You want to compare the ratios 3:12 and 7:28 to see if they're equal. You know that you need to compare the products of the extremes against the product of the means. Which two values are the means for this comparison? A. 3 and 7 B. 12 and 28 C. 3 and 28 D. 12 and 7
Answer:
Step-by-step explanation:
3:12 7:28
The means are the second and third terms in the proportion.
The extremes are the two outside terms.
12 and 7 are the means.
(3 and 28 are the extremes.)
So thre answer is D. 12 and 7.
Hello, I am stuck on this question which is a exchange rate question
if 1 sar is worth 0.05 US dollars, how many south african rand is 1 US dollar worth?
Answer:
0.05 US$=1 sar
then,1 US$=1/0.05 sar.
1. Let
U = {(x, y, z) = R³ | x+y=2z = 0 = x - y},
and let
V = span {(1, 0, -1), (3, 1, 2)}.
Determine the dimensions of both U and V, proving your results.
Note that to prove the dimension, you should use the definition, which
means you need to find a basis. It is not enough to just state a basis,
you must explain why it is a basis.
The dimension of V is 2, and it is spanned by the basis vectors (1, 0, -1), (3, 1, 2).
The dimension of a vector space is the number of vectors in a basis for the space. To find a basis for a subspace of R³, we need to find a set of linearly independent vectors that span the subspace.
First, let's consider U. The subspace U is defined by the equations x + y = 2z and x - y = 0.
Solving these equations for x and y, we can express them in terms of z: x = 2z and y = -2z. Therefore, every vector in U can be written as (x, y, z) = (2z, -2z, z) = z(2, -2, 1).
Since z is a scalar, the vector (2, -2, 1) is the only vector needed to span the subspace U, which means that it is a basis for U.
Therefore, the dimension of U is 1, and it is spanned by the basis vector (2, -2, 1).
Now let's consider V. The subspace V is defined by the set of vectors that can be written as a linear combination of the vectors (1, 0, -1) and (3, 1, 2). We can start by showing that these vectors are linearly independent. Suppose that there are scalars a and b such that a(1, 0, -1) + b(3, 1, 2) = (0, 0, 0). Then we have:
a + 3b = 0
b = 0
-a = 0
Since a and b are real numbers, the above equation only holds if a = 0 and b = 0. This shows that (1, 0, -1) and (3, 1, 2) are linearly independent, and a basis of V.
Therefore, the size of V is 2, and it is traversed by the basis vectors (1, 0, -1), (3, 1, 2).
Learn more about the vectors here :
https://brainly.com/question/17254148
#SPJ1
his mapping shows a functional relationship. A mapping diagram shows a relation, using arrows, between domain and range for the following ordered pairs: (2, 4), (negative 3, 0), (negative 1, negative 1), (4, 3). When f(x)=4, what is the value of x? 0 2 3 4
when f(x)=4, then the value of x is 2
What is a function?A relation is a function if it has only One y-value for each x-value.
Given that A mapping diagram shows a relation, using arrows, between domain and range for the following ordered pairs:
The ordered pairs are (2, 4), (-3, 0), (- 1, -1), (4, 3)
We need to find value of x when f(x)=4
In the (x, y) ordered pair the x place represents the domain value and y place represents the range.
In the order pairs we have to look for the y value which has 4.
The corresponding element of 4 is the x value
So the value of x is 2 if f(x)=4
Hence, when f(x)=4, then the value of x is 2
To learn more on Functions click:
https://brainly.com/question/21145944
#SPJ1
*will give brainlist*
A town has 1.500 households. The number of people per
household is normally distributed with a mean of 3.67 and
a standard deviation of .34.
Approximately, how many
households have between 3.67 and 4.35 people?
0 510 households
o 945 households
a 715 households
o 660 households
Answer: The question is asking for the number of households that have between 3.67 and 4.35 people, which corresponds to the number of households whose number of people per household falls within one standard deviation of the mean.
A normal distribution is symmetric, so approximately 68% of the data falls within one standard deviation of the mean. So, we can estimate that approximately 68% of the 1,500 households have between 3.67 and 4.35 people.
The calculation is:
1,500 households x 68% = 1,020 households
So, approximately 1,020 households have between 3.67 and 4.35 people.
This is a rough estimate and the actual number may be slightly different, but it can be considered as a good approximation. From the given options, The answer closest to 1,020 is 945 households.
Step-by-step explanation:
. If Mario was 32 years old 8 years ago, how old was he x years ago?
Answer: He was 32 years old 8 years ago, than a) x-40 b) x-24 c) 40-x d) 24-x e) 24+x
Step-by-step explanation:
Mario was '40 - x' years old when he was 'x' years old.
If he was 32 years old, 8 years ago, then he is 40 now as (32+8) equals 40.
If he is 40 years old now, then he was '40 - x', x years ago.
Hence, '40 - x' is the answer to this sum.
To learn more about age-related algebraic sums, refer to
https://brainly.com/question/22875998
First five terms to the sequence a(n+1) = 5a(n) and a(1)=2 for n[tex]\geq[/tex]1
The required first five terms of the sequence are 2, 10, 50, 250, and 1250.
What is an arithmetic sequence?An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.
The first five terms of the sequence, a(n), defined by the recurrence relation a(n+1) = 5a(n) and a(1) = 2, are as follows:
a(1) = 2
a(2) = 5a(1) = 5 × 2 = 10
a(3) = 5a(2) = 5 × 10 = 50
a(4) = 5a(3) = 5 × 50 = 250
a(5) = 5a(4) = 5 × 250 = 1250
Therefore, the first five representations of the sequence are 2, 10, 50, 250, and 1250.
Learn more about arithmetic sequence here:
brainly.com/question/21961097
#SPJ1
Find the total surface area of the net below
Therefore ,answering the offered question, we can state that the figure's surface area is SA = 2(9 11+11 9+11 * 11), which equals SA = 638 in2.
What precisely is surface area?Surface area is a measure of how much space an object's surface takes up overall. The total area of a three-dimensional shape's surroundings is its surface area. Surface area refers to the total surface area of a three-dimensional shape. You may compute the contact area of a cube with six square faces by adding together their individual areas. Alternatively, you can use the following formula to name the box's dimensions: Surfaces (SA) = 21 h + 2 lw + 2 hw. A tri shape's surface area is calculated as the total amount of space it occupies.
Here,
Front = rear = 11*11
top = bottom = 9*11
sides = 11*9;
SA= 2(911+119+1111)
SA=2(9999 +121)
SA = 2(319) (319)
SA = 638 in²
To know more about surface area visit:
brainly.com/question/2835293
#SPJ1
3. Function G is defined by the equation G(x) = [x].
Function R is defined by the equation R(x) = x/+2.
Describe how the graph of function R relates to the graph of G, or sketch the graphs
of the two functions to show their relationship.
Answer: The function G(x) = [x] returns the greatest integer less than or equal to x. This means that for any value of x, G(x) will be the largest integer that is less than or equal to x. For example, G(3.5) = 3 and G(5) = 5.
The function R(x) = x/+2, x is any real number, this function returns the value of x incremented by 2. In other words, it is the result of adding 2 to x.
On the other hand, the graph of R(x) is a line that goes through the point (0, 2) and has a slope of 1, this means that for every change of 1 unit in the x-axis, the y-axis will change by 1 unit as well.
When we compare the two graphs, we can see that the graph of R(x) is shifted up 2 units from the graph of G(x) . If the graph of G(x) is thought of as the "ground", the graph of R(x) is "floating" two units above it. Also, the graph of R(x) is continuous while the graph of G(x) is not.
To sum up:
-The graph of G(x) is a step function, which start at the negative infinity and jumps up to the next integer at every point.
The graph of R(x) is a line that goes through the point (0, 2) and has a slope of 1
-R(x) is always two units above G(x) , and is a continuous function, while G(x) is not.
Step-by-step explanation:
Solve for p if L = 2 1/2 ft and W = 3 2/5 ft. P = 2L + 2W
Answer:
P = 59/5
Step-by-step explanation:
The total cost (t) after 8% sales tax is added to an item's price (p): 1.08p= t
The total cost of the item after the sales tax of 8 % is given by the equation t = 1.08p , where p is the initial price of the item
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total cost price of the item be represented as t
Let the initial cost price of the item be represented as p
Now , the sales tax percentage = 8 %
So , the equation will be
The total cost price of the item t = sales tax percentage ( initial cost price of the item ) + initial cost price of the item
Substituting the values in the equation , we get
The total cost price of the item t = 8 % ( p ) + p
On simplifying the equation , we get
The total cost price of the item t = ( 8/100 ) p + p
The total cost price of the item t = 0.08p + p
The total cost price of the item t = 1.08p
Hence , the equation is t = 1.08p , where p is the initial price of the item
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
4. Find the sum of the first 21 terms in a series where a = 20 and t21= 400.
5. Find the sum of the first 100 terms in a series where a = 0 and t100= 99.
6. Find the sum of the first 50 terms in a series where a = 4 and t50= 196.
7. Find the sum of the first 100 terms in a series where a = 0 and t100= 99.
8. Find the sum of the first 10 terms in an arithmetic series where t7= 7 and t10= 13.
9. Find the sum of the first 10 terms in an arithmetic series where t5= 15 and t10= 45.
10. Find the sum of the first 30 positive multiples of 5.
The first 100 terms of a series add up to 4950, and the first 21 terms of a series where a = 20 and t21 = 400 add up to 4410
what is arithmetic progression ?An arithmetic progression is when the difference between each phrase that follows another in a sequence is always the same. For instance, the sequence 5, 7, 9, 11, 13, and 15 is an example of an arithmetic progression with a 2 tolerance. A progression having a set tolerance between any two consecutive numbers is known as a "arithmetic progression" (A.P.). Two alternative types of mathematical progression exist: finite-length mathematical series A series that has a limited number of terms is a finite geometric progression. One may calculate the early, late, tolerance, and number of terms in a series using the terms in the series.
given
1) n6 = 6 where a = 5 and d = 5 = 105
2)n6 =6 where a = 9 and d = 12 = 234
3) n5= 5 where a = 5.7 and d = 1.4 = 42.5
4) a = 20 and t₂₁ = 400 ,
= 380
Therefore, Sum of 21 terms = 4410
5) In series a = 0 and t₁₀₀ = 99 = 4950
The first 100 terms of a series add up to 4950, and the first 21 terms of a series where a = 20 and t21 = 400 add up to 4410
To know more about arithmetic progression visit:
https://brainly.com/question/16947807
#SPJ1
Scores on the Wechsler Adult Intelligence Scale (a standard IQ test) for the 20-to-34 age group are approximately normally distributed with μ = 110 and σ = 25. What percent of people aged 20 to 34 have IQs between 125 and 150?
The percentage of people aged 20 to 34 that have IQs between 125 and 150 of people aged 20 to 34 have IQs between 125 and 150 is 21.94%
What is percentage?Percentage simply means a proportion of the number as a fraction of 100
What percent of people aged 20 to 34 have IQs between 125 and 150?
Let X = Scores on the standard IQ test for the 20 to 34 age group
This implies that X ~ Normal(x=110, б² = 25)
The z-score probability distribution for the normal distribution is given by; Z = (x-ц)/б ~ N(0,1)
Recall that population mean = 110 and standard deviation = 25
Now, the percent of people aged 20 to 34 have IQs between 125 and 150 is given by = P(125 < X < 150) = P(X < 150) - P(X 125)
P(X < 150) = P( < ) = P(Z < 1.60) = 0.9452
P(X 125) = P( ) = P(Z 0.60) = 0.7258
The above probability is calculated by looking at the value of x = 1.60 and x = 0.60 which has an area of 0.9452 and 0.7258.
Therefore, P(125 < X < 150) = 0.9452 - 0.7258 = 0.2194 or 21.94%
Learn more about percentages on https://brainly.com/question/29306119
#SPJ1
1 yard in 6 minutes
Question 1
Part A
Find the unit rate.
Enter the correct answer in the box.
Answer: 0.166666667 yards OR 0.1524 meters OR 0.5 feet
Step-by-step explanation:
1 / 6 = 0.166666667 yards
1 yard = 0.9144 meters
0.9144 / 6 = 0.1524 meters
1 yard = 3 feet
3 / 6 = 0.5 feet
Determine if the equation given in slope-intercept form represents the graph. If the equation is correct support your reasoning with why it is correct. If the equation is incorrect, give the correct slope-intercept form equation explaining how you determined it.
The equation of the line would be y = (4/5)x + 4 which in slope-intercept form represents the graph.
The graph is given in the question.
As per the given line, we take two points (0, 4) and (5, 8)
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = 0, y₁ = 4
x₂ = 5, y₂ = 8
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute values in the equation, we get
⇒ y - 4 = (8 - 4)/(5-0 )[x -0]
⇒ y - 4 = (4/5)x
⇒ y = (4/5)x + 4
The given equation of the line y = 4x + 5 is incorrect because its slope is not correct.
So, the equation of the line would be y = (4/5)x + 4.
Learn more about the Slope of the Line here:
brainly.com/question/14511992
#SPJ1
For the system of equations shown, tell whether it would take fewer steps to solve by substitution or elimination. Then use that strategy to solve the system. Explain your reasoning.
-3x - 4y = 15
9x + 7y = 25
Answer:
Step-by-step explanation:
Step: Solve−3x−4y=15for x:
−3x−4y=15
−3x−4y+4y=15+4y(Add 4y to both sides)
−3x=4y+15
−3x
−3
=
4y+15
−3
(Divide both sides by -3)
x=
−4
3
y−5
mila was baking cookies this weekend. she took 3 over 20 of the cookies to school on monday. and she gave 7 over 20 of the cookies to her neigbor. how much of the cookies did she gave away?
A
G
O
N
S
A
Answer:
Step-by-step explanation:
As she is baking cookies = 3/20
she egave it to her neigbour = 7/20
Remaining = ?
R = 3/20 -7/20 = -1/5
Express as a single fraction and find the domain
A single fraction will be;
⇒ 1/(y + 12)
And, Domain of this expression is,
⇒ Domain = (-∞, ∞) - { 12 }
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The expression is,
⇒ 4 / (y + 2) - 3 / (y - 2) + 12/ (y² - 4)
Now,
Since, The expression is,
⇒ 4 / (y + 2) - 3 / (y - 2) + 12/ (y² - 4)
Simplify the expression as;
⇒ 4 (y - 2) - 3 (y + 2) / (y-2) (y+2) + 12 / (y² - 4)
⇒ 4y - 8 - 3y - 6 / (y² - 4) + 12 / (y² - 4)
⇒ (y - 14) / (y² - 4) + 12 / (y² - 4)
⇒ (y - 14 + 12) / (y² - 4)
⇒ (y - 12) / (y- 12) (y + 12)
⇒ 1/(y + 12)
Hence, A single fraction will be;
⇒ 1/(y + 12)
And, Domain of this expression is,
⇒ Domain = (-∞, ∞) - { 12 }
Learn more about the fraction visit:
https://brainly.com/question/5454147
#SPJ1
A survey was given to a random sample of 550 voters in the United States to ask about their preference for a presidential candidate. Of those surveyed, 264 respondents said that they preferred Candidate A. Determine a 95% confidence interval for the proportion of people who prefer Candidate A, rounding values to the nearest thousandth.
The 95% confidence interval for the proportion of people who prefer Candidate A is given as follows:
(0.438, 0.522).
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The parameters for this problem are given as follows:
[tex]n = 550, \pi = \frac{264}{550} = 0.48[/tex]
Hence the lower bound of the interval is obtained as follows:
[tex]0.48 - 1.96\sqrt{\frac{0.48(0.52)}{550}} = 0.438[/tex]
The upper bound of the interval is obtained as follows:
[tex]0.48 + 1.96\sqrt{\frac{0.48(0.52)}{550}} = 0.522[/tex]
More can be learned about the z-distribution at https://brainly.com/question/25890103
#SPJ1
Swimming Pool B is also rectangular and has a perimeter of 90m. Its length is 25m. What is the width?
By using the formula for the perimeter, we will get that the width of the pool is 20 meters.
What is the width of the swimming pool?
Remember that for a rectangle of length L and width W, the perimeter is given by the formula:
P = 2*(L + W)
In this case, we know that the perimeter is 90m, and the length is 25m, then we know that:
P = 90m
L = 25m
Replacing that in the formula above we will get:
90m = 2*(25m + W)
now we can solve this for W.
90m/2 = 25m + W
45m - 25m = W
20m = W
The width of the pool is 20 meters.
Learn more about perimeter:
https://brainly.com/question/24571594
#SPJ1
3/5 of carl's money is $27.00. how much is 1/2 of his money
Answer:
$22.5
Step-by-step explanation:
$27.00/3/5=45
45*1/2=$22.5
Rewrite the radical expression as an expression with a rational exponent.
the seventh root of x to the thrid power
x to the three sevenths power
x to the seven thirds power
x^21
x^4
Answer:
To rewrite the radical expression "the seventh root of x to the thrid power" as an expression with a rational exponent, we need to use the property that allows us to rewrite a root of a power as a power with a rational exponent. This property states that "the nth root of x to the mth power" is equal to "x to the m/nth power".
Using this property, we can rewrite "the seventh root of x to the thrid power" as "x to the 3/7th power". Therefore, the correct answer is "x to the 3/7th power".
The other answer choices are not equivalent to the original expression. "x to the seven thirds power" is not a valid expression because "thirds" is not a unit of measurement. "x^21" is not equivalent to the original expression because the base and exponent are not related in the same way as in the original expression. "x^4" is not equivalent to the original expression because the base is the same but the exponent is not.
Answer: x to the 3/7th power
Step-by-step explanation:
so you dont have to read a essay to get the answer lol
Please help me solve
Answer:
The number of shuttles completed successfully is recorded as the score of that runner. The score is recorded in Level. Shuttles format (e.g. 9.5). The maximum laps on the PACER test is 247, which former Central Middle School student Dennis Mejia achieved, the only person to ever reach such a level.
Step-by-step explanation:
$640 , 3% , 2 years Find the simple interest earned to the nearest cent for each principal , interest rate , and time
The simple interest for principal of 640 and rate of 3% and time of 2 years is $3.84
How to find the simple interestThe Simple interest the end of 2 years is calculated using the simple interest formula
The formula is stated as
Simple interest = Principal * time * rate / 100
In the problem the give data include
principal = $640
rate= 3%
time = 2 years
plugging in the values
Simple interest = Principal * time * rate / 100
Simple interest = 640 * 2 * 3 /100
Simple interest = 3840 / 100
Simple interest = $3.84
The simple interest is $3.84
Learn more on simple interest at:
https://brainly.com/question/29785550
#SPJ1
$34,100 at 4% for 3 years
Simple interest
The 3 year simple interest at 4% will be $38,192.
What is Simple interest?A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
The principal amount = $34,100
Interest rate = 4%
Time = 3 years Now,
Since, We know that;
Where, A is final amount.
P is principal amount.
r is interest rate.
t is time.
Substitute all the values, we get;
A = $34,100 (1 + 4/100)³
A = $34,000 (104/100)³
A = $34,000 × 104/100 × 104/100 × 104/100
A = $38,192
Thus, The Simple interest will be $38,192.
To know more about Simple interest visit :-
brainly.com/question/20690803
#SPJ1
A shipping container will be used to transport several 150-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 8700 kilograms have already been loaded into the container. Use the drop-down menu below to write an inequality representing cc, the total number of 150-kilogram crates that can be loaded into the shipping container.
Answer:
Below
Step-by-step explanation:
(27500 - 8700) >= 150 x where x is the number of 150 kg containers
17v = 62 (exponential equations with logarithms, solve)
Therefore v = log(62) / log(17) is the solution for v, the unknown variable in the equation.
Define log(Logarithm).The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be increased in order to obtain a number x is the logarithm of x to the base b. For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3.
What is a function?A function in mathematics is an expression, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable). Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
To solve this exponential equation, we can use the logarithms property that is log(a^b) = b*log(a).
Given the equation 17v = 62, we can take the logarithm base 17 of both sides:
log(17^v) = log(62)
v*log(17) = log(62)
Dividing both sides by log(17) gives us:
v = log(62) / log(17)
This is the solution for v, the unknown variable in the equation.
To know more about Exponential equation visit: https://brainly.com/question/29506679
#SPJ1
What is the reciprocal of 1 4/13
Answer:
Step-by-step explanation:
Find the equation of a line that passes through the points (2,7) and (4,6). Leave your answer in the form y = mx + c
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{6}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{6}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{2}}} \implies \cfrac{ -1 }{ 2 } \implies - \cfrac{ 1 }{ 2 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{- \cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{2}) \\\\\\ y-7=- \cfrac{ 1 }{ 2 }x+1\implies {\Large \begin{array}{llll} y=- \cfrac{ 1 }{ 2 }x+8 \end{array}}[/tex]
-15 POINTS-
What’s the length of GH