The length of the rectangle is 3 times it width. The width size is given as 2 inches.
Therefore,
width = 2 inches
length = 3(2) = 6 inches
The area of the rectangle can be calculated below
[tex]\begin{gathered} \text{area}=\text{length}\times\text{width} \\ \text{area}=6\times2 \\ \text{area}=12inches^2 \end{gathered}[/tex]The answer is B.
The tree in Bob's backyard is 8.5m high. How high is it in centimeters?Be sure to include the correct unit in your answer.
We know that
1 m = 100 cm
Then to change from meter to centimeter, multiply by 100
Since the tree in Bob's backyard is 8.5 m
Then to change it to cm, multiply 8.5 by 100
[tex]\begin{gathered} 1m=100cm \\ 8.5m=8.5\times100 \\ 8.5m=850cm \end{gathered}[/tex]The height of the tree is 850 cm
-7×+8=-4x = ? trying to understand this
Here, we want to get the value of x
We can get this by isolating x
We start by bringing like terms together
[tex]\begin{gathered} -7x\text{ = -4-8} \\ \\ -7x\text{ = -12} \\ \\ x\text{ = }\frac{-12}{-7} \\ \\ x\text{ = }\frac{12}{7} \end{gathered}[/tex]4. The ages of the members of a volunteer group are shown below: 13, 14, 14, 14, 15, 15, 15, 16, 16, 21, 23 Which box plot best represents this data? F 13 15 17 19 21 23 13 15 17 21 23 H < 15 19 15 17 19 21
First, we need to calculate the median
13, 14, 14, 14, 15, 15, 15, 16, 16, 21, 23
we have 11 values the media is the 6th value in this case 15.
the lower extreme is 13 the upper extreme is 23.
The lower quartile is 14 and upper quartile is 16
the box plot is
Please help I’ll mark you as brainliest if correct!!
Answer: 3
Step-by-step explanation:
1. 2 packs of 6
2. 6 packs of 2
3. 3 packs of 2 and one pack of 6
Selene's checking account balance was -$32, and then she withdrew $43 more. What is her checking account balance after the withdrawal?
Answer: $-75
Step-by-step explanation:
She took out money therefore the balance will go down. If we take 43 dollars from $-32 then we will get -75.
Find the equation of the line connecting the points (2, 0) and (3, 15).
Answer:
y = 15x - 30
Hope this helps!
Step-by-step explanation:
The slope can be found with the equation [tex]\frac{y_{2} -y_{1} }{x_{2} - x_{1} }[/tex].
Add in the numbers from the two points to get [tex]\frac{15-0}{3-2}[/tex] which is [tex]\frac{15}{1}[/tex] : 15.
That means slope is 15. To get the other numbers, you can do y = 15x and then plug in one of the points, for example (0) = 15(2), which is 0 = 30. To make this equation true, you need to minus 30 so it would be 0 = 30 - 30 and this is true, so putting it all together would get y = 15x - 30.
The water pressure on a submerged object is given by P = 64d, where P is the pressure in pounds per square foot, and d is the depth of the object in feet.
a. solve the formula for d.
b. Find the depth of a submerged object if the pressure is 672 pounds per square foot.
The water pressure on a submerged object is given by P = 64d, then the
a. The answer to the subject of the formula, "d," is d = P/64.
b. A submerged object will be 10. 5 feet deep at a pressure of 672 pounds per square foot.
What is a function?A function can be defined as an expression, law or rule that shows the relationship between two variables.
These variables are namely;
Independent variableDependent variablegiven the role as;
P = 64d
Where;
P stands for pounds per square foot of pressure.
d represents the object's depth in feet.
Let's now make the variable "d" the focus of the formula.
The coefficient of the variable "d," which is 64, is used to divide both sides of the equation. So that the variable can stand on its own, this is done.
We get,
P/64 = 64d/64
d = P/ 64
P equals 672 pounds per square foot if there is pressure.
When the variable's value is substituted into the formula, we get;
d = P/64
Then,
d = 672/64
Discover the quotient.
d = 10. 5 ft.
The value is 10.5 feet.
Therefore,
a. The answer to the subject of the formula, "d," is d = P/64.
b. A submerged object will be 10. 5 feet deep at a pressure of 672 pounds per square foot.
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Ava's pin code is a 4-digit number.The some of the four digits is 22.Reading from left to right,the first and second digits are the same.The second digit is twice the third digit.The first digit is four times the fourth digit.What is Ava's pin code?
From the provided information we get that Ava's Pin code is 8842.
Ava's pin code is a 4-digit number.
Let the first digit = x equation 1
Reading from left to right, the first and second digits are the same. So,
Second digit = x equation 2
Let, third digit = y
The second digit is twice the third digit. So,
x = 2y
⇒ y = x/2
Third digit = x/2 equation 3
Let, fourth digit = z
The first digit is four times the fourth digit. So,
x = 4z
⇒ z = x/4
Fourth digit = x/4 equation 4
Sum of the four digits is 22. So, using equation 1 , equation 2 , equation 3 and equation 4 , we can write
x + x + (x/2) + (x/4) = 22
2x + (x/2) + (x/4) = 22
Multiplying both sides by 4 , we get
8x + 2x + x = 88
11x = 88
x = 8
First digit = x = 8
Second digit = x = 8
Third digit = x/2 = 8/2 = 4
Fourth digit = x/4 = 8/4 = 2
So, we can conclude that the Ava's Pin code is 8842.
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X+ 2y = 166 -7x-3y = 24
We are asked to solve the following system of equations using the elimination method:
x + 2 y = 16
-7 x- 3 y = 24
so we select to multiply the first equation by "7", that way we will be able to eliminate the term in "x" by simple combining term by term the two equations:
7 (x + 2 y) = 7*16
7 x + 14 y = 112
now we combine this new expression term by term with the second equation:
7 x + 14 y = 112
-7 x - 3 y = 24
_____________
0 + 11 y = 136
solve for y by dividing both sides by 11:
y = 136/11
Now we use this value to solve for x in the first equation:
x + 2 (136/11) = 16
x +
please help me with this question anyone
If x and y vary directly and y is 120 when x is 15, find y when x is 6.
Based on the direct variation between x and y, the value of y is 48
How to determine the value of y when the value of x is 6?The given statements are:
If x and y vary directlyy is 120 when x is 6From the above points, we understand that:
The variation is a direct variation
A direct variation is represented as
y = kx
Where k represents the constant of variation
The above equation is a linear equation
As a general rule, linear equations are equations that have constant average rates of change.
So, we have
y = kx
y is 120 when x is 15
This means that
120 = 15k
Divide by 15
k = 8
So, we have
y = 8x
The value of y when x is 6 is
y = 8 x 6
Evaluate
y = 48
Hence, the value of y when the value of x is 6 is 42
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Solve each system by graphing, and then write the solution. x + 4 = - y-6y + 9x = - 6
To solve the given system of equation by graphing you only have to graph both lines. The solution is the intersection between the lines.
According to this, the intersection of the two lines is (-2, -2). It means that the solution is (-2, -2).
A dealer sold a watch 130% of his cost. If the sale price was $39, how much did the cost the dealer? Please show your work.
The cost of the watch which sold at 130% of its cost and sale price is $39 is equal to $30.
As given in the question,
Sale price of the watch for which dealer sold = $39
Let $'x' be the cost of the watch with which dealer purchase
A dealer sold a watch 130% of its cost
Required expression to show the given condition of a dealer is given by:
130% of x = $39
⇒ (130 /100) × x = $39
⇒ x = ( 39 × 100 ) / 130
⇒ x = $30
Therefore, the cost of the watch which sold at 130% of its cost and sale price is $39 is equal to $30.
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Which angle is NOT congruent to 4
The angle not congruent to the angle 4 in the options is angle 7(∠7)
How to find congruent angles?When parallel lines are cut by a transversal, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.
Therefore, corresponding angles are equal, alternate angles are equal and vertically opposite angles are equal.
Therefore,
∠4≅∠6(vertically opposite angles)
∠4≅∠2(corresponding angles)
∠4≅∠8(alternate exterior angles)
Therefore the angle not congruent to ∠4 among the option is ∠7
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Perform the following division: -48 / 5
A. 9.6
B. 8.1
C. -8.1
D. -9.6
Give a counterexample to the following conditional statement. Write your answer as a number. If |x+ 4|= 8, then x=−12
he Solution:
iven in the question that if
[tex]|x+4|=8\text{ then x=-12}[/tex]We are required to give a counterexample to the given conditional statement above.
[tex]\begin{gathered} |x+4|=8 \\ \text{Means that} \\ x+4=8\text{ or x+4=-8} \end{gathered}[/tex]Solving each of the equations above, we get
[tex]\begin{gathered} x+4=-8 \\ x=-8-4 \\ x=-12 \\ Or \\ x+4=8 \\ x=8-4 \\ x=4 \\ \text{ So, } \\ x=-12\text{ or x=4} \end{gathered}[/tex]So, the counterexample to the given conditional statement is x = 4.
4 ≤-3x - 1≤9
What is the compound inequality
Answer:
−1≤x<3
Step-by-step explanation:
−4≤3x−1<8
−4≤3x−1and3x−1<8
3x−1≥−4and3x−1+1<8+1
3x≥−3and3x<9
x≥−1andx<3
−1≤x<3
01In Will's garden, 71 out of 200 plants have developed seends. Which is closest tothe percent of his plants that have developed seeds?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
plants have developed seeds = 71
total plants = 200
Step 02:
% = part / whole * 100
[tex]\text{percentage \% = }\frac{71}{200}\cdot100[/tex]% = 35.5
The answer is:
35.5 %
At age 19, someone sets up an IRA (individual retirement account) with an APR of7 %. At the end of each month he deposits $20.00 in the account. How much will the IRA contain when he retires at age 65? Compare that amount to the total deposits made over the time period.
The amount of IRA when he will retire at age 65 = $83448.27
And the total deposits made over the time period is less than the the amount of IRA
We have been given, at age 19, someone sets up an IRA (individual retirement account) with an APR of7 %. At the end of each month he deposits $20.00 in the account.
We need to find the IRA when he retires at age 65.
here, 65 - 19 = 46 years
So, the period would be,
46 × 12 = 552 months
Monthly deposit= $20
And the interest rate would be,
Interest = 0.07/12
= 0.0058
To calculate the future value, we need to use the following formula:
FV= {A × [(1 + i)^n-1]} / i
A= monthly deposit
i = interest rate
n = period
So, the Future Value of Annuity
= 20 × ([1 + 0.0058]^552 - 1 ) / (0.0058)
= 20 × 24.2 / 0.0058
= $83448.27
So, the amount of IRA when he will retire = $83448.27
Deposits made over the time period = 20 × 46 × 12 = $11040
Difference = 83448.27 - 11040
= $72408.27
This means, the total deposits made over the time period is less than the the amount of IRA he will get when he retires at age 65.
Therefore, the amount of IRA when he will retire at age 65 = $83448.27
And the total deposits made over the time period is less than the the amount of IRA
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3 is grater than or equal to W and -5 is less than W write as an inequality
Answer: 3 ≥ W > -5
Step-by-step explanation:
Just look at the way the question is asked, that is the best I can explain. Sorry.
3x – 2 ( 6x – 3 ) = 42
Answer:
x=-4Step-by-step explanation:
3x−(12x−6)−42=0
−9x+6−42=0
(−9)⋅x+(−36)=0
x=−(−36)/−9
x=-4
a bank features a savings account that has an annual percentage rate of 4.7% with interest compounded monthly.Sean deposits $3500 into the account. How much money will sean have in the account in 1 year
Based on the interest compounded by the bank monthly, and the amount deposited by Sean in the account, the amount of money that will be in that account in a year is $3,668.09
How to find the amount saved?First, find the monthly rate because the interest is compounded monthly:
= 4.7% / 12
= 4.7/12 %
The number of periods would be:
= 1 x 12 months a year
= 12 periods
The amount that Sean will have in a year can be found by the formula:
= Amount invested x (1 + periodic rate) ^ number of periods
Solving for the amount in the account after 1 year gives:
= 3,500 x (1 + 4.7%/12) ^ 12
= 3,500 x 1.0480257937581146250656044647993
= $3,668.09
In conclusion, the amount that Sean will have after saving for a year in the account would be $3,668.09
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5. Sales at Borders Books and Music stores increased from $2503 million in 1997 to $3699
million in 2003. Assuming that sales have been increasing exponentially, find an equation of
the form P = Poat, where P is Borders sales in millions of dollars and t is the number of years
since 1997. What is the percent growth rate?
B
Which of the following tables of values
In linear relationship, 199.333 million dollers per year is the percent growth rate.
What is linear relationship in math?
A statistical word used to express a straight-line relationship between two variables is a linear relationship (or linear association). Linear relationships can be represented graphically or mathematically as the equation y = mx + b.Given , t Rs numbers of year since 1997 .
t = 0 corresponds to year 1997
t = 6 corresponds to year 2003
Let s(t) = sales of the year
So, given that
sales in 19997 is $2503 millions
so s(0) = 2503 million dollers
Sales in 2003 is $3699 millions
so s(6) = 3699 million dollers
Now apply formula of linear relation ship
s - s(0) = s(6) - s(0)/6 - 0 ( t - 0)
s - 2503 = 3699 - 2503/6 (t)
s = 1196* t /6 + 2503
so s(t) = 598t/3 + 2503
so now average rate of change of function over on interval is given by
= s(b) - s(a)/b - a
= s(6) - s( 0)/6 - 0
= 3699 - 2503/6
= 598/3
= 199.333 million dollers per year .
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a brigde connecting 2 cities separted by lakes has a lenght of 5927.61 find lenght of bridge in miles round to nearest tenth
The length of the bridge that connect the two cities separated by the lake is 3.4 miles.
What is the length of the bridge?The mathematical operation that would be used to convert yards to miles is division. Division is the process of putting a number into equal groups using another number. For example, when 6 is divided by 3, 3 divides 6 into 2 equal groups.
In order to convert yards to miles, divide the given length in yards by 1760.
1 yard = 1 / 1760 miles
5927.61 / 1760 = 3.36796 miles
= 3.4 miles
To round off to the nearest tenth, since the hundredth digit is greater than 5, 1 is added to the tenth digit and the digits less than the tenth digit is replaced with zero.
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Identifying each relation, decide wether or not it is a function
For the following relations, using the condition for a relation to represent a function, we have that:
Relation 1 is not a function.Relation 2 is a function.When does a relation represents a function?A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.
The input may also be called domain, while the output may also be called range.
For a point in the standard format (x,y), we have that:
x is the input or domain.y is the output or range.The meaning is that the input given by the x-coordinate is mapped to the output given by the y-coordinate.Hence, in the context of this problem, we have that:
Relation 1 is not a function, as the domain of f is mapped to different ranges of f and g.Relation 2 is a function, as each domain is mapped to only one range.More can be learned about relations and functions at https://brainly.com/question/12463448
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Write an equation of the line passing through the point (9, 6) that is parallel to the
line y = -6x - 6.
⇒Parallel line have the same gradient if the gradient of the given equation is m=-6 it means that the gradient of the new equation is also m=-6
The general equation of a straight line is y=mx+c
⇒plug in the points and find the value of the unknown c
[tex]6=-6(9)+c\\6=-54+c\\c=6+54\\c=60[/tex]
⇒This means that the new equation parallel to the given equation is⇒
[tex]y=-6x+60[/tex]
Pls help and thanks!
the multiplication of 2 matrices A and B
a11 a12 a13 ...
a21 a22 a23 ...
a31 a32 a33 ...
...
b11 b12 b13 ...
b21 b22 b23 ...
b31 b32 b33 ...
is
a11×b11+a12×b21+a13×b31+... a11×b12+a12×b22+a13×b32 ...
a21×b11+a22×b21+a23×b31+... a21×b12+a22×b22+a23×b32
a31×b11+a32×b21+a33×b31+... a31×b12+a32×b22+a33×b32
...
in other words, we combine the rows of the first matrix with the columns of the second matrix.
the rows of the result matrix are driven by the rows of the first matrix and the columns of the second matrix.
formally :
we can multiply a m×n matrix only with a n×o matrix.
the number of columns in the first matrix must be equal to the number of rows in the second matrix.
the result matrix is then sized m×o.
the first element (first row first column) of the result matrix is the sum of the products of the elements of the first row of the first matrix with the elements of the first column of the second matrix.
the element in the (x,y) position in the result matrix is the sum of the products of the elements of the xth row of the first matrix with the elements of the yth column of the second matrix.
so, when multiplying 2 2×2 matrices, the condition is automatically fulfilled : m = n = o = 2
ST =
4×0+1×-4 4×4+1×3
-3×0+-2×-4 -3×4+-2×3
=
-4 19
8 -18
and TS =
0×4+4×-3 0×1+4×-2
-4×4+3×-3 -4×1+3×-2
=
-12 -8
-25 -10
as we can see, the 2 results are completely different.
Which set of ordered pairs does not represent a function?
O {(-6, 9), (-7, 1), (-4,-2), (-4,5)}
O {(-6,-8), (-9, 8), (6, 9), (5,8)}
O {(3,-8), (-4,0), -9,-1), (8,0)}
O {(6,4), (-1,-9), (-9, 1), (-2,-1)}
Answer:
The top set does not represent a function because -4 corresponds to two y-values.
Simplify this expression 2 x x 3 x y
Answer:
6[tex]x^{2}[/tex]y
Step-by-step explanation:
If I ready your explanation correctly it is
2x3xy We multiply the 2 and 3 and the xx would be [tex]x^{2}[/tex]
Name:
Math for College Liberal Arts
Classifying Data and Frequency Tables
Classify the following variables as qualitative (C) or quantitative (Q). (1 point each)
1. A list of telephone numbers:
3. Types of animals at a zoo :
11th graders
12th graders
Students at a local high school in grades 11 and 12 are asked what gaming system they
prefer. The results are summarized below in a two-way frequency table.
5. Complete the table. (6 points)
TOTAL
Nintendo Switch
132
11th graders
12th graders
TOTAL
Date:
?
?
2. Heights of players on a basketball team
4. Number of children in a family:
PS4
?
127
?
Neither
?
PS4
95
182
TOTAL
?
Use the table above to answer these questions. (1 point each)
6. How many 12th graders do not like either gaming system?
7. How many total students like the Nintendo Switch?
8. What is the total number of 11th grade students?
9. How many total students are there?
10. How many 11th graders like the PS4?_
11. Create a relative frequency table from the table above. Write the relative frequencies as decimals
rounded to two decimal places. (12 points)
Nintendo Switch
Neither
315
655
TOTAL
Numerical variables are the subject of quantitative data. Qualitative data can be represented by a name, symbol, or number code and are measures of "types."
What are qualitative variables and quantitative variables?Numerical variables are the subject of quantitative data. Qualitative data can be represented by a name, symbol, or number code and are measures of "types." Data concerning categorical variables make up qualitative data.
Quantitative Variables with values obtained through measurement or counting. Variables that exists not measurement variables are referred to as qualitative variables. Their values are not determined by counting or measuring. Values that are used to identify people in a table are called designators. While qualitative research focuses on words and meanings, quantitative research deals with figures and statistics.
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