Meera works at the zoo's information desk. The total amount of time she spends giving directions is equal to 4 times the total amount of time she spends answering phone calls plus twice the amount of time she spends answering the phone and responding to emails. Which simplified expression represents the amount of time Meera spends giving directions?
A. 12a + r
B. 8s + r
C. 4a + 2 (a + r)
D. 6a + 2r
The simplified expression represents how much Meera spends giving directions is D. 6a + 2r.
What is a simplified expression?A simplified expression is a mathematical expression that has completed the mathematical operations of adding, subtracting, multiplying, and dividing with the known values.
Given a simplified expression, the work left would be to fill in the independent variables.
Data and Calculations:The total time spent answering phone calls = a
The total time spent responding to emails = r
The total time spent giving directions = 4a + 2(a + r) = 6a + 2r
Thus, we can conclude that Meera spends six times the amount she spends answering the phone and two times the time she spends responding to emails to give directions.
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(ECSEPTEMBER 2019) QUESTION 8 8.1 8.2 Determine f'(x) from first principles if f(x) = 3 - 2x² Determine: 8.2.1 D₂[x(x-2)²] 8.2.2 dx MATHEMATICS PI if y = ax 2x √x +3
After differentiating the function f(x)=3 - 2 x ², we get the result as d y / d x = - 4 x
Differentiation is a process applied to a function which finds the function's rate of change compared to the rate of change of the independent variable.
We are given the function as:
f(x)=3 - 2 x ²
We need to find d y / d x
For this we need to differentiate the function with respect to x.
Differentiating the function with respect to x, we get that:
d y / d x = ( 0 ) - 2 ( 2 x ) ( 1 )
d y / d x = 0 - 4 x
d y / d x = - 4 x
Therefore, after differentiating the function f(x)=3 - 2 x ², we get the result as d y / d x = - 4 x
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Find the area of a rectangle that has a length of (x + 5) and a width of (x-3)
Answer:
(x^2+2x-15) units
Step-by-step explanation:
Area=LW
=(x+5)(x-3)
=x^2-3x+5x-15
(x^2+2x-15) units
1
A=h(B+b); A = 39, B = 8, b = 5
Solution,
Given,
A = 39
B = 8
b = 5
A = h(B+b)
Now,
A = h(B+b)
Putting the given values,
39 = h(8+5)
or, 39 = h×13
or, 39÷13 = h
or, 3 = h
or, h = 3
Therefore,the value of h is 3
In a circle of radius 6 miles, the length of the arc that subtends a central angle of 1 radians is
We get the length of the arc that subtends a central angle of 1 radians as 6 miles with radius as 6 miles also.
We are being asked to solve for the length of the arc of a circle.
For this, we are given that:
A radius of around 6 miles.
And a central angle that is subtended by the arc which is equal to 1 radians.
In order to solve for this, we need to use the length of the arc formula.
The formula is:
s = r θ
Where r = is the radius
and
θ = is the subtended central angle given in radians
Now, by substituting the values in the formula, we get that:
s = 6 mi (1 rad) = 6 miles
Therefore, we get the length of the arc that subtends a central angle of 1 radians as 6 miles with radius as 6 miles also.
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Find the perimeter of the regular polygon ?
The perimeter of the regular polygon is 232
How to find the perimeter of the regular polygon?The side lengths of the regular polygon are given as
4/3x - 1/3 and x + 7
The sides of regular polygon are equal
So, we have:
4/3x - 1/3 = x + 7
Multiply both sides by 3
4x - 1 = 3x + 21
Collect like terms
4x - 3x = 1 + 21
Evaluate the like terms
x = 22
Substitute x = 22 in x + 7
Side = 22 + 7
Side = 29
The perimeter of the regular polygon is calculated as:
Perimeter = Number of sides x Side length
So, we have
Perimeter = 8 * 29
Evaluate
Perimeter = 232
Hence, the perimeter of the regular polygon is 232
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You are building a model of a new roller coaster with a scale factor of 1/51. The model is 4ft yall. How tall is the actual roller coaster?
The actual roller coaster is 204 ft tall.
Given that, the length of the model roller coaster is 4 ft and the scale factor is 1/51.
What is a scale factor?The scale factor is defined as the number or the conversion factor which is used to change the size of a figure without changing its shape. It is used to increase or decrease the size of an object.
Let the length of the actual roller coaster be x.
We know that Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Now, 1/51 = 4 / x
⇒x=204 ft
Therefore, the actual roller coaster is 204 ft tall.
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0.789x10^5
is this correct scientific notation
The correct scientific notation of [0.789×(10⁵)] is 78900.
As per the question statement, we are provided with a multiplication of a decimal number and an exponential number.
We are required to determine its correct scientific notation.
A decimal number, say 0.059, can be expressed as a multiplication of a decimal number and an exponential number, such as [5.9×(10)⁻²].
But in our case, after performing the multiplication of the given values, we get, [tex][0.789*10^{5}]=(\frac{789}{1000}*100000)=(789*100)=78900[/tex]
And 78900 is not a decimal value. Hence, the correct scientific notation of [0.789×(10⁵)] is 78900.
[Note: Here, we need to know the procedure to convert a decimal into a fraction, using which we converted 0.789 into [tex]\frac{789}{1000}[/tex]. First, we will need to eliminate the decimal point and consider the digits in the same order as a complete number which will be our numerator. Secondly, we will use (10ⁿ) as the denominator, where "n" is the number of digits to the right side of the decimal point in the original decimal number. Thus, 0.789 can be written as [tex]\frac{789}{1000}[/tex], as there are three digits to the right of the decimal point in 0.789]
Scientific Notation: It is a method of expressing numbers that are too large or too small to be conveniently written in decimal form.Exponential Number: Any number which is in the form of (aⁿ), is known as an exponential number.To learn more about Scientific Notations, click on the link below.
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A rectangular tiled floor is composed of 70 square tiles. The rectangular floor is rearranged so that 2 tiles are removed from each column and 4 tiles are added to each row. After the change in layout, the floor will still have 70 tiles, and still be rectangular. How many columns are in the tile floor before the change in layout?
The number of columns is in the title floor before the change in layout is 10
Given that A rectangular tiled floor is composed of 70 square tiles. The rectangular floor is rearranged so that 2 tiles are removed from each columns and 4 tiles are added to each row. After the change in layout, the floor will still have 70 tiles, and still be rectangular asked to find the number of columns in the tile floor before the change in layout.
Let's assume the number of rows is x
The number of columns will be [tex]\frac{70}{x}[/tex]
After the changing, the rows can be x+4
The number of columns will be [tex]\frac{70}{x}[/tex]-2
The equation will be (x+4)([tex]\frac{70}{x}[/tex]-2)=70
⇒[tex]x^{2} +4x-140=0[/tex]
⇒x=10
Therefore,The number of columns is in the title floor before the change in layout is 10
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The Chen family and the Aoki family each used their sprinklers last summer. The water output rate for the Chen family's sprinkler was 40L per hour. The water output rate for the Aoki family's sprinkler was 25L per hour. The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 2000L. How long was each sprinkler used?
Answer:
Chen family used the sprinklers for 25 hours
Aoki family used the sprinklers for 40 hours
Step-by-step explanation:
Let C be the number of hours the Chen family used the sprinklers and let A be the number of hours the Aoki family used the sprinklers
Total hours used
=> C + A = 65 (1)
Total water usage for Chen family = 40C (40 L per hour x no. hour)
Total water usage for Aoki family = 25C (25 L per hour x no. hours)
Total used by both families = 2000 L
So
40C + 25A = 2000 (2)
Therefore we have two equations in 2 variables which can be solved simultaneously
Multiply (1) by 25:
==> 25C + 25A = 25 x 65
==> 25C + 25A = 1,625 (3)
Subtract (3) from (2) to eliminate the A term:
(2) - (3) ==>
40C + 25A - (25C + 25A ) = 2000 - 1625
40C + 25A - 25C - 25A = 375
40C - 25C = 375
15C = 375
C = 375/15
C = 25
So the Chen family used the sprinklers for 25 hours
Since C + A = 65
A = 65 - C
==> A = 65 - 25
A = 40
The Aoki family used the sprinklers for 40 hours
2) At a bake sale there were 48 raisin cookies sold. If the ratio of raisin cookies sold to
oatmeal cookies sold was 8: 5, what is the combined amount of raisin and oatmeal cooki
sold?
Answer: The combined amount of raisin and oatmeal cookies sold=80. Step-by-step explanation: Let x be the combined amount of raisin and oatmeal cookies sold.
Step-by-step explanation: i really hope this helps but lmk if i am wrong have a good day/night (: <3
Can anyone help me with this
Answer:
B. SAS
Step-by-step explanation:
Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.
Please help !
What is the coefficient in the term 4w?
4
w
0
1
Answer:
4
Step-by-step explanation:
the coefficient is usually a constant factor for a variable.
so, the answer here is 4.
I need help pls and thank u What is 5.3=z-2.7?
Answer: z=8
Step-by-step explanation:
5.3=z-2.7
5.3+2.7=z-2.7+2.7 ==> remove the 2.7 in 'z-2.7' to single out the variable z.
z=5.3+2.7
z=8
z = 8 ✅
Step-by-step explanation:Step 1:
Add 2.7 to both sides
5.3 = z - 2.7
5.3 + 2.7 = z - 2.7 + 2.7
⬆️ ⬆️
Step 2:
Simplify
5.3 + 2.7 = z - 2.7 + 2.7
( = 8 ) ⬇️ ( = 0 )
⬇️ ⬇️
8 = z
Do the following sets of data represent a function? Justify your answer.
1. (1,4), (2, 4), (3, 5), (2, 2)
2. (10, 5), (12, 5), (7, 12), (12, 2)
3. (0, 0), (5, 4), (4, 5), (1, 0)
1. No, the set of data does not represent a function.
A function relates an input to an output. It is like a machine that has an input and an output. And the output is related somehow to the input.
We are given with (1,4), (2, 4), (3, 5), (2, 2)
This is because every output of this data does not have unique input.
4 and 2 have the same input i.e. 2.
2. Yes, the set of the data represents a function.
We are given with (10, 5), (12, 5), (7, 12), (12, 2)
It is a function as every input has a single output.
So, (10, 12, 07) are the elements of the domain and (2, 5, 7, 12) is the range of the function.
3. Yes, it is a function as every input of this data represents the single and unique output.
We are given with (0, 0), (5, 4), (4, 5), (1, 0)
It has its unique elements and domain (0,1,4,5) and range is from (0, 1, 2, 3, 4, 5).
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Please help me
"The verticles of ABC are A(-4,5,)B(-2,4), and C(-3,2). If ABC is reflected across the line y = - 2 to produce the image ABC, find the coordinates of the vertex C.
The coordinates of C' after a reflection across the line y = -2 are ___
The coordinates of C' after a reflection across the line y = -2 are (3, -2).
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.
Given that the verticles of ABC are A(-4,5,)B(-2,4), and C(-3,2). If ABC is reflected across the line y = - 2 to produce the image ABC, then we need to find the coordinates of the vertex C.
Let (x, y) represent the coordinate of the point C
x-coordinate value:
The line y = -2 is parallel to the x-axis, therefore the x-value will remain the same following a reflection across the x-axis.
Taking the point C' as the image of the corresponding point C(-3,2), we need that the x-coordinate of the point C' is also 3
x = 3
y-coordinate value:
The difference between the coordinate of the pre-image and the reflecting line is same as difference between the reflecting line and the coordinates of the image.
Therefore, the coordinates of the point C' is (x, y) = (3, -2)
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Data was collected on salaries of compliance specialists in corporate accounting firms. The salaries ranged from $58,000 to $238,000
If these values are grouped into six class intervals, indicate the class boundaries.
What class interval width was chosen?
What are the six class midpoints?
The class boundaries are:
1 58000 but less than 88,000
2 88,000 but less than 118,000
3 118,000 but less than 148,000
4 148,000 but less than 178,000
5 178,000 but less than 208,000
6 208,000 but less than 238,000
The class interval width for the distribution that we have here is given as $30000.
The six midpoints and the class boundaries are:
73000103,000133,000163000193000223000How to solve for the class boundary238,000 - 58,000= 180000
180000 / 6 = 30000
Class Boundaries1 58000 but less than 88,000
2 88,000 but less than 118,000
3 118,000 but less than 148,000
4 148,000 but less than 178,000
5 178,000 but less than 208,000
6 208,000 but less than 238,000
What is the class interval width?238,000 - 58,000= 180000
180000 / 6 = 30000
width = 30000
The six class midpoints58000 + 88000 / 2 = 7300088000 + 118000 / 2 = 103,000118000 + 148000 / 2 = 133,000148000 + 178000 / 2 = 163000178000 + 208000 / 2 = 193000208000 + 238000 / 2 = 223000Read more on class intervals here;
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Tell whether the angles are complementary or supplementary. Then find the value of x.
Step-by-step explanation:
SUPPLEMENTARY because they are on a staright line and add up to 180°
[tex]76 + (2x + 4) = 180 \\ 2x + 76 + 4 = 180 \\ 2x = 180 - 76 - 4 \\ 2x = 100 \\ \frac{2x}{2} = \frac{100}{2} \\ x = 50[/tex]
x=50°
Evaluate the expression ab, for a = 4 and b = 7.
Answer:
28
Step-by-step explanation:
4 x 7 = 28
What is
1
4
+
9
10
y
−
3
5
y
+
7
8
written in simplest form
Jesse has 414 inches of ribbon for making bows. She uses 3 inches of ribbon for each bow. How many bows can she make?
Write a division expression that can be used to answer this question.
Answer:
414/3
Step-by-step explanation:
If she has 414 inches of ribbon and uses 3 inches for each bow then that means that you would have to divide 414 by 3 in order to find the amount of bows that Jesse could make
2^n * 3 * 5^m
Write 8A as a product of powers of its prime factors
8A = [tex]2^{n + 3} * 3 * 5^{m}[/tex] is a product of powers of its prime factors of Polynomials.
What is Polynomials ?
Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The concepts degree, standard form, monomial, binomial, and trinomial are all covered in this video.Given - [tex]2^{n} * 3 * 5^{m}[/tex]
The numbers 2, 3 and 5 are already prime numbers.
Multiplying 8 on both sides
8 × A = [tex]2^{n} * 3 * 5^{m} * 8[/tex]
Expressing 8 as the product of prime numbers
8A = [tex]2^{n} * 3 * 5^{m} * 2 * 2 * 2[/tex]
8A = [tex]8A = 2^{n} * 3 * 5^{m} * 2^{3}[/tex] (When the base is same, the power is added)
Adding the power of base 2, we add n and 3
8A = [tex]2^{n + 3} * 3 * 5^{m}[/tex]
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(a) Write the next whole number after 222three in the base-three system.
Answer:
1000
Step-by-step explanation:
You want the next number after 222 in base 3.
Counting sequenceIn any useful number base, the counting at any given integer position is ...
0, 1, 2, 3, ..., (base -1), 0 and add 1 to the next number position
For base 3, this is ...
0, 1, 2, 10
When the digit in the next higher position is also (base -1), then it gets incremented to 0 and the carry is propagated to the left.
In base 10, the equivalent is ...
999 +1 = 99(9+1) = 99(10) = 9(9+1)0 = 9(10)0 = (9+1)00 = 1000
In base 3, your incremented value is ...
222 +1 = 22(2+1) = 22(10) = 2(2+1)0 = 2(10)0 = (2+1)00 = 1000
The next whole base 3 number after 222 is 1000.
Help me please !!!!
2. In the number 928,547,136, which digit is in the hundred thousands place?
Answer:
5.
Step-by-step explanation:
5 is in the hundred thousand place because starting from the right it goes ones, tens, hundreds, thousands, then thousands, and hundred thousand meaning 5 would be in that place.
Idrissa collected pennies in a fundraiser. He measured the mass of all the pennies he collected to be 2,400 grams. Two pennies put together have a mass of 5 grams. How much money did Idrissa raise in this fundraiser?
Answer: Idrissa collected 240 pennies
Step-by-step explanation:
2400/5=480
What is the missing table value?
A. 9.4
B. 9.84
C. 10.16
D. 11.2
Answer: the answer is C. 10.16
Step-by-step explanation: on the right each value is going up by 2.54 cm so for the forth row on the right you just need to multiply 2.54 x 4 which equals 10.16
hope this helps
A data set had values ranging from 117 to 139. A new data point of 30 was
added to the data set. Would this point affect the mean or the median more? How
(increase/decrease) and why? (2 points)
Answer:
This point would affect the mean more because the median is less sensitive to outliers.
Step-by-step explanation:
Hope this helps!
A washer and a dryer cost $565 combined. The washer costs $85 less than the dryer. What is the cost of the dryer?
what is the arctan (-1)?
B. [tex]-\frac{\pi }{4}[/tex]
Answer:
Option B. is correct.
Step-by-step explanation:
arctan(y) = tan - 1(y) = x+ kπ
for k = {...,-2,-1,0,1,2,...}
➫ e.g tan(45°) = 1
➫ and that would mean the arctangent of 1 is 45 degrees(We represent this in π/? form)
arctan(1) = tan-1(1) = 45° = -π/4
Hope this helps!