We have to solve this inequality:
[tex]\begin{gathered} |4x+5|+2>10 \\ |4x+5|>10-2 \\ |4x+5|>8 \end{gathered}[/tex]We now use the properties of the absolute value. We will have two boundaries: one corresponding to when 4x+5 is negative and the other is when 4x+5 is positive.
When 4x+5 is negative, the absolute value function will change the sign of the expression, so we will have:
[tex]\begin{gathered} -(4x+5)>8 \\ -4x-5>8 \\ -4x>8+5 \\ -4x>13 \\ x<\frac{13}{-4} \\ x<-3.25 \end{gathered}[/tex]The other interval will be defined when 4x+5 is positive. In this case, the absolute function does not change the sign and we get:
[tex]\begin{gathered} 4x+5>8 \\ 4x>8-5 \\ 4x>3 \\ x>\frac{3}{4} \\ x>0.75 \end{gathered}[/tex]Then, the solution set is the union of the intervals x < -3.25 and x > 0.75.
We can express the interval as (-∞, -3.25) ∪ (0.75, ∞).
Answer: (-∞, -3.25) ∪ (0.75, ∞)
Use the standard algorithm to solve the equation 36 x 25 =
Answer: 900
Step-by-step explanation:
Column method
Tiffany works at a lawnmower store.Part AA portion of Tiffany's monthly salary is based on commission. She earns 21% of everything she sells. This month she sold $27,000 worth of lawnmowers. Howmuch was her sales commission this month?Part BThe store purchased one riding lawn mower for $1,500 and sold it for $2025. What percentage was the markup for the mower?PartTiffany earns $15 per hour. The store offers her a raise-a 2% increase per hour. After the raise, how much will Tiffany make per hour?
1) Gathering the data
Part A
Tiffany's Commission: 21%
Sales Revenue: 27,000
2) In this case, we can figure out how much has she earned by doing this:
[tex]27,000\text{ }\times0.21=5,670[/tex]Part B)
$1,500
$ 2,025
We can solve it in 2 steps. Firstly let's find the equivalence of 2025 in percentage.
1500-------100%
2025- ----x
1500x = 202500
x=202500/1500
x =135%
Now we need to subtract from 100%. 135%-100%= 35%
So the percentage (markup) was 35%. That lawnmower was sold 35% above the price.
Part C)
$15 per hour
2% per hour (0.02)
In this, case we need a simple calculation multiplying that 15 by (1 +0.02)
15 x ( 1 +0.02)
15 x (1.02)
15.3
After the raise, Tiffany earns $15.30 per hour
Jess's age is six years less than three times Ethan's age. The product of their ages is 45. What are their ages? Hint: Write an equation to represent the product of their ages, using x to represent Ethan's age, then solve this quadratic equation. Connect each person to their correct age.
Jess's age is six years less than three times Ethan's age. The product of their ages is 45. What are their ages?
Hint: Write an equation to represent the product of their ages, using x to represent Ethan's age, then solve this quadratic equation. Connect each person to their correct age.
Let
x ------> Ethan's age
y -----> Jess's age
we have that
y=3x-6 -------> equation A
xy=45 ------> equation B
substitute equation A in equation B
x(3x-6)=45
solve for x
3x^2-6x=45
3x^2-6x-45=0
Solve using the formula
so
a=3
b=-6
c=-45
substitute
[tex]x=\frac{-(-6)\pm\sqrt[]{-6^2-4(3)(-45)}}{2(3)}[/tex][tex]\begin{gathered} x=\frac{6\pm\sqrt[]{576}}{6} \\ \\ x=\frac{6\pm24}{6} \end{gathered}[/tex]the solutions for x are
x=5 and x=-3 (is not a solution)
Find the value of y
y=3(5)-6
y=9
therefore
Ethan's age is 5 years
Jess's age is 9 years
Short steps pleaseFind the mean and variance of the binomial experiment in which n 5 and p 0.7. a. Mean b. Variance
Given
n= 5
p = 0.7
Find:
a. mean
b. variance
sol:
Mean d
[tex]\begin{gathered} mean\text{ =n}\times\text{p} \\ \\ \text{ = 5}\times\text{0.7} \\ \\ \text{ =3.5} \end{gathered}[/tex][tex]\begin{gathered} variance=np(1-p) \\ \\ =\text{ }5\times0.7(1-0.7) \\ \\ =3.5(0.3) \\ \\ =1.05 \\ \\ \end{gathered}[/tex]Given a function described by the table below, what is y when x is 5?XY264859612
Given a function described by the table
We will find the value of (y) when x = 5
As shown in the table
When x = 5, y = 9
so, the answer will be y = 9
What is the slope of the line in the graph?A. 2/3B. -2/3C. 3/2D. -3/2
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
graph
Step 02:
slope of the line:
we must analyze the graph to find the solution.
point 01 (0, 8)
point 02 (12, 0)
slope:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{0-8}{12-0}=\frac{-8}{12}=\frac{-2}{3}[/tex]The answer is:
m = - 2/3
I need help on writing the table and graphing it please !!
Given:
[tex]f(x)=2-\sqrt[]{x+6}[/tex]Calculate the values for f(x),
[tex]\begin{gathered} \text{for x=-6 , f(-6)=}2-\sqrt[]{-6+6} \\ f(-6)=2 \\ \text{for x=3 ,f(6)=2-}\sqrt[]{3+6} \\ f(3)=2-3=-1 \\ \text{for x=-2 f(-2)=2-}\sqrt[]{-2+6} \\ f(-2)=2-2=0 \\ \text{for x=1, f(1)=2-}\sqrt[]{1+6} \\ f(1)=-0.6 \end{gathered}[/tex]The graph of given function is,
need help with this problem answer in a quick and clear response
Answer:
A system of inequalities with parallel boundaries doesn't have a solution when the regions for each inequality don't intersect. This region depends on the sign of inequality, so the signs of inequality determine if the system has solutions.
What’s the last number in row 8 for the new number triangle I made
We have the sequence, shown as a number triangle, where in each step we add 5 (that is the constant difference).
We can write:
1
6 11
16 21 26
31 36 41 46
51 56 61 66 71
76 81 86 91 96 101
106 111 116 121 126 131 136
141 146 151 156 161 166 171 176
Answer: The last number in row 8 is 176.
Answer:
thr last number in row eight is 176
what is the volume of a pipe that has a diameter of 8 meters and a height of 3 meters of water, round to the nearest tenth
The pipe is in the form of cylinder.
[tex]\begin{gathered} d\text{ = 8 m} \\ r\text{ = 4 m} \\ h\text{ = 3 m} \end{gathered}[/tex]The volume of the pipe is calculated as,
[tex]\begin{gathered} \text{Volume = }\pi\times r^2\times h \\ \text{Volume = 3.14 }\times\text{ 4}\times4\times3 \\ \text{Volume = 150.72 }\approx150.70m^3 \end{gathered}[/tex]Thus the volume of water is 150.70 cubic m .
To graph the inequality y>-3x-4, you would draw a dashed line.O A. TrueO B. False
True.
Since it is strictly greater
In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 57 inches, and standard deviation of 7.3 inches.What is the probability that the height of a randomly chosen child is between 49.55 and 73.35 inches? Do not round until you get your your final answer, and then round to 3 decimal places.
0.834
Explanations:The formula calculating the z-score is expressed as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Given the following parameters
• x1 = 49.55
,• x2 = 73.35
,• mean μ = 57inches
,• standard deviation σ = 7.3in
Convert the x-values to z-score
[tex]\begin{gathered} z_1=\frac{x_1-\mu}{\sigma} \\ z_1=\frac{49.55-57}{7.3} \\ z_1=-\frac{7.45}{7.3} \\ z_1=-1.02 \end{gathered}[/tex]For z2;
[tex]\begin{gathered} z_2=\frac{73.35-57}{7.3} \\ z_2=\frac{16.35}{7.3} \\ z_2=2.24 \end{gathered}[/tex]Determine the required probability
[tex]\begin{gathered} P(-1.02Hence the probability that the height of a randomly chosen child is between 49.55 and 73.35 inches is 0.834The width of a rectangle measures (5v-w)(5v−w) centimeters, and its length measures (6v+8w)(6v+8w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
The most appropriate choice for perimeter of rectangle will be given by -
Perimeter of rectangle = (22v + 14w) cm
What is perimeter of rectangle?
At first it is important to know about rectangle.
Rectangle is a parallelogram in which every angle of the parallelogram is 90°.
Perimeter of rectangle is the length of the boundary of the rectangle.
If l is the length of the rectangle and b is the breadth of the rectangle, then perimeter of the rectangle is given by
Perimeter of rectangle = [tex]2(l + b)[/tex]
Length of rectangle = (5v - w) cm
Breadth of rectangle = (6v + 8w) cm
Perimeter of rectangle = 2[(5v - w) + (6v + 8w)]
= 2(11v + 7w)
= (22v + 14w) cm
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Complete Question
The width of a rectangle measures (5v−w) centimeters, and its length measures(6v+8w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
what is the slope of the line represented by y = -5 + 2?
Question:
Find the slope of
[tex]y=-5x+2[/tex]Answer:
Remember that when we have the equation of a line in the form
[tex]y=mx+b[/tex]The slope of the line is the number that accompanies x (A.K.A Coefficient)
Therefore, the slope of the line is -5
HELP PLEASEEEEE!!!!!!
The solutions of the indices are;
1) 2^7
2) 3^-4
3) 3^4
4) 2^4
What is the power?We know that in this case, we would have to apply the laws of indices and the particular law that we are to apply in each case is dependent on the nature of the problem that have been posed. Let us recall that we are asked to ensure that we express the answer or the solution to the problem as a single power.
1) 64 * 256/128
2^6 * 2^8/2^7
2^6 + 8 - 7 = 2^7
2) 3^4/3^3 * 3^5
3^4 - (3 + 5) = 3^-4
3) 3^9/ (3^4)^1/2 * 3^3
3^9/ 3^2 * 3^3
3^9 - (2 + 3)
3^4
4) (2^3)^4 * 2^4 ÷ 32/ 2 * 64
2^12 * 2^4 ÷ 2^5/2^1 * 2^6
2^12 + 4 -5/2^1 + 6
2^16 -5/2^7
2^11/2^7
2^11 - 7
2^4
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-Exponential and Logarithmic Functions- Solve the following, round the answer to the nearest hundredth.
Answer:
x = 1.70
Explanation:
We were given that:
[tex]\begin{gathered} 5^x=15.4 \\ \text{Take the natural logarithm of both sides, we have:} \\ \ln 5^x=\ln 15.4 \\ x\cdot\ln 5=\ln 15.4 \\ \text{Divide both sides by ''ln5'', we have:} \\ x=\frac{\ln 15.4}{\ln 5}=1.699 \\ x=1.699\approx1.70 \\ x=1.70 \\ \\ \therefore x=1.70 \end{gathered}[/tex]Therefore, x = 1.70
The table shows the cost for a clothing store to buy jeans and khakis. The total cost for Saturday's shipment, $1,800, is represented by the equation 15x + 20y = 1,800. Use the x- and y-intercepts to graph the equation. Then interpret the x- and y-intercepts.
I have attached the question
The following are the primary factors that the Cvp analysis employs to determine if the sales price per unit and variable costs per unit are impacted
Describe CVP Analysis?This is the term used to describe the cost-volume-profit analysis, which is used to determine how changes in cost and volume might directly affect operating costs.With this in mind, it is clear that the primary component that businesses utilize in their CVP analyses to ensure that their operational costs don't fluctuate arbitrary is cost changes. Profit = revenue - costs is the fundamental CVP formula. Naturally, you must understand how to calculate your revenue in order to use this formula:(Retail price * Units Sold)Additionally, you must understand how to calculate your costs: fixed costs plus (unit variable cost x number of units). Y = a + bx is the cost volume formula. Y = Total expense = Total fixed expense (that is, a cost that does not vary in proportion to activity)B is the variable cost per unit of activity; this cost does vary in relation to activity. Contribution/Sales is the P/V ratio. It is employed to gauge the company's profitability. The surplus of sales over variable costs is known as contribution. In essence, the P/V ratio is utilized to assess the level of contribution provided at various sales volumes.To learn more about Cpv analysis refer
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If y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8?
1/9
2/3
54
96
Answer:
2/3
Step-by-step explanation:
y = xk
6 = 72K Solve for k Divide both sides by 72
[tex]\frac{1}{12}[/tex] = k
y = xk
y = [tex]\frac{8}{1}[/tex] x [tex]\frac{1}{12}[/tex]
y = [tex]\frac{8}{12}[/tex] I can simplify by dividing the numerator and denominator by 4
y = 2/3
13. The population of Maryland was 5.17 million in 1999, and it grew to 6.05 million in 2019.(a) Assuming that the population is growing exponentially, find the growth rate r for Maryland's population. Give your answer as a percentage, rounded to the nearest hundredth of a percent.r = %(b) Write an exponential model to describe the population of Maryland from 1999 onward (let t=0 in 1999).Pt = (c) What is Maryland's population expected to be in 2030? Round your answer to one decimal place. million people(d) When do you expect that Maryland's population will reach 7.5 million? Give your answer as a calendar year (ex: 1999).During the year
Answer:
a) r = 0.79%
b)
[tex]P_t=5.17(1.0079)^t[/tex]c) 6.6 million people
d) 2046
Explanation:
We'll use the below formula for exponential growth;
[tex]P_t=a(1+r)^t[/tex]where a = initial amount
r = growth rate
t = number of time intervals
a) From the question, we have that
a = 5.17 million
P(t)= 6.05 million
t = 20 years
Let's go ahead and substitute these values into our formula, and solve for r as shown below;
[tex]\begin{gathered} 6.05=5.17(1+r)^{20} \\ \frac{6.05}{5.17}=(1+r)^{20} \\ (1+r)=\sqrt[20]{\frac{6.05}{5.17}} \\ r=\sqrt[20]{\frac{6.05}{5.17}}-1 \\ r=0.00789 \\ r=0.79\text{\%} \end{gathered}[/tex]b) The exponential model can be written as shown below;
[tex]\begin{gathered} P_t=5.17(1+0.0079)^t \\ P_t=5.17(1.0079)^t \end{gathered}[/tex]c) When t = 31 years, let's go ahead and find P as shown below;
[tex]\begin{gathered} P_t=5.17(1.0079)^{31} \\ P_t=6.6\text{ million people} \end{gathered}[/tex]d) When P = 7.5 million, let's go ahead and solve for t as shown below;
[tex]\begin{gathered} 7.5=5.17(1.0079)^t \\ 1.45=(1.0079)^t \\ \log 1.45=\log (1.0079)^t \\ \log 1.45=t\times\log (1.0079) \\ t=\frac{\log 1.45}{\log (1.0079} \\ t=47.2\text{years} \\ \end{gathered}[/tex]So to get the particular year all we need to do is add 47 years to the initial year. That will us 1999 + 47 = 2046
Beginning in 1995,( 1995= 0 years) the Chicago Cubs decreased its ticket price by a constant amount each year until 2016 when they finally won the World Series. A ticket cost $77.50 in 2005, but only $49.50 in 2012. How much did a ticket cost in 2000?
The cost of the Chicago Cubs ticket in the year 2000 was $97.50.
What is defined as the constant rate of change?A rate of change is defined as the ratio of change in dependent values as well as outputs to change in independent variables or inputs. The change, also known as the function's slope, describes what numbers change between 2 points on the a coordinate plane.For the given question.
The price of the Chicago Cubs ticket in year 2005 is $77.50.
The price of the ticket reduced in year 2012 as $49.50.
There is a constant amount of decrease in the price.
Thus, difference in years;
= 2012 - 2005
= 7 years.
Difference in amount;
= 49.50 - 77.50
= -28
Price decreased in one year = 28/ 7 = -4 per year.
For the price of the ticket in the years 2000.
= 2005 - 2000
= 5 years.
Price decreased in 5 years is;
= -4 x 5
= -20
The price is 2000 is 77.50 + 20 = 97.50
Thus, the cost of the Chicago Cubs ticket in the year 2000 was $97.50.
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State all integer values of X in the interval that satisfy the following inequality.
Solve the inequality
-5x - 5 < 8
for all integer values of x in the interval [-4,2]
We solve the inequality
Adding 5:
-5x - 5 +5 < 8 +5
Operating:
-5x < 13
We need to divide by -5, but we must be careful to flip the inequality sign. It must be done when multiplying or dividing by negative values
Dividing by -5 and flipping the sign:
x > -13 / 5
Or, equivalently:
x > -2.6
I am here, I'm correcting the answer. the interval was [-4,2] I misread the question. do you read me now?
Any number greater than -2.6 will solve the inequality, but we must use only those integers in the interval [-4,2]
Those possible integers are -4, -3, -2, -1, 0, 1, 2
The integers that are greater than -2.6 are
-2, -1, 0, 1, 2
This is the answer.
Twenty students choose a piece of fruit from a list of 4 fruits: apple, banana, grape, and pear. The theoretical probability that a student will choose a banana is .25. Only 1 student chooses a banana. How can the experimental probability get closer to the theoretical probability?A. only give two choices of fruitB. use a smaller sample size of studentsC. use a larger sample size of studentsD. provide more choices of fruit
Total number of student 20.
Total number of fruits are 4.
The theoretical probability that a student will choose a banana is 0.25
The experimental probability is 1/20=0.05.
Thus there is a huge difference in the theoritical probability and experimental probability.
Thus the experimental probability get closer to the theoretical probability is:
A. only give two choices of fruit.
Use a proportion to solve the problem. 34% of 83x/100=34/83;40.96x/100=34/83;2.822x/83=34/100;28.22x/83=34/100;56.44
34% in decimal is equal to 0.34, which in fraction is equivalent to 34/100.
Therefore we can solve this as
x/83 = 34/100; 28.22.
What polynomial identity should be used to prove that 40 = 49 − 9?
a
Difference of Cubes
b
Difference of Squares
c
Square of a Binomial
d
Sum of Cubes
A polynomial identity that should be used to prove that 40 = 49 − 9 is: B. Difference of Squares.
What is a polynomial function?A polynomial function is a mathematical expression which comprises variables (intermediates), constants, and whole number exponents with different numerical value, that are typically combined by using the following mathematical operations:
AdditionMultiplication (product)SubtractionIn Mathematics, the standard form for a difference of two (2) squares is modeled or represented by this mathematical expression:
a² - b² = (a + b)(a - b).
Where:
a and b are numerical values (numbers or numerals).
Given the following equation:
40 = 49 − 9
40 = 7² - 3³
40 = (7 + 3)(7 - 3).
40 = (10)(4)
40 = 40 (proven).
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The ratio of boys to girls in a school is 5:4. if there are 500 girls , how many boys are there in the school?
Answer:
The number of boys in the school is;
[tex]625[/tex]Explanation:
Given that the ratio of boys to girls in a school is 5:4;
[tex]5\colon4[/tex]And there are 500 girls in the school.
The number of boys in the school will be;
[tex]\begin{gathered} \frac{B}{G}=\frac{5}{4} \\ G=500 \\ B=\frac{5\times G}{4}=\frac{5\times500}{4} \\ B=625 \end{gathered}[/tex]Therefore, the number of boys in the school is;
[tex]625[/tex]write the vertex form equation of the parabola with, vertex: (10,9), passes through: (12,-7)
Th equation of a parabola in its vertex form is;
y = a(x-h)² + k
(h,k) are the coordinates of the vertex and a is a constant
(h, k) = (10, 9)
substitute the above into the equation
y = a(x- 10)² + 9 -------------------(1)
Next is to find the value of a
substitute x=12 and y= -7 into equation (1)
-7 = a (12 - 10)² + 9
-7 - 9 = 4a
-16 = 4a
a = -4
The equation of the parabola will be formed by substituting a = -4 in equation (1)
y = -4(x - 10)² + 9
I have answer for the question it in the image but I don't know if it right and I don't know any other formulas to find the area of a triangle
Hello there. To solve this question, we'll have to remember which other formulas for area of triangles can be used.
Most specifically, it asks for a formula that works on an obtuse triangle, that is, a triangle that haves an angle that measures more than 90º.
Besides the formula BH/2, that refers to half of the product between the measurements of the base and the height of the triangle, of course, this height must be a projection perpendicular to the base, as in the following drawing:
Another formula that can be used is Heron's formula;
Knowing the measures of all the sides of the triangle (no matter if it is an obtuse, acute or right triangle), say a, b and c, Heron's formula states that the area S of the triangle is given by:
[tex]S=\sqrt{\rho\cdot(\rho-a)\cdot(\rho-b)\cdot(\rho-c)}[/tex]Where
[tex]\rho=\dfrac{a+b+c}{2}[/tex]is the semiperimeter of the triangle.
This is the answer we've been looking for.
It takes 6 eggs, 5 oz of cheese, and 2 oz of butter to make twoomelets. What is the cost per omelet if eggs cost $.99 per dozen,1 lb of cheese costs $4.29, and 1/2 lb of butter costs $1.25?a. $2.15b. $1.34c. $1.08d. $.31
Given:
It takes 6 eggs, 5 oz of cheese, and 2 oz of butter to make two
omelets
Eggs cost per dozen = $0.99
So, the cost of 6 eggs = 0.99/2 = 0.495
1 lb of cheese costs $4.29
1 lb = 16 oz
So, the cost of 5 oz =
[tex]\frac{5}{16}\cdot4.29=1.34[/tex]1/2 lb of butter costs $1.25
So, the cost of 2 oz =
[tex]\frac{2}{8}\cdot1.25=0.3125[/tex]So, the cost of two omelets = 0.495+1.34+0.3125 = 2.1475
So, the cost of one omelet = 2.1475/2 ≈ 1.08
So, the answer will be option c. $1.08
Daisy is buying a video game in the shop. The price before tax is $21, and after sales tax is $24.74. What is the sales tax plied to the video game? Round to the nearest hundredth
Recall that:
[tex]\text{salesprice}=\text{originalprice+taxes.}[/tex]Therefore Daisy pays:
[tex]24.74-21=3.74\text{ dollars}[/tex]in taxes for the videogame.
Now, recall that to determine the percentage that a represents from b we use the following expression:
[tex]\frac{a}{b}\cdot100.[/tex]Therefore, the sales tax applied to the videogame is:
[tex]\frac{3.74\text{dollars}}{21\text{dollars}}\cdot100\approx17.81[/tex]percent.
Answer: The tax applied to the videogame is 17.81%, in this case, the sales tax is 3.74 dollars.
