Since the total percent of the employees is 100%
Since 40% of them took the bus
Since 5% walk
Add them and subtract the sum from 100% to get the percentage of who take the car
[tex]\begin{gathered} 40+5=45 \\ 100-45=55 \end{gathered}[/tex]Then 55% of the employees use cars
Since the total number of employees is 140, then
Let us find 55% of 140
Change 55% to a number by divide it by 100, then multiply it by 140
[tex]\begin{gathered} N=\frac{55}{100}\times140 \\ N=77 \end{gathered}[/tex]There are 77 employees who use cars
Sofia ordered sushi for a company meeting. They change plans and increase how many people will be at the meeting, so they need at least 100 pieces of sushi in total. Sofia had already ordered and paid for 24 pieces of sushi, so she needs to order additional sushi. The sushi comes in rolls, and each roll contains 12 pieces and costs $8. Let R represent the number of additional rolls that Sofia orders.Which inequality described this scenario?What is the least amount of additional money sofia can spend to get the sushi they need?
Answer:
the least amount Sofia can spend is $608
Approximately how old would you be in the years if you lived 1,000,000 hours? round your answer to the nearest whole number.
First let's see how many hours are in a year:
[tex]\begin{gathered} 1\text{ year }\rightarrow\text{ 365 days} \\ 1\text{ day }\rightarrow\text{ 24 hours} \\ \Rightarrow1\text{ year }\rightarrow365\cdot24=8760\text{ hours} \end{gathered}[/tex]We found that 1 year has 8769 hours, then if we lived 1,000,000 hours, we have to divide it by 8760 to know the number of years lived:
[tex]\frac{1000000}{8760}=114.15[/tex]therefore, you would have lived 114.15 years
Robin is saving money to buy a 720$ phone. she has 105$ saved, and each week she adds 30$ to her savings. write an equation to find the number of weeks (w) until she has enough savings to buy the phone.
Let call w the number of weeks she has been saving.
Then, we can write the expression for her saving in function of the number of weeks as:
[tex]S(w)=105+30\cdot w[/tex]We now have to find the number of weeks it will take for her savings to reach $720.
We can find it by calculating w for S(w)=720:
[tex]\begin{gathered} S(w)-105+30w=720 \\ 105+30w=720 \\ 30w=720-105 \\ 30w=615 \\ w=\frac{615}{30} \\ w=20.5\approx21 \end{gathered}[/tex]Answer: it will take her 21 weeks to have enough savings.
Xandro's Lighting Company purchased a dozen light bulbs for 900 pesos each. This purchased was subject to a trade discount of 25%. What was the total net price?
Total price of one dozen light bulbs will be equal to
[tex]12\times900=10800[/tex]Total trade discount is equal to (list price x trade discount rate)
[tex]\text{Discount }=10800\times0.25=2700[/tex]So, the net price will be (List price - discount)
[tex]\text{Net price = 10800-2700=}8100[/tex]Therefore, the total net price is 8100 pesos.
Algebra Find the value(s) of the variables in each kite.
56º,34º
1) A kite is a quadrilateral that according to the following theorem:
2) And examining that picture, we can tell that the angle labeled as 8x is congruent to its opposite counterpart.
3) In addition to this, but not less important that bigger diagonal bisects that the other pair of opposite angles. So we can sketch the following
So we can pick one triangle and write out the following according to the Triangle sum theorem:
[tex]\begin{gathered} 8x+(5x-1)+90=180 \\ 8x+5x-1+90=180 \\ 13x+89=180 \\ 13x=180-89 \\ \frac{13x}{13}=\frac{91}{13} \\ x=7 \end{gathered}[/tex]4) Finally, let's plug into each one the quantity of x and get the measure of those angles:
Which of the following are a qualitative catecorical variables
A qualitative variable, also called a categorical variable, is a variable that isn’t numerical. It describes data that fits into categories.
From the given options below, the arrival status of a train ( early, on time, late, canceled) and a person's blood type are the only qualitative variables.
Hence, Option 3 and Option 5 are the correct answers.
Write a situation for this equation
1.5 < 1.67
The inequality equation is correct the way it is in the form 1.5 < 1.67 and will continue to be correct if 1.5x < 1.67 where x is
negative numberx less than or equal to 1What are inequalities?Inequalities as used in mathematics refers to the symbol that is used to related the values in the left hand side and the values at the right hand side of the expression
The symbol used in the inequality expression are
less than or equal togreater than or equal toless thangreater thanThe given expression is less than and read as 1.5 is less than 1.67
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find the coordinates of the midpoint of the line joining the points and show your work.
formula of midpoint
[tex](\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]the we replace (7,1) and (-1,3)
[tex](\frac{7+(-1)}{2},\frac{1+3}{2})[/tex]simplify to solve
[tex]\begin{gathered} (\frac{7+1}{2},\frac{4}{2}) \\ \\ (\frac{8}{2},\frac{4}{2}) \\ \\ (4,2) \end{gathered}[/tex]Midpoint is (4,2)
Graph
a polynomial function has four turning points and two zeros. it’s degree could be ___? select all that apply 4567
SOLUTION
A polynomial function with real coefficients has four turning points and two zeros could be a degree 6 or any higher even degree because a polynomial with degree n has at most (n - 1) turning points.
So, it cannot be a degree 4.
It cannot be a degree 5 because it has two real zeros, and then three complex roots. A polynomial function with real coefficients cannot have an odd number of complex roots.
Answer:
6
Step-by-step explanation:
edge 23
Express your answer as a polynomial in standard form.f(x) = x^2 + 6x +7g(x) = x + 2Find: g(f(x)
1) Firstly, let's find the composite function g(f(x)) plugging into the x variable in g(x) the function f(x):
[tex]\begin{gathered} g(f(x))=(x^2+6x+7)+2 \\ g(f(x))=x^{2}+6x+9 \end{gathered}[/tex]2) To write that as the standard form, let's replace g(f(x)) with "y" and write the polynomial orderly to the greatest coefficient to the least one.
[tex]y=x^2+6x+9[/tex]what is the volume of a right triangular pyramid whose base is 5 meters on each side and whose altitude is 4 meters? round to the nearest hundred
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Right triangular pyramid
base = 5 meters
altitude = 4 meters
Volume = ?
Step 02:
The volume of a right triangular pyramid
V = 1/3 B * h
B = 1/2 b * h
[tex]\begin{gathered} B\text{ = }\frac{1}{2}\cdot5m\cdot4m \\ B=\text{ }10m^2 \end{gathered}[/tex][tex]V\text{ = }\frac{1}{3}\cdot10m^2\cdot4m=\text{ }13.3333m^3[/tex]The answer is:
The volume of the pyramid is 13.33 m³.
Solve the quadratic equation using any algebraic method.
X²-11x+30=0
Answer:
5, 6
Step-by-step explanation:
using Vieta's formulas:
x₁ + x₂ = 11
x₁*x₂ = 30
x₁ = 5
x₂ = 6
Find a polynomial function P(x)with the given zeros.4, 3, 8
Given the word problem, we can deduce the following information:
The zeroes are: 4, 3, 8
To determine the polynomial function P(x) with the given zeroes, we follow the process as shown below:
[tex]\begin{gathered} (x-4)(x-3)(x-8)=0 \\ \\ \end{gathered}[/tex]We first expand (x-4)(x-3):
[tex](x-4)(x-3)=x^2-7x+12[/tex]Next, we expand (x^2-7x+12)(x-8):
[tex]\begin{gathered} (x^2-7x+12)(x-8)=x^2(x)+x^2(-8)-7x(x)-7x(-8)+12(x)+12(-8) \\ Simplify \\ =x^3-15x^2+68x-96 \end{gathered}[/tex]Hence,
[tex]x^3-15x^2+68x-96=0[/tex]Therefore, the polynomial function is:
[tex]P(x)=x^3-15x^2+68x-96[/tex]How can I know how many students scored 5 in their test?
Based on the given table, consider that the value in the column frequency specifies the number of times that a certain score (first column) is repeated in a given data.
In this case, the value of the frequency for a specific score determines the number of students with such a score in their tests.
As you can notice, for the value of the frequency equal to 3, the corresponding value of the score is 5. It means that 3 student get 5 scores in their tests.
What is the volume of this triangle right prism 8 cm 15 cm 12 cm
The volume of a triangle right prism is given by the formula
The day's high temperature in Detroit, Michigan was recorded as 50°F. Use the formula C=59(F−32) to write 50°F as degrees Celsius.
Given:
The day's high temperature in Detroit, Michigan was recorded as 50°F.
[tex]C=\frac{5}{9}(F-32)[/tex]Required:
To convert the 50°F as degrees Celsius.
Explanation:
Consider
[tex]C=\frac{5}{9}(F-32)[/tex]For F=50,
[tex]\begin{gathered} C=\frac{5}{9}(50-32) \\ \\ =\frac{5}{9}(18) \\ \\ =5\times2 \\ \\ =10\degree C \end{gathered}[/tex]Final Answer:
[tex]C=10\degree C[/tex]Find the distance between the two points. Write your answer as a decimal rounded to the hundredths place if needed.
We need to find the distance between the two points given. Use the distance formula:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Replace using P1(3,-9) and P2(-2,4):
[tex]d=\sqrt[]{((-2)_{}-3_{})^2+(4_{}-(-9)_{})^2}[/tex][tex]d=\sqrt[]{(-5)^2+(13)^2}[/tex][tex]d=13.9283[/tex]Rounded to the hundredths:
[tex]d=13.93[/tex]Apply the product rule to rewrite the product below using a single base and exponent then simplify: 3^2 *3^3 our base is Answerour exponent is Answerthis simplifies to Answer
Explanation:
[tex]3^2\text{ }\times3^3[/tex][tex]\begin{gathered} \text{The expression has same base.} \\ \text{Base = 3} \\ We\text{ take one base and bring the exponents together} \\ \text{The sign betw}en\text{ them changes from multiplication to addition} \end{gathered}[/tex][tex]\begin{gathered} 3^2\text{ }\times3^3\text{ = }3^{2\text{ + 3}} \\ \text{Exponent = 2 + 3} \\ \text{Exponent = 5} \end{gathered}[/tex][tex]\begin{gathered} \text{Simplifying:} \\ 3^{2+3}=3^5 \\ 3^5\text{ = 243} \end{gathered}[/tex]find the value or measure. Assume all lines that appear to be tangent are tangent. mPM=
Segments that crosses around a circle
MN ^2 = OP • ON
mm
then 59° = (
For which equation would x = 12 not be a solution?96 ÷ x = 89 x - 7 = 101x + 4 = 105 + 4 x = 53
Notice that:
1)
[tex]\frac{96}{12}=8.[/tex]Therefore x=12 is a solution to
[tex]96\div x=8.[/tex]2)
[tex]9*12-7=108-7=101.[/tex]Therefore x=12 is a solution to:
[tex]9x-7=101.[/tex]3)
[tex]12+4=16\ne10.[/tex]Therefore x=12 is not a solution to:
[tex]x+4=10.[/tex]4)
[tex]5+4*12=5+48=53.[/tex]Therefore x=12 is a solution to:
[tex]5+4x=53.[/tex]Answer: Third option:
[tex]x+4=10.[/tex]1. What would you do with each problem in order to get it in its simplest properform? Use words to explain the specific details to why you used thatprocess/rule.Number 2 a and b
Given
[tex]-6y^0\text{ and \lparen-6y\rparen}^0[/tex]The solutions can be seen below.
Explanation
[tex]\begin{gathered} a)\text{ }-6y^0=-6\times y^0=-6\times1=-6 \\ b)\text{ }(-6y)^0=1 \end{gathered}[/tex]In "a," only the y-value is raised to the power of 1 hence, the reason why y^0 became 1 which then multiplies -6 to get -6. However, in "b", the entire expression is raised to the power of zero, which will then give 1 as the answer.
(X-3) times (4x+2) yawing distributive property
For two binomials, the distributive property is:
[tex](a+b)\cdot(c+d)=a\cdot c+a\cdot d+b\cdot c+b\cdot d[/tex]So, let's solve this problem.
Step 01: Multiply the first term of the binomial (x - 3) by both terms of the binominal (4x + 2).
[tex](x-3)\cdot(4x+2)=x\cdot4x+x\cdot2+\cdots_{}[/tex]Step 02: Multiply the second term of the binomial (x - 3) by both terms of the binominal (4x + 2).
[tex](x-3)\cdot(4x+2)=x\cdot4x+x\cdot2+(-3)\cdot4x+(-3)\cdot2[/tex]Step 03: Multiply the terms.
[tex]=4x^2+2x-12x-6[/tex]Step 04: Add like terms.
[tex]=4x^2-10x-6[/tex]Answer:
[tex]4x^2-10x-6[/tex]find the surface area of the figure and round to the nearest
The figure in the image is a Hemisphere.
The surface area of a hemisphere is given as:
[tex]3\text{ }\times\text{ }\pi\text{ }\times r^2[/tex]Thus, the surface area is:
[tex]\begin{gathered} 3\text{ }\times\text{ 3.142 }\times8.6^2 \\ 697.15ft^2 \end{gathered}[/tex]Hence, the surface area of the figure, to the nearest whole number is 697 square feet.
solve the equation 3x^2 - 5x + 1 = 0 expressing your answer correct to two decimal places
You have th following equation;
[tex]3x^2-5x+1=0[/tex]In order to find the solution to the previous equation, use the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this case, a = 3, b = -5 and c = 1. By replacing these values into the quadratic formula, you obtain:
[tex]\begin{gathered} x=\frac{-(-5)\pm\sqrt[]{(-5)^2-4(3)(1)}}{2(1)} \\ x=\frac{5\pm\sqrt[]{25-12}}{2}=\frac{5\pm\sqrt[]{13}}{2} \\ x=\frac{5\pm3.60}{2}=2.5\pm1.80 \end{gathered}[/tex]Hence, the solutions are:
x = 2.5 + 1.80 = 4.30
x = 2.5 - 1.80 = 0.70
In physics, the Ideal Gas Law describes the relationship among the pressure, volume, and temperature of a gas sample. This law is represented by the formula PV = nRT, where P is the pressure, V is the volume, T is the temperature, n is the amount of gas, and R is a physical constant. Select all the equations that are equivalent to the formula PV = nRT.
The equations that are equivalent to the formula PV = nRT are V = nRT/P, n = PV/RT and R = PVnT. Option B, C and D
How to determine the equationsFrom the information given, we have that;
The Ideal Gas law is represented as;
PV = nRT
Given that;
P is the pressure V is the volumeT is the temperaturen is the amount of gasR is a physical constantSubject of formula is described as the variable expressed in terms of other variables in an equation.
It is made to stand on its own on one end of the equality sign.
Let's make 'V' the subject of formula
Divide both sides by the coefficient of V which is the variable 'P', we have;
V = nRT/P
Making 'R' the subject of formula, we have
R = PV/ nT
Making 'n' the subject of formula, we have;
n = PV/RT
Hence, the equations are options B, C and D
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The complete question:
In physics, the Ideal Gas Law describes the relationship among the pressure, volume, and temperature of a gas sample. This law is represented by the formula PV = nRT, where P is the pressure, V is the volume, T is the temperature, n is the amount of gas, and R is a physical constant. Which of the equations below are equivalent to the formula PV = nRT? Select all that apply. A. P = VnRT B. V = nRT/P C. n = PV/RT D. R = PVnT E. T = nR/PV
Answer:Pv=NRT
Step-by-step explanation:
A scientist needs 270 milliliters of a 20% acid solution for an experiment. The lab has available a 25% and a 10% solution. How many milliliters of the 25% solution and how many milliliters of the 10% solution should the scientist mix to make the 20% solution?
Given:
A scientist has 5% and a 10% acid solution in his lab.
He needs 270 milliliters of a 20% acid solution.
To find the amount of 25% solution and how many milliliters of the 10% solution should the scientist mix to make the 20% solution:
Here,
The dearer percentage is 25%.
The cheaper percentage is 10%.
The mean percentage is 20%.
Using the mixture and allegation method,
The ratio of the litters of cheaper (10% solution) to dearer value (25% solution) is,
[tex]\begin{gathered} (\text{Dearer value-mean): (Mean-Ch}eaper\text{ value)} \\ (25-20)\colon(20-10) \\ 5\colon10 \\ 1\colon2 \end{gathered}[/tex]So, the number of liters to be taken from 10% solution is,
[tex]\frac{1}{3}\times270=90\text{ liters}[/tex]So, the number of liters to be taken from 25% solution is,
[tex]\frac{2}{3}\times270=180\text{ liters}[/tex]Hence, the answer is
11) Describe the number and type of roots for 2x2 + 19x - 33 = 0.[A] 2 real solutions [B] 2 complex solutions [C] 1 real solution[D] 1 complex solution
Explanation:
The first thing we will do is to solve for x in the equation:
Using factorization method:
The factors are +22 and -3. This because the addition of this number will give you the coefficient of x (19) while the multiplication will give -66
Evaluate h(x) at x = 6, x = 8, and x= 12. h(x)=1.31^×
Answer : h(6) = 5.054
h(8) = 8.673
h(12) = 25.542
Given that h(x) = 1.31^x
[tex]\begin{gathered} h(x)=1.31^x \\ \text{ find the value of h(6) when x = 6} \\ h(6)=1.31^6 \\ h(6)\text{ = 5.05}4 \\ \text{when x = 8} \\ h(8)=1.31^8 \\ h(8)\text{ = 8.67}3 \\ \text{when x = 12} \\ h(12)=1.31^{12} \\ h(12)\text{ = 25.54}2 \end{gathered}[/tex]Therefore,
h(6) = 5.054
h(8) = 8.673
h(12) = 25.542
solve for rv=r+at, for r
Since we need to solve for r we have to leave that variable alone in one side of the equation. We notice that at is adding in the right side, then it goes to the left side substracting, that is:
[tex]v-at=r[/tex]Therefore:
[tex]r=v-at[/tex]in the last part we only switch the sides of the equation.
Solve the equation for y in terms of x. After that, replace y & solve with function notation f(x). Once you solve that, find f(4).y+3x^2=4f(x)=____f(4)=____
Given:
[tex]y+3x^2=4[/tex]We have that y f(x), so solve for f(x):
[tex]\begin{gathered} y+3x^2-3x^2=4-3x^2 \\ y=4-3x^2 \\ f(x)=4-3x^2 \end{gathered}[/tex]And for f(4):
[tex]f(4)=4-3(4)^2=4-3(16)=4-48=-44[/tex]Answer:
[tex]\begin{gathered} f(x)=4-3x^{2} \\ f(4)=-44 \end{gathered}[/tex]