There are 36 males and 45 females in the sales field.
Ratio of the number:
Ratios compare two numbers, usually by dividing them.
For example,
If you are comparing one data point (A) to another data point (B), your formula would be
=> A/B.
This means you are dividing information A by information B.
Given.
Suppose that the ratio of males to females in the sales field of a large company is 4:5.
Total number of representatives = 81.
Now, we need to find the number of males and number of females.
Let x be the number of representatives.
So, based on the ratio we have written this as,
=> 4x : 5x = 81
So, the total number of representatives is,
=> 4x + 5x = 81
=> 9x = 81
=> x = 81/9
=> x = 9
So, the number of males is
=> 4x => 4(9) = 36
And the number of females is,
=> 5x => 5(9) = 45
Therefore, there are 36 males and 45 females in the sales field.
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With steps please, if it’s correct I’ll give full rate please
A gull can fly at a speed of 22 miles per hour i.e. equal to 116,160feett/hour and An AMTRAK train travels at 125 miles per hour i.e. equal to 2.1 miles/minute
Given that 1)A gull can fly at a speed of 22 miles per hour and asked to convert its units to foot/hour
2)An AMTRAK train travels at 125 miles per hour and is asked to convert its units to miles/minute
1 mile=5280 feet
22 miles/hour=22 × 5280 foot/hour
22 miles/hour=116,160 foot/hour
1 hour=60 minute
125 miles/hour= 125/60 miles/minutes
125 miles/hour= 2.083 miles/minutes≈ 2.1miles/minutes
Therefore, A gull can fly at a speed of 22 miles per hour i.e. equal to 116,160 feet/hour and An AMTRAK train travels at 125 miles per hour i.e. equal to 2.1 miles/minute
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What is 210 divided by 5
Answer:42
Step-by-step explanation:
Complete the standard form equation representing the quadratic relationship displayed above, where a,b, and c are consonants.
Answer:
y = - 2x² + 8x + 5
Step-by-step explanation:
the equation of a quadratic function in standard form is
y = ax² + bx + c ( a ≠ 0 )
to find a, b and c use ordered pairs from the table
(0, 5 )
5 = a(0)² + b(0) + c = 0 + 0 + c = 5 ⇒ c = 5 , then
y = ax² + bx + 5
(1, 11 )
11 = a(1)² + b(1) + 5 = a + b + 5 ( subtract 5 from both sides )
a + b = 6 → (1)
(2, 13 )
13 = a(2)² + b(2) + 5 = 4a + 2b + 5 ( subtract 5 from both sides )
4a + 2b = 8 → (2)
solve the 2 equations simultaneously to find a and b
multiplying (1) by - 2 and adding to (2) will eliminate b
- 2a - 2b = - 12 → (3)
add (2) and (3) term by term to eliminate b
2a + 0 = - 4
2a = - 4 ( divide both sides by 2 )
a = - 2
substitute a = - 2 into (1) and solve for b
- 2 + b = 6 ( add 2 to both sides )
b = 8
then a = - 2, b = 8 and c = 5 gives the standard quadratic function
y = - 2x² + 8x + 5
Step-by-step explanation:
standard equation would be
y = ax² + bx + c
out of that we know already from (0, 5) that c = 5, as
a×0² + b×0 + c = 5.
because of (-1, -5) we see
-5 = a×1 + b×-1 + 5 = a - b + 5
-10 = a - b
or
a = b - 10
because of (1, 11) we see
11 = a×1 + b×1 + 5 = a + b + 5
6 = a + b
now we use the previous equation :
6 = (b - 10) + b = 2b - 10
16 = 2b
b = 8
.
a = b - 10 = 8 - 10 = -2
so, our standard equation is
y = -2x² + 8x + 5
Jeff makes $25 per Nike and $50 per Adidas sold at Foot Locker. Jeff can get no more than
20 shoes per week. He wants to make at least $100 a week. Write the system of inequalities to represent this scenario where x represents Nike
and y represents Adidas.
Answer: 4 Nike shoes a week
Step-by-step explanation:
Janet rents a car while spending her vacation traveling in Argentina. When she returns the car, she has driven 1400 miles and used about 56 gallons of gas. If gas costs an average of $4.099 per gallon, estimate how much she spent on fuel.
Janet spent $230 on fuel
How to calculate the amount of money spent on fuel ?Janet rented a car to travel to Argentina
After the journey, she discovered that she had driven 1400 miles and used 56 gallons of gas
The gas costs $4.099 per gallon
Therefore the amount Janet spent thought out the journey for fuel can be calculated as follows
= 4.099 × 56
= 229.5
= 230
Hence when estimated, Janet spent $230 on fuel
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Here is a liner equation in two variables 2x + 4y - 31 = 123 determine whether each statement is true or false. the equation solved for x is x = 154 - 4y true or false ?
the equation solved for y is y = 77-x- 2 true or false ?
Answer:
Both sentences are false.
Step-by-step explanation:
Let's solve for x:
2x + 4y - 31 = 123
2x = 123 - 4y + 31
2x = 154 - 4y
x = 77 - 2y
Let's solve for y:
x = 77 - 2y
2y = 77 - x
y = 38.5 - 0.5x
16 2/3% to simplified question w explination pls
Bonjour,
Answer:
16 2/3 = 50/3
Step-by-step explanation:
16 2/3 = 16.6666666…
Change the percent to a decimal number by moving the decimal two places to the left.
Call this x = 0.16666666…
10x = 1.66666666…
100x 16.66666666…
Subtract 100x - 10x = 15
90x = 15
x = 15/90 = 1/6
16 2/3 % = 1/6
PLS HELPPP
identify the graph of the ellipse.
[tex]\frac{(x-3)^{2} }{16} +\frac{y-4^{2} }{9} =1[/tex]
The correct graph of the ellipse is identified and attached below.
Given the equation is (x₋3)²/16 ₊ (y₋4)²/9 = 1
step 1: identify the center (h,k) of the ellipse in standard form:
(x₋h)²/a² ₊ (y₋k)²/b² = 1
In the standard form of an ellipse, notice that there is a minus sign in front of the h and k.
In our equation (x₋3)²/16 ₊ (y₋4)²/9 = 1 , we have:
h = 3 and k = 4
Therefore, center (h,k) = (3,4)
Step 2: Identify the orientation by determining the major axis and minor axis in (x₋h)²/a² ₊ (y₋k)²/b² = 1
if a>b, the major axis is horizontal and the minor axis is vertical, making the ellipse a horizontal ellipse.
if a<b, the minor axis is horizontal and the major axis is vertical, making the ellipse a vertical ellipse.
For (x₋3)²/16 ₊ (y₋4)²/9 = 1
a² = 16, a = 4 and b² = 9 , b = 3
so, 4>3, the major axis is horizontal and the minor axis is vertical, making the ellipse a horizontal ellipse.
Step 3:
Plot the co-vertices along the minor axis and the vertices along the main axis (endpoints). No matter which way around, draw points a horizontal distance of a to the left and right from the center and points b above and below the center.
Therefore the vertices are marked along the major axis.
vertices are (3,7) and (3,1)
and co vertices are marked along the minor axis
co vertices are (₋1,4 ) and (7,4)
step 4: connect the vertices and co vertices making a smooth horizontal ellipse.
Hence a horizontal ellipse is made.
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To complete bookshelves a customer at your store needs to purchase vertical brackets to attach to the wall the customer wants the shelving to be 9 ft high and 10 ft long the wall brackets come in 48 in and 60-in sections the 48-in sections cost $12.95 each the 60-in sections cost $16.95 each the brackets should be 1 ft from each end and no more than 24 inches apart what will be the total cost of the brackets before tax
The total cost of the brackets before tax = $89.70
Height = 9 feet
length = 10 feet
Wall brackets come in 48-in cost $12.95 and 60-in costing $16.95
Distance of brackets from ends = 1 foot
Maximum distance between brackets = 24 inches
The brackets are:
48/12= 4feet, and 60/12 = 5feet
One of each must be used to cover the height of the shelf.
The length of the shelf is 60 inches
On subtracting 1 foot from each side of the allowance we get, 60-2 = 58-in
Then dividing by 24 we get
58/24 ≈3
The Total cost = (12.95 + 16.95)×3
= $89.70
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Triangle BCD is rotated 80° clockwise about the origin to form ΔKLM. If m∠KLM = 30°, what is m∠BCD?
A.
80°
B.
110°
C.
50°
D.
30°
Rewrite (4^7)^3 using a single exponent
Answer:
[tex]4^{21}[/tex]
Step-by-step explanation:
7 * 3 = 21
Add it as the exponent.
x - 4y=-20
x - 4y=-26
Answer:
x − 4y = −20x − 4y = −26
Step-by-step explanation:
After making several plates of empanadas, you are down to your last bag of shredded cheese. You realize that it’s not full; there is about / three-fourths of a bag left. If you want to make 4 plates with the remaining cheese, what fraction of a bag can you put on each plate?
The fraction of a bag that you can put on each plate is 3 /16.
What is the fraction you can put on each plate?A fraction is a non-integer that is made up of a numerator and a denominator. The numerator and the denominator are divided by a line. An example of a fraction is 1 / 2.
The fraction of the cheese that you can put on each plate can be determined by dividing the amount of cheese left by the number of plates. Division is the process of grouping a number into equal parts using another number.
Amount that can be put on each plate = fraction left / number of plates
3 /4 ÷ 4
3/4 × 1/4 = 3 /16.
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Find the equation of the line shown.
Answer:
y = -2x + 9
Step-by-step explanation:
The standard form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.
The line intersects the y-axis at 9, thus b = 9.
The slope formula is rise/run. The line falls 2 and runs 1, thus m = -2/1, or -2.
y = -2x + 9
Add. (x^2+1−4x^3+3x^4)+(−x^2−2x^4+x^3+4) Express the answer in standard form.
Answer:
x^4−3x^3+5
Step-by-step explanation:
Simplify the answer and convert it to standard form.
Answer: ANSWER
The simplified polynomial in standard form is
EXPLANATION
The given expression is
We group the terms with the same exponents,
We simplify to obtain,
Since the expression is a polynomial, writing it in standard form means writing the simplified form in descending powers of x.
Step-by-step explanation: gl
Loren already knows that he will have $500,000 when he retires. If he sets up a payoutannuity for 30 years in an account paying 10% interest, how much could the annuity provideeach month?
The annuity could pay $221.19 per month.
ANNUITY FORMULA: [tex]P_t=\frac{d\left[\left(1+\frac{s}{n}\right)^{n t}-1\right]}{\frac{s}{n}}[/tex]
Where,
[tex]P_t[/tex] is the account balance after t years.The regular deposit (the amount you deposit each year or month) is denoted by d.r denotes the annual interest rate in decimal form.n represents the number of compounding periods in a year.t consider the number of years.So,
Loren anticipates having $500,000 when he retires.
[tex]P_t[/tex] = $500,000He establishes a 30-year payout annuity at a 10%interest.
t = 30 years r = (10/100) = 0.1Each month, the annuity could provide
n = 2In the formula, replace the above values as follows:
500,000 [tex]=\frac{d\left[\left(1+\frac{1.1}{12}\right)^{(12)(30)}-1\right]}{\frac{11-1}{12}}[/tex]500,000 [tex]=\frac{d\left[(1.00833333)^{300}-1\right]}{0.00833333}[/tex]500,000 = d [2260.487925]Now, divide both sides by: 2260.487925
d = $221.19Therefore, the annuity could pay $221.19 per month.
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5/6 - 1/9 = ?/? - ?/? = ?/?
please help 20 points
i need to know what each ( ?/? ) is
5/6 - 1/9=?/? - ?/? = ?/? , value of each (?/?) is
5/6 -1/9 =15 /18 -2/18 =13 /18.
As given,
5/ 6 - 1/9 =?/? -?/? =?/?
Convert the given terms into like terms
Least common multiple of (6,9)=18
Value of each ( ?/?)
(5/6 ) × ( 3/3) -(1/9) × (2/2)
= 15 /18 - 2/18
= 13 /18
Therefore,5/6 - 1/9 = ?/? - ?/? = ?/? , value of each (?/?) is equal to
5/6 -1/9 = 15 /18 -2/18 = 13/18.
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help help help help help help help help help help help help help help help help help help help help help help help help help help
Answer:
1. [tex](x-6)^{2}[/tex]
2. [tex](x +11)^2[/tex]
3. [tex](x-4y)^{2}[/tex]
4. [tex](5x - y)^2[/tex]
Step-by-step explanation:
1. [tex]x^{2} -12x +36[/tex] ---> [tex](x-6)^{2}[/tex]
2. [tex]x^{2} +22x + 121[/tex] ---> [tex](x +11)^2[/tex]
3. [tex]x^{2} -8xy+16y^{2}[/tex] ---> [tex](x-4y)^{2}[/tex]
4. [tex]25x^2-10xy + y^2[/tex] ---> [tex](5x - y)^2[/tex]
The product of two number is -100. One of the factor is less than 10 and more than 0
The given problem has 4 different solutions as below.
(1, -100)(2, -50)(4, -25)(5, -20)Given that the product of the two numbers is -100.
And one of the factors is less than 10 and more than 0.
Assume c and d are the two required numbers.
Then we have cd = -100, here 0 < c <10.
We know that the factors of 100, which are less than 10 and greater than 0 are 1, 2, 4, and 5.
When c = 1, we get 1 x d = -100 ⇒ d = -100
When c = 2, we get 2 x d = -100 ⇒ d = -100/2 = -50
When c = 4, we get 4 x d = -100 ⇒ d = -100/4 = -25
When c = 5, we get 5 x d = -100 ⇒ d = -100/5 = -20
So, the other factors corresponding to the above factors are -100, -50, -25, and -20.
Therefore, the given problem has 4 different solutions as below.
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through: (1, −5), parallel to` y = −8x +4
Answer: y=-8x+3
Step-by-step explanation:
Parallel lines have the same slope.
y=-8x+b
-5=-8(1)+b
-5=-8+b
b=3
y=-8x+3
Which is equivalent to 6
41/4
Answer:
16 1/4
Step-by-step explanation:
4*10=40, add one more 1/4 and you get 41. So simplified, 41/4 = 10 1/4
Add the 6 and you get 16 1/4
how do you write 4.93 as a percentage
Answer:
493%
Step-by-step explanation:
To convert a decimal to percentage, muiltiply the decimal by 100.
An engineer created a scale drawing of a building using a scale in which 0.25 inch represents 2 feet. The length of the actual building is 250 feet. What is the length in inches of the building in the scale drawing?
The length of the building in the scale drawing is 31. 25 Inches
How to determine the value
From the information given, we have that;
Scale drawing was used0. 25 inches represents 2 feetThe length of the building is 250 feetThen,
If 0. 25 inches = 2 feet
Then x inches = 250 feet
cross multiply
x × 2 = 0. 25 × 2500
Multiply through, we have;
2x = 62. 5
Make 'x' the subject by dividing both sides by 2
2x/2 = 62. 5/ 2
x = 31. 25 Inches
Thus, the length of the building in the scale drawing is 31. 25 Inches
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Answer:
Step-by-step explanation:
31.25
How many ounces of a 12% alcohol solution must be mixed with 9 ounces of a 20% alcohol solution to make a 16% alcohol solution?
Answer:
9 ounces
Step-by-step explanation:
Let x = number of ounces of 12% solution.
0.12x + 0.2 × 9 = 0.16(x + 9)
0.12x + 1.8 = 0.16x + 1.44
-0.04x = -0.36
x = 9
Answer: 9 ounces
Quadrilateral WXYZ with vertices W(0,-4), X(13,0), Y(9,-12), and Z(5,-12); scale factor: k = 3/4, center of dilation: (1,0)
Dilation involves changing the size of a quadrilateral or any shape
The coordinates of the image of the dilation are: [tex]W^{\prime}=(1 / 4,-3), X^{\prime}=(10,0)$, $Y^{\prime}=(7,-9)$[/tex] and [tex]$Z^{\prime}=(4,-9)$[/tex]
This is further explained below
How to determine the vertices of the image?The vertices of the pre-image are given as:
W=(0,-4)
X=(13,0)
Y=(9,-12)
Z=(5,-12)
The scale factor is given as:
k=3 / 4
The center of dilation is given as:
(a, b)=(1,0)
To calculate the vertices of the image, we make use of the following formula [tex]$\left(x^{\prime} y^{\prime}\right)=(k(x-a)+a, k(y-b)+b)$[/tex]
So, we have:
W'=(3 / 4(0-1)+1,3 / 4(-4-0)+0)
W'=(1 / 4,-3)
X'=(3 / 4(13-1)+1,3 / 4(0-0)+0)
X'=(10,0)
Y'=(3 / 4(9-1)+1,3 / 4(-12-0)+0)
Y'=(7,-9)
Z'=(3 / 4(5-1)+1,3 / 4(-12-0)+0)
Z'=(4,-9)
Hence, the coordinates of the image of the dilation are:
W'=(1 / 4,-3),
X'=(10,0),
Y'=(7,-9)
Z'=(4,-9)
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thirty-four and twelve hundredths is standard form
34.12
{thirty four, (34) and, (decimal) twelve hundredths (.12)}.
So it would end up being 3412. Hope i helped!
4 .3
is V = πr³, wh
3
what is the formula in terms of r? please help
The rearranged formula for volume in terms of radius,r is [tex]\sqrt[3]{\frac{V}{\pi } }[/tex].
What is volume?
Volume is a measure of enthralled three-dimensional space.It's frequently quantified numerically using SI-deduced units or by colorful Homeric units( similar to the gallon, quart, boxy inch). The description of length( cubed) is interrelated with volume. The volume of a vessel is generally understood to be the capacity of the vessel; i.e., the quantum of fluid( gas or liquid) that the vessel could hold, rather than the quantum of space the vessel itself displaces.In ancient times, volume is measured using analogous-structured natural holders and latterly on, standardized holders. Some simple three-dimensional shapes can have their volume fluently calculated using computation formulas. Volumes of more complicated shapes can be calculated with integral math if a formula exists for the shape's boundary.Volume, V = [tex]\pi r^3[/tex]
Rearranging,
r =[tex]\sqrt[3]{\frac{V}{\pi } }[/tex]
The rearranged formula for volume in terms of radius,r is [tex]\sqrt[3]{\frac{V}{\pi } }[/tex].
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Pleaseeeee I really need some help here
Answer:
a) 17 b)22
Step-by-step explanation:
a) 3 - (-14)
Negative minus Negative is positive so we get
3+14
which is
17
drawing that on the number line:
<-20---------------0-------------17--20>
b) -36 + 58
we can rearrange the numbers to get
58-36
which is equal to
22
drawing that on the number line:
<-20---------------0---------------20--22>
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O Solve questions Pg #61 Prá
1 Correct 78. 4695 to
a) 1 decimal place.
c) the nearest hundredth
The number corrected to 1 decimal place is 78.5
The number corrected to the nearest hundredth is 78.47
EstimationFrom the question, we are to estimate the given number to the nearest 1 decimal place
The given number is
78.4695
Correcting to 1 decimal place
In the given number, we can observe that the hundredth digit is greater than 5, thus we will add 1 to the tenth digit
Thus,
78.4695 corrected to 1 decimal place is 78.5
Correcting to the nearest hundredth
The thousand digit is greater than 5, thus we will add 1 to the hundredth digit
Thus,
78.4695 corrected to the nearest hundredth is 78.47
Hence,
The number corrected to 1 decimal place is 78.5
The number corrected to the nearest hundredth is 78.47
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The branch of statistical studies called descriptive statistics summarizes important aspects of a data set. True or false?.
The branch of statistical studies called descriptive statistics summarizes important aspects of a data set is true.
It is required to find the statement.
What is a statement?A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.
Given:
The branch of statistical studies called descriptive statistics summarizes important aspects of a data set.
Descriptive statistics refers to the summary of important aspects of a data set.
Therefore, the branch of statistical studies called descriptive statistics summarizes important aspects of a data set is true.
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