
2. The P'(11) in 2 decimal places is: 28.95.
What is population?Population refers to the total number of people residing in a given region or area. In most cases, it is expressed as the number of people in relation to a unit of area, like a square kilometer or square mile. A census, which is a count of every person residing in a specific area, can be used to estimate the population of a nation or region.
Many variables, such as birth, mortality, and migration rates, can have an impact on population size.
1. The initial flounder population:
[tex]\frac{4t + 216}{0.6t^{2} + 1 } = \frac{4 + 216}{0.6t + 1} = \frac{220}{0.6t + 1}[/tex]
2. The P'(11) will be:
where t = 11
[tex]\frac{220}{0.6(11) + 1} = \frac{220}{7.6} = 28.9473[/tex]
= 28.95 (2d.p.)
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there are 215% 224 mangoes in a bag what is the greatest number of children to distribute these FL in mangoes equally how many fruits of each kind will eachget
The greatest number of children that can distribute the mangoes equally is 481. Each child will receive 481/481 = 1 mango.
In order to distribute the mangoes equally among children, we first need to determine the total number of mangoes in the bag.
If there are 215% (or 2.15) of 224 mangoes in the bag, we can calculate the total number of mangoes by multiplying these values: 2.15 * 224 = 481.6 mangoes.
Since we cannot have fractional mangoes, we round down to the nearest whole number, which gives us a total of 481 mangoes in the bag.
To distribute these mangoes equally among the children, we divide the total number of mangoes by the number of children. Let's assume there are 'x' children.
Each child will receive 481/x mangoes.
To determine the greatest number of children, we need to find a value for 'x' that evenly divides 481. We can do this by finding the factors of 481. The factors of 481 are 1, 13, 37, and 481.
Therefore, the greatest number of children that can distribute the mangoes equally is 481. Each child will receive 481/481 = 1 mango.
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Can someone answer this for me and explain how to do it? Thanks! I will give brainliest.
Check the picture below.
so the part on the left is a template for transformations, and we can look at g(x) like this
[tex]{\Large \begin{array}{llll} g(x)=\stackrel{A}{-3} ~~ (\stackrel{B}{1}x+\stackrel{C}{4})^2 ~~ \stackrel{D}{-3} \end{array}}[/tex]
now, if you look at the template, we do +4 first, then -3 shift down, then 3 vertical shrink, and then the negative of -3, landing at g(x) from our parent f(x).
(5^2+7)÷4 evaluate it
Answer:
8
Step-by-step explanation:
(5² + 7) ÷ 4 ← evaluate terms in parenthesis
= (25 + 7) ÷ 4
= 32 ÷ 4
= 8
2.
You are building a rectangular chest. You want the length to
be 6 feet, the width to
be 2 feet, and the volume to be 24 cubic feet. What should
the height be?
Step-by-step explanation:
Volume = 24 ft^3 = L x W x H
24 = 6 x 2 x H
H = 24 / ( 6 x 2) = 2 ft
I Need help with this
The angle pairs are given as follows:
a) Alternate exterior: <2 and <8.
b) Corresponding angles: <2 and <6.
c) Alternate interior: <3 and <5.
How to obtain the angle pairs?Item a:
Alternate exterior angles are two angles that are on the exterior of the two parallel lines, on opposite sides of the transversal line, hence they are given as follows, for item a:
<1 and <7.<2 and <8.Item b:
Corresponding angles are angles that are on the same position relative to the transversal line, but on different parallel lines, hence one example is given as follows, for item b:
<2 and <6.
Item c:
The two alternate interior angles are positioned on the inside of the two parallel lines, and on opposite sides of the transversal line, hence they are given as follows, for item c:
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What is the volume of the sphere? Write your answer in terms of pi (for example, 25 pi cubic units).
Answer:
4/3 ×π×r³
4/3 × 22/7 ×3³
88/21 ×27
Please help. Use the alternative form of definition of derivative to find the slope of the line tangent. Please show work. 100 points. Will give brainliest, when it comes up.
The slope of the line tangent to the graph of h(x) = 1/x + 3 at the point when x is -6 is -1/36.
What is the slope of the line tangent to the equation?To determine the slope of the line tangent to the graph of the given function when x = -6;
Using alternative form of the definition of derivative.
f'(a) = lim (h->0) [f(a+h) - f(a)] / h
Using this formula for the given function;
h'(a) = lim (h->0) [h(a+h) - h(a)] / h
Now, substitute a = -6 into the formula:
h'(-6) = lim (h->0) [h(-6+h) - h(-6)] / h
Next, simplify the expression by plugging in the values:
h'(-6) = lim (h->0) [1/(-6+h) + 3 - (1/-6 + 3)] / h
Simplifying further:
h'(-6) = lim (h->0) [1/(-6+h) - 1/-6] / h
Now, let's combine the fractions with a common denominator:
h'(-6) = lim (h->0) [(-6 - (-6+h))/((-6+h)(-6))] / h
Simplifying the numerator:
h'(-6) = lim (h->0) [-h / ((-6+h)(-6))] / h
Canceling out the h's:
h'(-6) = lim (h->0) [-1 / ((-6+h)(-6))]
Taking the limit as h approaches 0:
h'(-6) = -1 / ((-6)(-6))
Simplifying further:
h'(-6) = -1 / 36
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Use the graph below to determine the values of x
at which the function is not continuous.
Step-by-step explanation:
This graph shows a vertical asymptote at x = 0
this is where it is not continuous
What is the volume of this cone? Use π =3.14 and round to the nearest hundredth
Answer:
If the height and radius of a cone are both 9 yards, then you can use the formula for the volume of a cone to calculate its volume. The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone. Plugging in the values for r, h, and π gives us:
V = (1/3)πr^2h
= (1/3)(3.14)(9 yd)^2(9 yd)
= (1/3)(3.14)(81 yd^2)(9 yd)
= (1/3)(254.34 yd^3)
≈ 84.78 yd^3
So, the volume of a cone with a height and radius of 9 yards is approximately 84.78 cubic yards, rounded to the nearest hundredth.
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find the first four terms of the infinite sequence un= 1/7n-2
To find the first four terms of the infinite sequence u_n = 1/(7n - 2), we substitute the values of n from 1 to 4 into the formula:
For n = 1:
u_1 = 1/(7(1) - 2) = 1/5
For n = 2:
u_2 = 1/(7(2) - 2) = 1/12
For n = 3:
u_3 = 1/(7(3) - 2) = 1/19
For n = 4:
u_4 = 1/(7(4) - 2) = 1/26
Therefore, the first four terms of the infinite sequence are:
u_1 = 1/5
u_2 = 1/12
u_3 = 1/19
u_4 = 1/26
Can some hell me find the area and arc length for each of these circles?
Answer:
please see detailed answers below
Step-by-step explanation:
1) circumference = πd = 16π inches.
arc length = (15/360) X πd = (2/3)π inches.
area of circle = πr² = π(8)² = 64π square inches.
area of sector = (15/360) X 64π = (8/3)π square inches.
2) circumference = πd = 30π inches.
minor arc length = (60/360) X 30π = 5π inches.
major arc length = (300/360) X 30π = 25π inches.
area of circle = πr² = π(15)² = 225π square inches.
area of minor sector = (60/360) X πr² = (75/2)π square inches.
area of major sector = (300/360) X πr² = (375/2)π square inches.
3) circumference = πd = 40π inches.
arc length = (125/360) X 40π = (125/9)π inches.
area of circle = πr² = π(20)² = 400π square inches.
area of sector = (125/360) X 400π = (1250/9)π square inches.
Question 10
A car park has 880 parking spaces.
Some of the spaces are reserved.
The ratio of reserved spaces: not reserved spaces = 1:10.
Work out the number of spaces that are not reserved.
Step-by-step explanation:
work he in a department store
transformed to create the graph of Y3x?
How is the graph of the parent function
O It is horizontally stretched by a factor of 3 and reflected over the y-axis.
It is translated 3 units down and reflected over the x-axis
It is horizontally compressed by a factor of 3 and reflected over the x-axis
It is translated 3 units down and reflected over the y-axis.
Answer:
The graph of the parent function y = 2^x can be transformed to create the graph of y = 2^(3x) by horizontally compressing by a factor of 3. Therefore, the correct answer is C.
Dian is 8 years older than his brother.In 5 years Dian will be twice as old as his brother.How old is his brother now?
Dian's family is 3 times old now.
Let's call Dian's family's age" x" now.
According to the problem,
Dian is 8 times aged than his family, so Dian's age is x 8 now.
In 5 times, Dian's age will be x 8 5, and his family's age will be x 5.
The problem also states that in 5 times, Dian will be doubly as old as his family,
so we can set up the equation
x+ 8+ 5 = 2( x +5)
Simplifying the equation x +13 = 2x+ 10
Obtaining x from both sides
13 = x +10
Obtaining 10 from both sides
3 = x
thus,X=3
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convert 349 rands to cents
Answer:
1 South African Rand is equal to 100 cents. Therefore, 349 South African Rands is equal to 34900 cents.
Answer:
349 South African Rand equals
United States Dollar
17.95
South African Rand
349
help its due tomorrow
Answer:
c) The equation of this line is y = 3x + 12.
anyone knows how to solve this
Answer:
x = 4
Step-by-step explanation:
the angle immediately to the left of 20x must be 25x. that's because the two lines with double arrows at the top are parallel lines.
the angle to the left of 20x and the 25x are called alternate angles. they are equal.
also, 20x and the angle to the left of it are on a straight line. angles on a straight line add up to 180°.
so, we now have 20x + 25x = 180.
45x = 180
divide both sides by 45:
x = 180/45
= 4.
x = 4.
a study of long-distance phone calls made from general electric reveled the length of the calls, in minutes, follows the normal probability distribution. the mean length of time per call was 4.5 minutes and the standard deviation was 0.70 minutes. what is the probability that calls last between 4.0 and 6.0 minutes?
The probability that calls last between 4.0 and 4.6 minutes will be around 0.4332.
we have to standardize the values and utilize the standard typical dispersion table or calculator.
To discover the z-scores for 4.0 and 6.0 minutes:
z1 = (4.0 - 6.0 ) / 0.70 = 2.8
z2 = (4.5 - 6.0 ) / 0.70= 2.1
Since Employing a standard ordinary conveyance table, we are able to discover the likelihood of the calls enduring between 4.0 and 4.6 minutes:
P(0 ≤ Z ≤ 2.1) = 0.4332
However the likelihood that calls final between 4.0 and 4.6 minutes is 0.4332, or around 0.4332.
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The graph below shows a line of best fit for data collected on the distance drivers traveled as a function of time. Which of the following is the equation of the line of best fit? A. B. C. D.
The equation for the line of best fit is given as follows:
y = 50x/3.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b.
The parameters of the definition of the linear function are given as follows:
m represents the slope of the function, which is by how much the dependent variable y increases(positive) or decreases(negative) when the independent variable x is added by one.b represents the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On the case of the graph, the intercept is given by the value of y at which the graph crosses or touches the y-axis.From the graph, when x = 0, y = 0, hence the intercept b is given as follows:
b = 0.
Hence:
y = mx.
When x = 3, y = 50, hence the slope m is given as follows:
3m = 50
m = 50/3.
Hence the equation is:
y = 50x/3.
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In the figure below, points D, E, and F are the midpoints of the sides of ΔABC
Suppose AB = 48, BC = 56, and DE = 32.
Find the following lengths
The values of
1. DF = 28cm
2. AC = 64 cm
3. CF = 32 cm
What is segment theorem?It states that the line segment in a triangle joining the segment of any two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”
Therefore we can say that;
triangles , BDE, AD ,EFC, DE are congruent.
congruent triangles are triangles with equal sides and equal angles.
D = BE
BE = 56/2 = 28cm
A = DE = 32 cm
AC = 2AF
= 2 × 32 = 64 cm
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Find the measure of each angle in the isosceles trapezoid.
PLEASE HELP!
Answer:
A= 158
B=158
D=22
Step-by-step explanation:
An isosceles trapezoid has 2 pairs of equal angles.
A=B
C=D
Also A+C=180
So we have that A=158
B=158 and D=22