Given that the meals in a hospital cafeteria are discounted 15% for all hospital employees,
The price an employee will pay for the grill chicken lunch worth of $8.00 will be,
[tex]\text{ \$8.00}-(15\text{ \% of \$8.00)}[/tex][tex]\begin{gathered} \text{ \$8.00-(}\frac{\text{15}}{100}\times\text{ \$8.00)} \\ \text{ \$8.00-(0.15}\times\text{ \$8.00)}=\text{\$8.00- \$1.2=\$6.8} \end{gathered}[/tex]Hence, the hospital employee will pay $6.8 for the grilled chicken lunch.
✓
3 sisters age combined are 57. Jenny is 6 years
older then Lynn. Kim is 5 less then twice the age of
Lynn age. What are the sisters ages.
Jenny's age is 20 years, Lynn is 14 years and Kim is 23 years.
Let's take Jenny as J, Kim as K and, Lynn as L.
From the given statement we get the equation.
As the sum of the age of the three sisters is 57. So we have an equation,
J + K + L = 57 ........(i)
Jenny is 6 years older than Lynn. So the next equation is,
J = 6 + L .......(ii)
Kim is 5 years less than twice her age Lynn. So the equation is,
K = 2L -5 .........(iii)
Putting equations (ii) and (iii) in equation (i)
6 +L + 2L - 5 + L = 57
4L = 56
L = 14
Put the value of L in equations (ii) and (iii)
J = 6 + 14
= 20
K = 2(14) -5
= 28 - 5
= 23
Therefore the age of Jenny is 20 years, Lynn is 14 years and Kim is 23 years.
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what is three.twenty-seven times one hundred
Answer:
32,700
Step-by-step explanation:
On your own paper, graph the system of equations and identify the solution.−+=−22+=10
The system of equations is given as
[tex]\begin{gathered} -x+y=-2 \\ 2x+y=10 \end{gathered}[/tex]To plot the graph for each equation, we can prepare a table of values taking
[tex]x=2,4,6,8,10[/tex]EQUATION 1: -x +y = -2
EQUATION 2: 2x + y = 10
The graph can then be drawn as shown below:
The solution to the system of equations is the point where the two graphs intersect.
This is seen in the graph above as (4, 2).
Hence, the correct option is the FOURTH OPTION.
2x-5y = 10
x-intercept:
y -intercept:
Answer:
x-intercept: (−5, 0)
y-intercept: (0, 2)
Step-by-step explanation:
FOR X INTERCEPT WE KNOW THAT Y WILL BE A AT THE AXIS LINE WE CAN SUBSTITUTE THW VALUE O IN THE PLACE OF Y TO GET X-INTERCEPT
[tex]2x - 5(0) = 10 \\ 2x = 10 \\ \frac{2x}{2} = \frac{10}{2} \\ x = 5[/tex]
5 is the x-intercept
(5,0)
FOR Y INTERCEPT ON THE Y AXIS X IS EQUAL TO 0 WE CAN PLUG IN TO FIND THE VALUE OF THE Y -INTERCEPT IN THE EQUATION
[tex]2(0) - 5y = 10 \\ - 5y = 10 \\ \frac{ - 5y}{ - 5} = \frac{10}{ - 5} \\ y = - 2[/tex]
-2 is the Y-intercept
(0,-2)
Hope this helps
The manager of a theater wants to know whether the majority of its patrons are adults or children. One day, 5400
tickets were sold and the receipts totaled $23,258. The adult admission is $5.50, and the children's admission is $3.50.
How many adult patrons were there?
There were adult patrons.
In linear equation, No of Adults = 2,179, No of Children = 3,221 .
What in mathematics is a linear equation?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x).The dependent variable in this scenario is y since it depends on the independent variable, x.Let Number of Adult admission be x
Number of children's admission be y
Total tickets were sold = 5400
so x+y= 5400 ....... eq 1
One adult ticket costs $5.50 ,so total Adult ticket costs = 5.50x
One Child ticket costs $ 3.50, so total Children tickets cost= 3.50 y
receipt totaled = $23,258
so 5.50x+3.50y= $23,258....... eq 2
multiply 5.50 to the eq 1, we get,
5.50x +5.50y = 29,700...... eq 3
subtract eq 2 from eq 3, we get,
5.50y-3.50y = 29,700- 23,258
2y= 6,442
divide by 2 both sides ,we get, y= 3,221
substitute the value of y in eq 1, we get,
x+ 3,221 =5400
x= 5400- 3221
x= 2,179
No of Adults = 2,179, No of Children = 3,221
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In class of 35 students, 19 take Spanish, 18 take French and 3 Take neither. Calculate
how many takes:
A) Both French and Spanish
B) Just Spanish
C) Just French
Students takes both French and Spanish is 5 members
Student takes just Spanish = 14 members
Student takes just French = 13 members
Given :
Total numbers of students in class = 35
how many members take spanish = 19
how many members take french = 18
students take neither = 3
To find :
A) Both French and Spanish
B) Just Spanish
C) Just French
Solution :
from venn diagram
a+b+c+d = 35 → 1
b+c = 19 → 2
c+d = 18 → 3
a = 3 → 4
Substract equation 1 and equation 2
a+b+c+d-b-c=35-19
a+d=16 → 5
substract a=3 in the eqution 5
3+d=16
d=13
put d=13 in equation 3
c+d=18
c+13=18
c=5
Students takes both French and Spanish is 5 members
Student takes just Spanish = 14 members
Student takes just French = 13 members
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100 students took an exam, the maximum score was 90. From the graph, 1.what was the median score?2.Also, find the lower quartile score. in reference to the first question. 3. what is the inter-quartile score range score?
0. From the given graph, the cumulative frequency value indicates the number of students, we have 100 total number of students .
• so,Median is half of the students = 100/2 = 50
the value of test score that corresponds with 50 = 55 test score
• This means that the median , 50 students scored 55 % in the exa,m.
2. Finding the lower quartile Q1 :
since we have 100 students , 100/4 = 25, so Q1 = 25
the value that corresponds with cumulative frequency of 25 = 45
• This means that 25 students scores 45 %
3. Finding the Interquartile range :
IQR = Upper Quartile -Lower Quartile
Upper quartile = Q3 = 75 students : 60 %
and lower quartile = 45%
So,
IQR = 60-45
= 15
• This means that 15 students got 35 %
2. If y = x3 + 2x + 5 and z = x2 + 7x + 1, what is 2y + z in terms of x? (A) 3x3 + 11x + 11 (B) 2x3 + x2 + 9x + 6 (C) 2x3 + x2 + 11x + 11 (D) 2x3 + 2x2 + 18x + 12
the given equation is,
[tex]y=x^3+2x+5[/tex]and
[tex]z=x^2+7x+1[/tex]now the expression is,
2y + z
put the values,
[tex]2(x^3+2x+5)+x^2+7x+1[/tex][tex]\begin{gathered} 2x^3+4x+10+x^2+7x+1 \\ 2x^3+x^2+11x+11 \end{gathered}[/tex]thus, the correct answer is option C
Monica has a yearly salary of $29,700. Her employer withholds $2948 in state and federal taxes and $2573 in FICA taxes throughout the year. She has the following monthly costs: transportation is $140, cell phone bill is $65, student loans require $300 in repayment, and rent is $675. She is using the average monthly costs for each of the following in order to gain an idea of other monthly expenses: utilities are $130, internet is $55, health insurance is $278, and groceries are $220. What is Monica’s monthly net pay amount? Round your answer to the nearest cent, if necessary.
Step-by-step explanation:
your teacher is not very precise, I fear.
the yearly salary ($29,700) is the gross pay she gets.
the gross pay minus the taxes ($2,948 and $2,573) is then the net pay she receives.
in many cases the employer also withholds the health insurance premium (and then that has to be subtracted too before getting the net pay).
I just think your teacher means by "net pay" how much she will have left are all the monthly costs.
her annual net pay amount is
$29,700 - $2,948 - $2,573 = $24,179
the monthly net pay is $24,179/12 = $2,014.916666... ≈
≈ $2,014.92
she has to pay monthly
$140
$ 65
$300
$675
$130
$ 55
$278
$220
---------
$1,863
based on her monthly net pay she has left
2,014.916666...
- 1,863
---------------------------
151.9166667 ≈ $151.92
per month
please pick based on what you think your teacher means by net pay : the actual net pay by her employer, or how much money she has monthly left after paying all bills.
Simplify the expression to a + bi form:(12 – 6i)(3 – 10i)
Solution:
Given the expression:
[tex](12-6i)(3-10i)[/tex]To simplify in the form:
[tex]a+bi[/tex]step 1:
Multiply the terms in the second parenthesis by each term in the first parenthesis.
Thus,
[tex]\begin{gathered} 12(3-10i)-6i(3-10i) \\ \Rightarrow36-120i-18i+60i^2 \end{gathered}[/tex]step 2:
Collect like terms.
[tex]\begin{gathered} 36-120i-18i+60i^2 \\ \text{but } \\ i^2=-1 \\ \text{thus,} \\ 36+60(-1)-120i-18i \\ \Rightarrow36-60-120i-18i \\ =-24-138i \\ \Rightarrow-24+(-138)i \end{gathered}[/tex]Hence, the expression is simplified as
[tex]-24+(-138)i[/tex]it cost $54.50 to put 24,000 in your bathroom how much would you expect it to cost if you wanted 36 tiles
Given, the cost of 24 tiles $54.50
Step 1: Calculate how much a tile cost. To obtain the cost per tile
[tex]1\text{ tile cost= \$}\frac{54.50}{24}[/tex]Step 2: Calculate the cost to put 36 tiles (i.e the cost per tile multiply by 36)
[tex]\begin{gathered} =\frac{54.50}{24}\times36 \\ =54.50\times1.5 \\ =\text{ \$81.75} \end{gathered}[/tex]Hence, it will cost $81.75 to put 36 tiles
A. A one-way train ticket in the city costs $1.65. A monthly pass costs $55. For what numbers of rides should you buy the monthly pass?
B. In February, there are exactly 4 weeks. You ride the train one time each weekday and two times on Saturdays and Sundays in February. About how much do you save by using the cheaper option?
A. you should buy pass for minimum 34 ride per month to get profit.
B. you save 4.4$ by using the monthly pass.
How to calculate profit?
if monthly pass cost you more than one way pass then you loss money. To calculate the minimum amount of rides to get profit from monthly pass. Divide the monthly pass cost by one-way ticket cost.
A. minimum rides= cost of monthly pass/cost of one way ticket
minimum rides=[tex]\frac{55}{1.65}[/tex]
minimum rides=33.33
you need to travel at least 34 times to purchase the pass
B. you have 9 rides per week. 5 on weekdays and 4 on weekends
total rides per month= 9×4
=36
cost of 36 rides=36×1.65
59.4
amount you save=59.4-55
=4.4$
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PLEASE ANSWER)At the grocery store, on 8-ounce bottle of salad dressing costs $1.76 A 28 ounce bottle costs 5.88. How much cheaper is it per ounce bottle rather then the 8 ounce bottle
A 28 ounce bottle is $0.01 per ounce cheaper than 8-ounce bottle of salad dressing.
What is termed as the unitary method?The unitary method is a process that determines the value of a single unit from value of multiple units, as well as the value of multiple units from value of a single unit. "It is a method in which we discover the value of a single unit by subtracting the value of multiple units as well as the value of multiple units by subtracting the value of a single unit."For the given question;
The 8-ounce bottle of salad dressing costs $1.76
This can be written as-
8-ounce bottle -----> $1.76.
For finding the price of one ounce divide both side by 8.
1-ounce bottle -----> $0.22
Now, for 28 ounce bottle.
28 ounce bottle costs $5.88.
28 ounce bottle-----> $5.88.
For finding the price of one ounce divide both side by 28.
1-ounce bottle -----> $0.21
Difference = 1-ounce for 28 bottle - 1-ounce for 8 bottle
Difference = $0.22 - $0.21
Difference = $0.01
Thus, 28 ounce bottle is $0.01 per ounce cheaper than 8-ounce bottle of salad dressing.
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Consumer Economics Each family in a neighborhood is contributing $20 worth of food to the neighborhood picnic. The Harlin family is bringing 12 packages of buns. The hamburger buns cost $2.00 per package. The hot-dog buns cost $1.50 per package. How many packages of each type of bun did they buy?Choose the correct equation that represents the number of buns purchased. [ Select ]Choose the correct equation that represents the cost of the buns. [ Select ][ Select ] packages of hamburger buns were bought.[ Select ] packages of hot dog buns were bought.
Explanation
In the question, we are given some important details to work with. Here is a list of them.
1) First, we must note that each family is contributing $20 worth of food.
2) Harlin's family brought 12 packages to the party.
3) The 12 packages consist of two types of buns namely hamburgers and hot dogs. The hamburger buns cost $2 per package while the hot-dog buns cost $1.50
Part A
Let's assume that the number of hamburger packages represents x and the number of hot dogs packages represents y. We can conclude that the sum of bought packages should be equal to 12. We can then translate this information into the equation below.
[tex]x+y=12[/tex]Answer A: x+y = 12
Part B
Now, we can figure out the equation that represents the cost of the buns. Since we know the cost of each buns package, we can multiply the cost of each buns package by the number of packages that were brought to the party by the Harlin family.
Also, we will add the resulting expressions and equate it to the cost of the worth of food each family will bring to the party.
Therefore,
[tex]\begin{gathered} Total\text{ cost of hamburgers = }2\times x=2x \\ Total\text{ cost of Hot dogs = 1.50 x y =1.5y} \\ \therefore\text{Tota cost of buns }\Rightarrow\text{ }2x+1.5y=20 \\ \\ \end{gathered}[/tex]Answer B: 2x+1.5y = 20
Part C And Part D
The above sections can be gotten by solving the previous systems of equations simultaneously. Therfore,
[tex]\begin{gathered} x+y=12\text{ -----1} \\ 2x+1.5y\text{ =20 -----2} \end{gathered}[/tex]Let's create equation three from equation 1
[tex]x=12-y-----3[/tex]Then we will substitute equation three into the untouched equation 2
[tex]\begin{gathered} 2(12-y)+1.5y=20 \\ 24-2y+1.5y=20 \\ 24-0.5y=20 \\ -0.5y=20-24 \\ -0.5y=-4 \\ y=\frac{-4}{-0.5} \\ y=8 \end{gathered}[/tex]
I need to write an explicit formula for this problem but I have not idea what I'm doing.
Given data:
The given series is -32, -25, -18, -11,....
The commo difference of the given series is,
[tex]\begin{gathered} d=-25-(-32) \\ =-25+32 \\ =7 \end{gathered}[/tex]The expression for the explicit formula for the given series is,
[tex]\begin{gathered} a_n=a+(n-1)d \\ =\text{ -32+(n-1)}(7) \\ =-32+7n-7 \\ =-39+7n \end{gathered}[/tex]The expression for recursive formula is,
[tex]\begin{gathered} a_n=a_{n-1}+d \\ =\lbrack-39+7(n-1)\rbrack+7 \end{gathered}[/tex]If the measure of angle 1 = 2x+3 and the measure of angle 2 = 3x+2, then what is the measure of angle 3?
Answer: 126°
Step-by-step explanation:
Step-by-step explanation: Since every triangle has 180 interior degrees, we can say 2x + 3x + 90° = 180°. Subtract 90° from each side and we get
2x + 3x = 90°
5x = 90°
x = 18°
Plug in x for Angle 2, giving us Angle 2 = 54°
Angle 1 and angle 2 must add up to 180°
Subtract 54° from 180° and we get 126°
PLS HELP SOLVE THE ABSOLUTE VALUE EQUATION
Answer:
See below
Step-by-step explanation:
If the question is SUPPOSED to be
| 2x +3 | = 3 you have to solve for the left side being positive or negative
Positive 2x + 3 = 3
2x = 0
then x = 0
Negative - ( 2x+3) = 3
-2x -3 = 3
-2x = 6
x = -3
So answer A
Write an equation for a line perpendicular to 3 y − 6 x = − 15 and passing through the point (6,-4) y =
The equation of the line perpendicular to 3y-6x = -15 and passing through the point (6,-4) is y = (-1/2)x - 1
The equation of the line is
3y-6x = -15
Convert the equation to the slope intercept form of the line
3y-6x = -15
3y = 6x-15
y = (6x-15)/3
y = 2x-5
The slope intercept form of the line
y = mx+b
By comparing the result with slope intercept form
slope of the line m = 2
The slope of the line perpendicular will be the negative reciprocal of 2
m = -1/2
Therefore the slope of the line will be
y = (-1/2)x+b
The line is passing through the point (6,-4)
Substitute the values in the equation
-4 = (-1/2)×6+b
-4 = -3+b
b = -4+3
b = -1
Substitute the values in the slope intercept form
The equation of the line perpendicular to 3y-6x = -15 and passing through the point (6,-4)
y = (-1/2)x - 1
Hence, the equation of the line perpendicular to 3y-6x = -15 and passing through the point (6,-4) is y = (-1/2)x - 1
The complete question is
Write an equation for a line perpendicular to 3y − 6x = −15 and passing through the point (6,-4).
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A clock has a minute hand that is 11 inches long and an hour hand that is 9 inches long. What is the
distance between the end of the hands at 9 o'clock? Round your answer to the nearest inch.
10 inches
14 inches
O16 inches
20 inches
The Pythagorean Theorem is used to determine that the distance between the hands at 9 o'clock is 14 inches.
What exactly is the Pythagorean theorem?The Pythagorean theorem, also known as the Pythagoras' theorem, is a fundamental relationship in Euclidean geometry between the three sides of a right triangle. It states that the area of the hypotenuse square is equal to the sum of the areas of the squares on the other two sides.It is implied that a clock has an 11-inch-long minute hand and a 9-inch-long hour hand.
We need to find the distance between the end of the hands at 9 o'clock.
At 9 o'clock, the hands form a right angled triangle.
Let the length of minute hand = x , hour hand = y and the distance between the end of the hands at 9 o'clock = z
Therefore, by using Pythagorean theorem,
x² + y² = z²
11² + 9² = z²
z = [tex]\sqrt{11^{2}+9^{2} }[/tex]
z = [tex]\sqrt{202}[/tex]
z = 14.21 rounded to 14 inch
Using the Pythagorean theorem, the distance between the ends of the hands at 9 o'clock is calculated to be 14 inches.
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Divide. Give the quotient and remainde 2249 = 3 x Quotient: S II I Remainder:
We will find the quotient and remainder as follows:
The quotient is 749 and the remainder is 2.
PLS HELP!
I’ll give brainliest if you also explain!
What are the equations of lines m and q?
Equation of 'm'
(y - 6) = - ³/₅ (x - 2) [point-slope form]
y = - ³/₅ x + ³⁶/₅ [slope-intercept form]
Equation of 'q'
(y - 6) = ⁵/₃ (x - 2) [point-slope form]
y = ⁵/₃ x + ⁸/₃ [slope-intercept form]
How to find the equations of lines m and q?To find the equation for both 'm' and 'q' requires a bit of work. Because neither 'm' nor 'q' has two points to find the slopes of the line, we have to get creative.
The Line 'n' has two points [ (4, 4) & (1, -1) ], and as such we can find the slope of that line. The line 'n' is parallel with 'q' and perpendicular with m.
For finding the slope of 'n'
The slope of the 'n' = (y₂ - y₁) ÷ (x₂ - x₁)
= (4 - (- 1)) ÷ (4 - 1)
= 5 ÷ 3
= ⁵/₃
To estimate the slope of 'q' and 'm'
When two lines exists parallel, they contain the exact slope.
Since 'n' and 'q' exists parallel,
then the slope of q = ⁵/₃
When two lines exists perpendicular, the product of their slopes exists -1. This means that the slopes exists negative-reciprocals of each other.
Since 'n' and 'm' exists perpendicular
then the slope of m = - ³/₅
Write the equation for 'q' and 'm'
We can now utilize the point-slope form (y - y₁) = m(x - x₁)) to write the equation for the lines
For both 'q' and 'm' let (x₁, y₁) be (2, 6)
Equation of 'm'
(y - 6) = - ³/₅ (x - 2) [point-slope form]
y = - ³/₅ x + ³⁶/₅ [slope-intercept form]
Equation of 'q'
(y - 6) = ⁵/₃ (x - 2) [point-slope form]
y = ⁵/₃ x + ⁸/₃ [slope-intercept form]
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Use the graph of the exponential function to answer the following question.Which statements about the graph are TRUE? Select all that apply. A. The x-intercept is 2. B. The y-intercept is 3. C. The asymptote is y = -1D. The range is all real numbers E. The domain is all real numbers F. The function shows growth G. As x increases, y approaches, but never reaches, -1
The curve intersect the x axis at x = 1. So x-intercept is 1. Statement A is false.
The curve intersect the y-axis at y= 3. So y intercept is 3. Statement B is correct.
The curve tends toward infinity at y = -1. So y = -1 asysmptote of the function. Statement C is correct.
The range of function is y > -1. So range is not all real number. Thus statement D is incorrect.
The function is defined for x > -0.5. At x = 0.5 function tends toward infinity. Thus statement E is incorrect.
As we move from left to right on x-axis then function decreases. So function shows decay. The statement F is incorrect.
The value of function approaches -1 as value of x increase but does not cross -1 ot touch the value y = -1. So statement G is correct.
Thus correct statement are,
B, C and G.
In order for the data in the table to represent a liner function with a rate of change of -8, what must be the value of a
By definition, the Rate of change is also called "Slope".
The slope of a line can be found dividing the difference between the y-coordinates of two points, by the difference between the x-coordinate of those points:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case you know that:
[tex]m=-8[/tex]Knowing the following point on the line:
[tex]\mleft(10,27\mright);(11,a)[/tex]You can set up the following (substituting the slope and the coordinates of those point into the formula)
[tex]-8=\frac{27-a}{10-11}[/tex]Now you can solve for "a":
[tex]\begin{gathered} (-8)(-1)=27-a \\ 8-27=a \\ -19=a \\ a=19 \end{gathered}[/tex]The answer is: Third option.
Line a is parallel to line b. Which list shows accurate angle relationships?
Given:
Line a is parallel to line b.
As shown:
m∠1 = m∠5 ; the corresponding angles are congruent
m∠2 = m∠2 ; the corresponding angles are congruent
So, the answer will be option 2
I need help writing the formula step by step please if anyone can help
f(x)=x ^2
Translate 8.5 units to the left
f(x)= (x + 8.5 )^2
vertical Stretch of a factor of 3
f(x)= 3 (x + 8.5 )^2
7 units down
f(x)= 3 (x + 8.5 )^2 - 7
4^6*3^4*2^2/4^2*3^4*2^6
Answer:
16
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors. Hope this helps! <3
When solving an equation with one variable on both sides what are three types of solutions youcan obtain?
whenever you have an equation with one variable on both sides, you might end up with one of the following case:
1. You might end up with an inconsistent equation, therefore there is not solution. Example
x = x+3. If you subtract x on both sides, you get 0=3 which is impossible.
2. You might end up having infinite solutions. Example:
x+6 = x+6. If you subtract x on both sides you get 6 =6 which is true regardless of the value of x.
3. You might end up having only one solution. Example:
3x +2 = x +5
If you subtract x on both sides and subtract 2 on both sides, you get
2x = 3.
then if you divide by two on both sides, you find
x = 3/2. So this equation has one unique solution.
Question 1 of 10
What is the slope of the line shown below?
A. 3
B. -1/3
C. -3
D. 1/3
001 (part 1 of 2) 10.0 points
A bug walking on the circular rim of a flower
pot completes one lap around the planter in
12.25 s.
If the radius of the planter is 11.3 em, how
fast was it traveling?
Answer in units of cm/s.
At State College last term, 57 of the students in a Physics course earned As, 79 earned Bs, 102 got Cs, 94 were issued Ds, and 53 failed the course. If this grade distribution was graphed on a pie chart, how many degrees would be used to indicate the A region?
Given:-
57 students in a physics course earned A.
79 students course earned B.
102 students course earned C.
94 students course earned D.
53 students failed the course.
To find:-
How many degrees would be used to indicate the region A.
Total number of students is,
[tex]57+79+102+94+53=385[/tex]Now we find the degrees to indicate the region A. we get,
[tex]\frac{57}{385}\times360=0.1480\times360=53.29[/tex]So the required soluion is 53.29 degrees.