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Related Questions
If a woman making $36,000 a year receives a cost-of-living increase of 2.1%, what will her new salary be?
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Answer:
Her new salary is $36756
Explanation:
We need to know how much 2.1% of 36000 is, so:
[tex]\begin{gathered} \frac{x}{2.1}=\frac{36000}{100} \\ x=\frac{36000\cdot2.1}{100} \\ x=756 \end{gathered}[/tex]That corresponds to the cost of living increase.
what is the positve solution for this equation? 4x2 + 12 x= 135
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We need to solve the following equation for x, and choose the positive solution
[tex]4x^2+12x=135[/tex]we substract 135 from both sides of the equation obtaining the canonical form of a quadratic equation, the we apply the quadratic formula with a=4, b=12 and c=-135 then x will be equal to:
[tex]x=\frac{-12+\sqrt[]{144-4(4)(-135)}}{8}=\frac{48-12}{8}=\frac{9}{2}=4.5[/tex]then the positive solution to the equation will be x=4.5Explain two ways to evaluate 32(13+18)
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The given expression is
[tex]32(13+18)[/tex]To evaluate this expression, first, we use the distributive property
[tex]32(13+18)=32\cdot13+32\cdot18=416+576=992[/tex]Therefore, the answer is 992.As a janitor you make a cleaning solution by mixing 30 g of concentrated powdered cleanser into 2 L of water how much powder will you need for 5L of water?
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30g - 2L
For 5L of water
[tex]\frac{5L\cdot30g}{2L}=75g[/tex]ANSWER
For 5L of water, we will need 75 g of concentrated powdered cleanser
A water sample shows 0.036 grams of some trace element for every cubic centimeter of water. Hudson uses a container in the shape of a right cylinder with a radius of 7.3 cm and a height of 12.2 cm to collect a second sample, filling the container all the way. Assuming the sample contains the same proportion of the trace element, approximately how much trace element has Hudson collected? Round your answer to the nearest tenth.
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We have a water that has a concentration of 0.036 grams per cm³ of some trace element.
We have to find how much of this trace element will be in the container with the sample of water.
This amount will be equal to the volume of the container times the concentration of the trace element.
We start by calculating the volume.
The container is a cylinder. Its volume will be the base area times the height.
We can calculate it as:
[tex]\begin{gathered} V=A_bh \\ V=(\pi r^2)h \\ V=\pi(7.3)^2(12.2) \\ V=\pi(53.29)(12.2) \\ V\approx2042.4688\text{ }cm^3 \end{gathered}[/tex]We can multiply this volume by the concentration as:
[tex]\begin{gathered} m=C\cdot V \\ m=0.036\text{ }\frac{g}{cm^3}\cdot2042.4688\text{ }cm^3 \\ \\ m\approx73.5\text{ }g \end{gathered}[/tex]Answer: 73.5 grams.
Solve this inequalityPlease be quick I only have one hour to finish and I still have a bunch of more questions
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Answer:
x >= -7
Explanation:
Given the below inequality;
[tex]5x\ge-35[/tex]To solve for x, all we have to do is divide both sides of the inequality by 5;
[tex]\begin{gathered} \frac{5x}{5}\ge-\frac{35}{5} \\ \therefore x\ge-7 \end{gathered}[/tex]So x >= -7
estimate the quotient 612 and 60
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612 is very close to 600 and 600 into 60 is 100
[tex]\frac{600}{60}=100[/tex]Also, we have 12 in front of 600 that makes it 612 and we know that 12 is not divisible by 60, and therefore, it will be the remainder.
Hence, the estimate of the quotient of 612 and 60 is 100
Solve: XC - XV. Show your answer as a Roman Numeral. Standard Number 1 5 10 50 100 500 1,000 Roman Numeral 1 V X Х L с D M A) V B) VI C) VIL
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To make this substraction, it is better to first convert into standard numbers then make the substraction.
In Romans,
A delivery servive charges $8 as base price for an overnight delivery of a package plus extra charge of $2.50 "PER" pound the package weighs.a. write and equation for the given information- y=_____x+_____b. Find the cost of shipping a 15-pound package.
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We know that
- $8 is the base price
- $2.50 "PER" pound
The more weight there is the more it will cost. In order to find the cost due to the weight we just have to multiply $2.50 by the number of pounds:
$2.50x
Since it will cost $8 more, then the total cost is $8 added to the cost due to the number of pounds:
y = $2.50x + $8In order to find the cost of shipping a 15-pound package,
we just replace x = 15 in the equation:
y = $2.50x + $8
y = $2.50 · 15 + $8
y = $37.5 + $8
y = $45.5
Answer: the cost of shipping a 15-pound package is $45.5If the function fis defined by f(x) = x ^ 5 - 1 then the inverse, f ^ - 1 is defined by f ^ - 1 * (x) =
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Given the function:
[tex]f(x)=x^5-1[/tex]We have that f(x) = y, so:
[tex]y=x^5-1[/tex]Substitute x with y:
[tex]x=y^5-1[/tex]And solve for y:
[tex]\begin{gathered} x+1=y^5-1+1 \\ x+1=y^5 \\ y=\sqrt[5]{x+1} \end{gathered}[/tex]Answer:
[tex]\sqrt[5]{x+1}[/tex]Solve the system of two equations in two variables. Y=1/4x+42x - 8y =9
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The given system is
[tex]\mleft\{\begin{aligned}y=\frac{1}{4}x+4 \\ 2x-8y=9\end{aligned}\mright.[/tex]To solve this system, we substitute the first equation in the second one.
[tex]2x-8(\frac{1}{4}x+4)=9[/tex]Now, we solve for x.
[tex]\begin{gathered} 2x-\frac{8}{4}x-32=9 \\ 2x-2x=9+32 \\ 0=41 \end{gathered}[/tex]This means the system has no solutions.In other words, the system represents parallel lines.
Can I get help with question 1? a,b,c and d? I couldn’t take a picture of question “d”but it says “construct a frequency histogram”
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The frequency histogram for the given data is attached below and the mean of the distribution is approximately 52.94°
The given frequency distribution table is given .
Using the data from the table we have to find the mean
We know that :
Mean = sum of all data/ total frequency.
From the table we see that
Mean = 52 + 7 × 5 /37 = 52.94
Standard deviation:
The formula for calculating this is given by:
[tex]{\displaystyle s_{N}={\sqrt {{\frac {1}{N}}\sum _{i=1}^{N}\left(x_{i}-{\bar {x}}\right)^{2}}}.}[/tex]
substituting the values we get :
sd = √(73.67/37)×5
sd = 7.0056
sd ≈ 7.01
When that is not possible, the standard deviation is determined by analysing a sample of the population that is representative of the entire population and creating a statistic that is used to estimate the standard deviation of the population as a whole.
This type of statistic is called an estimator, and the estimator itself is known as a sample standard deviation .
Hence the mean of the grouped data is 52.94 and the standard deviation is 7.01 .
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Which of the following sets of numbers could be the lengths of thesides of a triangle?11, 1,41, 14, 2016, 9, 1511, 8, 19
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as you may know the hypotenuse is the longest side in a triangle. So using pythagoras theorem:
c = √(a² + b²)
Where:
c = Hypotenuse
a = adjacent side
b = opposite side
11, 1,4 Since 11 is the greater number
c = 11
the others will be a and b, the order does not matter
a=1
b=4
11 = √(1² + 4²
Lyle is a car salesman and is planning to work 5 days this week. His goal is to sell 3 cars per day. How many carsdoes Lyle hope to sell by the end of the week?cars
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Firstly, there are 7 days in a week but from the information given, Lyle is planning to work for only 5 days in the week. Since his goal is to sell 3 cars per day, then the total number of cars that he would sell by the end of the week would be
5 * 3 = 15
Lyle would hope to sell 15 cars by the end of the week
Charlotte spent $26 at the hair salon. She wants to leave a 12% tip. About how much money should she leave?
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We will have the following:
[tex]t=26+(0.12)(26)\Rightarrow t=29.12[/tex]So, she shoulld leave $29.12 in total.
Find the length of x. Round answers to the nearest tenth if necessa 60° 30 у your answer
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From our trig ratios, we can see that,
[tex]\begin{gathered} \frac{1}{x}\text{ =}\sin 30,\text{ x = }\frac{1}{\sin 30}\text{ = 2} \\ x=2 \end{gathered}[/tex]I need help please it’s due tomorrow For lines a and b identify which inverse operation should come first
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Answer:
[tex]\begin{gathered} a\text{. }\frac{k}{7}=11+11\text{ Addition} \\ b\text{. }k=22\cdot7\text{ Multiplication} \\ c\text{. }k=154 \end{gathered}[/tex]Step-by-step explanation:
Solve the following equation:
[tex]\frac{k}{7}-11=11[/tex]To solve the following equation use inverse operations. Addition and subtraction are inverse operations, multiplication, and division too.
[tex]\begin{gathered} \frac{k}{7}-11=11 \\ \frac{k}{7}=11+11\text{ Addition} \\ k=22\cdot7\text{ Multiplication} \\ k=154 \end{gathered}[/tex]Draw the triangle and find the missing side then find the indicated trigonometric value. How do i solve this problem?
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Therefore
The initial value of your new car was $20,000. After one year, the value of the car is $18,000.What will the approximate value of the car be in 7 years?$8,000.00O $8,565.94$9,000.00$9,565.94
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Answer:
The approximate value of the car after 7 years is;
[tex]\text{ \$9,565.94}[/tex]Explanation:
Given that the initial value of the car is;
[tex]P=\text{ \$20,000}[/tex]after 1 year its new value is;
[tex]\text{ \$18,000}[/tex]The rate of depreciation is;
[tex]r=\frac{18000}{20000}=0.9\text{ per year}[/tex]After 7 years the value of the car can be calculated using the formula;
[tex]F=P(r)^t[/tex]where t equals 7 years.
substituting the values;
[tex]\begin{gathered} F=20000(0.9)^7 \\ F=\text{ \$9,565.94} \end{gathered}[/tex]Therefore, the approximate value of the car after 7 years is;
[tex]\text{ \$9,565.94}[/tex]Find the slope of the tangent to thefunction f(x) = 2x4 + 6x² +4 at x = -1
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-20
Explanations:Given the function f(x) = 2x^4 + 6x^2 + 4 at x = 1, the slope of the tangent of the function is expressed as:
[tex]f^{\prime}(x)=8x^3+12x[/tex]Substitute the value of x = -1 into the fucntion
[tex]\begin{gathered} f^{\prime}(-1)=8(-1)^3+12(-1) \\ f^{\prime}(-1)=8(-1)-12 \\ f^{\prime}(-1)=-8-12 \\ f^{\prime}(-1)=-20 \end{gathered}[/tex]Hence the slope of the tangent to the function at x = -1 is -20
Given the surface area of a sphere is 324ππ sq km, what is the radius of the sphere?
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The surface area S of sphere is given by
[tex]S=4\pi r^2[/tex]In our case
[tex]S=324\pi[/tex]Then, we have
[tex]324\pi=4\pi r^2[/tex]By moving 4Pi to the left hand side, we have
[tex]\frac{324\pi}{4\pi}=r^2[/tex]We can cancel Pi out in numerator and denominator, then ,we get
[tex]\begin{gathered} \frac{324}{4}=r^2 \\ 81=r^2 \\ \text{therefore} \\ r=\sqrt[]{81} \end{gathered}[/tex]and the answer is r= 9 kilometers, that is, the radius is 9 km
What is the range of the function f(x) = |x| + 5? R: {f(x) ∈ ℝ | f(x) < 5} R: {f(x) ∈ ℝ | f(x) ≥ 5} R: {f(x) ∈ ℝ | f(x) > 5} R: {f(x) ∈ ℝ | f(x) ≤ 5}
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Given:
[tex]f(x)=|x|+5[/tex]Find-: Range of a function.
Sol:
For |x| is always positive because |x| function is:
[tex]|x|=\begin{cases}-x\text{ at x<0} \\ x\text{ at x>0}\end{cases}[/tex]So the range is:
[tex]\lbrace f(x)\in\Re|f(x)\ge5\rbrace[/tex]Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=1024 and x=584 who said "yes"
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If a research institute poll asked respondents if they felt vulnerable to identity theft:
The best point estimate of the population proportion p is 0.57.The value of the margin of error E is 0.030The confidence interval 0.54; 0.6The statement that correctly interprets the confidence interval is: Option A.How to find the population proportion p?a) Population proportion p
Using this formula to find the population proportion p.
p = (x/n)
Let plug in the formula
p = 584/1024
p= 0.57
b) Margin of error
Value of z-score for a confidence level of 95%= 1.96
Using this formula to margin of error
MOE =( z alpha x √(p) (1-p) / n )
Let plug in the formula
MOE =( 1.96 x √(.57)(1-.57) / 1024)
MOE =( 1.96 x √(.57)(.43) / 1024)
MOE =( 1.96 x √0.000239
MOE =( 1.96 x 0.015459)
MOE = 0.030
c) Confidence interval
Confidence interval =0.57 ± 0.030
Confidence interval = (0.57 -0.030) , (0.57 +0.030)
Confidence interval = 0.54; 0.6
Confidence interval = 0.54 <p< 0.6
d) The statement that correctly interprets the confidence interval is:
a) One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.
Therefore the Population proportion p is 0.57, MOE is 0.030 and CI is 0.54; 0.6.
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The complete question is:
Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=1024 and x=584 who said "yes" Use a 95% confidence level.
a) Find the best point estimate of the population proportion p.
b) Identify the value of the margin of error E.
c) Construct the confidence interval.
d) Write a statement that correctly interprets the confidence interval. Choose the correct answer bellow
a) One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.
b) 95% of sample proportions will fall between the lower bound and the upper bound.
c) there is a 95% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
d) One has 95% confidence that the sample proportion is equal to the population proportion
Lacie pays a babysitter an initial fee of $30 in addition to $7 per hour. When trying to solve this problem,Juan created the function y = 30x + 7. Explain his error.Juan assigned the wrong coefficient to x. He should have written the equation
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he should have written the equation y=7x+30 because 30 is the fixed initial value and 7 is the value that increase with the number of hours
David drank 10 fluid ounces of juice. how much is this in cups? write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
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Given
David drank 10 fluid ounces of juice.
Find
how much is this in cups?
Explanation
As we know
1 cup = 8 ounces
so , 8 ounces = 1 cup
then
12 ounces =
[tex]\frac{1}{8}\times12=\frac{3}{2}=1\frac{1}{2}cups[/tex]Final Answer
hence , the required answer is
[tex]1\frac{1}{2}cups[/tex]You're having a breakfast party for 483 of your closet friends and 271 like chocolate donuts. In a dozen donuts, the probability of getting a chocolate donut is 1/5. How many dozen donuts would you have to buy to ensure that all 271 people get a chocolate donut?
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In a dozen donuts the probability of getting a chocolate donut is 1/5, meaning 1/5 of the 12 donuts are chocolate donuts.
Step 1.- Calculate how much 1/5 out of 12 is:
[tex]\frac{1}{5}(12)=\frac{12}{5}=2.4[/tex]In each dozen we would get 2.4 chocolate donuts
Step 2.- Calculate how many dozen are needed to get 271 chocolate donuts.
We divide 271 by 2.4 to get the answer:
[tex]\frac{271}{2.4}=112.92[/tex]Step 3: We round the answer to the nearest integer value, and we need 113 dozens of donuts to ensure that all 271 people get a chocolate donut.
Answer: 113
there are 117 staff members in your school. One third of them are going away for the Thanksgiving holiday. How many staff members are not traveling
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78 members are not traveling
Explanation
Step1
we need to use fractions to find the number of memebers are going away, so the whole number (117) is represented by 1
then,Let
whole number=full staff= 117
One third of them are going away for the Thanksgiving holiday, to find the number of members just do:(fraction by number)
[tex]\begin{gathered} \text{Members are going away=}\frac{1}{3}\cdot117 \\ \text{Members are going away=}39 \end{gathered}[/tex]Step 2
now, let's use subtraction to find the number of members that are not traveling
[tex]\begin{gathered} \text{Members are not traveling=full staff -member are going away} \\ \text{Members are not traveling=117-39} \\ \text{Members are not traveling=}78 \end{gathered}[/tex]I hope this helps you
Answer:
78
Step-by-step explanation:
So, to solve this problem, we have to divide 117 by 3, because one third of the staff is going away. 117 divided by 3 equals 39, which is number of staff this is going away. Next we have to subtract 39 from 117, which will give us our answer. 117 - 39 = 78
Happy Holidays!
Hello I'M Having trouble with this problem
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Percent decrease in average number of visit is 50%.
Define average.The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average. Because it offers a single, typical value to represent an entire data collection, the mean is useful. It is one of many approaches to identify central tendency and represents the arithmetic average.
Given,
Average in first week = 48000
Average in second week = 24000
Average decrease = 48000 - 24000
Average decrease = 24,000
Percent decrease in average number of visit:
24000/48000 × 100
1/2 × 100
50%
Percent decrease in average number of visit is 50%.
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please help, thank you!by the way this is a two-step equation with decimals
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Given data:
The given equaion is -0.9p+3.2= -1.7p.
The given equation can be written as,
[tex]\begin{gathered} -\text{0}.9p+3.2=-1.7p \\ 1.7p-0.9p=-3.2 \\ 0.8p=-3.2 \\ p=-4 \end{gathered}[/tex]Thus, the value of p is -4.
which question is the odd one out
III + MMM = 3003
L - XXIX = XXI
45 x 2 = 90.00000000000000000000000000000000000000000000000000001
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Here the odd one out is 45×2=90.00000000000000000000000000000000000000000000000000001.
What is roman numerals?These are the symbols used in the system of numerical notation. We can convert a natural number to a Roman numeral by modifying the placement of seven symbols. The symbol I stands for 1, V stands for 5, X stands for 10, L stands for 50, C stands for 100, and M stands for 1000. In this system, the numbers are represented by combinations of letters from the Latin alphabet. In roman numerals, alphabets are used to represent fixed positive numbers. There are mainly used by Romans. These are the symbols that are representing the numbers that do not follow the base 10 in the number system.
The numbers III + MMM = 3003 and L - XXIX = XXI are roman numerals but the number 45 × 2 = 90.00000000000000000000000000000000000000000000000000001 is a rational number.
So, the number 45 × 2 is the odd one out.
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