If Martin earns 7.50 per hour (that is h), then the equation for his weekly wage can be expressed as;
[tex]\begin{gathered} (A)f(h)=7.5h \\ (B)f(15)=7.5(15) \\ f(15)=112.5 \\ (C)f(25)=7.5(25) \\ f(25)=187.5 \end{gathered}[/tex]Therefore, answer number A shows the equation for his salary
Answer number 2 shows his salary at 15 hours ($112.5)
Answer number 3 shows his salary at 25 hours ($187.5)
Write a mathematical sentence that expresses the information given below. Use b as your variable name. If necessary:
type < = to mean
or > = to mean .
If you need to show multiplication, do not use the letter x. Use the asterisk ( * ) symbol instead, or simplify your answer.
Emily has 300 books. If Frank were to double the number of books that he now owns, he would still have fewer than Emily has.
The number of books owned by frank is represented as b < 150
What is inequality?Inequality represents the form of writing expressions where the left hand side of the expression is not exactly equal to the right hand side of the expression
How to represent the required expressionInformation gotten from the data include
Emily has 300 books
Frank were to double the number of books that he now owns, he would still have fewer than Emily has.
Let the number of books owned by frank be b and from the information we have that:
2b < 300
b < 150
hence the number of books owned by frank, b less than 150
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combine like terms
(x+3)+(9+x)
Answer:
[tex]x^{2}[/tex]+12x+27
Step-by-step explanation:
First, you need to distribute. You multiply x by 9 and x, and then multiply 3 by 9 and x, which results in 9x + [tex]x^{2}[/tex] +27 +3x.
Second, you collect like terms. In this case, there is only one like term, which is x. The results of this should be [tex]x^{2}[/tex] + 27 + 11x.
Lastly, reorder the terms properly, and you're done!
Hope this helps.
Question 6 What is the factored form of the expression below? 7 - 16 O OD (x-8)(x - 8) (x - 4)(x + 4) (x - 4)(x - 4) (x-8)(x + 8) Oo
If :
[tex]x^2-16[/tex][tex]\begin{gathered} \sqrt[]{x^2}=x \\ \sqrt[]{16}=4 \end{gathered}[/tex]Then:
[tex]x^2-16\text{ =(x-4)(x+4)}[/tex]Answer: ( x - 4 ) ( x + 4 )
CorrectBob's Golf Palace had a set of 10 golf clubs that were marked on sale for $840. This was a discount of 10% off the original selling price.Step 3 of 4: What was the store's percent of profit based on cost ($390)? Follow the problem-solving process and round your answer tothe nearest hundredth of a percent, if necessary.
The percent change is given by:
[tex]Percent_{\text{ }}change=\frac{New_{\text{ }}value-old_{\text{ }}value}{old_{\text{ }}value}\times100[/tex]The old value is $390
PLEASE help I'll send a picture in later.
Given
Table of names
Procedure
Names end with an E
Gabe
Steve
The probability would be independent and equal to:
[tex]\begin{gathered} \frac{2}{6}\cdot\frac{2}{6} \\ \frac{4}{36} \\ \\ \frac{1}{9} \end{gathered}[/tex]The probability would be 1/9
I need help on this question
Answer:
Real zeros are: x = 0, x = 1 and x =2
***Your graph is incorrect. See mine for the correct graph***
Step-by-step explanation:
We have the polynomial
[tex]$\displaystyle \:x^{4}-3x^{3}+2x^{2}\:=\:0$[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}x^2:\\\\[/tex]
[tex]=x^2\left(x^2-3x+2\right)[/tex]
[tex]\mathrm{Factor}\:x^2-3x+2:[/tex]
For an expression of the form ax² + bx + c we can find factors if we find two values u and v such uv = c and u + v =b and factor into (ax +ux)+ (vx+c)
We have here a = 1, b = -3 c = 2
==> u = -1, v = -2
[tex]\:x^2-3x+2 = (x-1)(x-2)[/tex]
So the original expression becomes
[tex]\:x^2-3x+2 = x^2\left(x-1\right)\left(x-2\right)[/tex]
To find the zeros, set this equal to 0 and solve for x
[tex]x^2\left(x-1\right)\left(x-2\right)=0[/tex]
We end up with 3 roots corresponding to the 0 values for each of the three terms
[tex]x^2 = 0 == > x = \pm 0 = 0\\\\[/tex]
[tex](x - 1) = 0 == > x = 1\\\\(x - 2) = 0 == > x = 2\\\[/tex]
Answer real zeros are: x = 0, x = 1 and x =2
**** Your graph is incorrect. Check mine. The zeros happen where the curve intersects the x axis and these are at x = 0, x = 1, x =2
What is an example of a situation from your professional or personal life that requires you to compare, understand, and make decisions based on quantitative comparison? Be sure to describe the types of quantitative comparisons you had to make, what decisions you made, and why.
An example of situation involving quantitative variables is given by:
The gameplan of an NFL coach.
What are qualitative and quantitative variables?The variables are classified as follows:
Qualitative variables are variables that assumes labels or ranks, such as good/bad, yes/no and so on.Quantitative variables are variables that Assume numerical values.In the context of this problem, we want to use quantitative variables, that is, numbers.
Multiple examples of this are given by the gameplan of NFL coaches, as the following example:
How often to blitz? The coach has to analyze the opposing offense statistics against the blitz or against standard pressure. For example, Patrick Mahomes is known to be a blitz killer, hence a coach should visualize the statistics and conclude that he has a better chance of stopping Mahomes playing standard coverage than blitzing.
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Rewrite the function by completing the square.
g(x)=x^2 − x − 6
g(x)= _ ( x + _ )^2 + _
The completed square function is (x - 1/2)² = 25/4
Square function:
A square function is a 2nd degree equation, meaning it has an x². The graph of every square function is a parabola.
Given,
Here we have the function g(x) = x² - x - 6
Now, we need to convert this into the complete square function.
In order to solve this we have to do the following:
Add 6 to both sides of the equation,
x² - x = 6
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of b.
(b/2)² = (-1/2)²
Add the term to each side of the equation.
x² - x + (-1/2)² = 6 + (-1/2)²
When we simplify the equation, then we get,
x² - x + 1/4 = 25/4
Factor the perfect trinomial square into,
(x - 1/2)² = 25/4
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The parabola f (x) = (x - 2)2 + 1 is graphed in the xy-coordinate plane.8Part ASelect from the drop-down menus to correctly complete the sentence.The vertex of the parabola is 2 units(a)(b) Part BSelect from the drop-down menus to correctly complete the sentence.How does the function f (x+3) compare to f (x)?f (x + 3) has avshift 3 unitsV the origin and 1 unitv f(x).the origin.
We will have the following:
a) The vertex of the parabola is 2 units right of the origin and 1 unit up from the origin.
b) We will have that:
f(x+3) has vertex shift 3 units left of f(x).
Draw a figure to use for numbers 13 - 15. Points A. B. and C are collinear and Bis the midpoint of AC. 13. If AB = 3x - 8 and BC = x + 4, find the length of AB 14. If BC = 6x - 7 and AB = 5x + 1. find the length of AC 15. If AB = 8x + 11 and BC = 12x - 1. find the length of BCAnswer 13
13.
Given:
AB = 3x - 8, BC = x + 4
A, B and C are collinear
B is a midpoint of AC
Since B is the midpoint, we can write:
[tex]\text{length of AB = Length of BC}[/tex]Hence, we have:
[tex]3x\text{ - 8 = x + 4}[/tex]Solving for x:
[tex]\begin{gathered} \text{Collect like terms} \\ 3x\text{ -x = 4 + 8} \\ 2x\text{ = 12} \\ \text{Divide both sides by 2} \\ x\text{ = 6} \end{gathered}[/tex]Hence, the length of AB is:
[tex]\begin{gathered} =\text{ 3x - 8} \\ =\text{ 3}\times\text{ 6 -8} \\ =\text{ 18 -8} \\ =\text{ 10} \end{gathered}[/tex]Answer:
The length of AB is 10 unit
1) The weights of a particular group of show dogs are normally distributed with a mean of 16.6 kg and astandard deviation of 2.2 kg. If a random show dog is selected from the group, what is the probability thatit would weigh less than 15.5 kg?
In order to determine the probability, first use the followinf formula to calculate the Z factorr:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]where:
x: specific value from the data = 15.5 kg
σ: standard deviation = 2.2 kg
μ: mean = 16.6 kg
replace the previous values to find the Z factor:
[tex]Z=\frac{15.5\operatorname{kg}-16.6\operatorname{kg}}{2.2\operatorname{kg}}=0.5[/tex]Next, search the corresponding value of the probability in a table of Normal distribution.
The correspondinf value of the probability for Z = 0.5 is P = 19.15%
This can be noticed in the following graph.
can you help me on the part 2 Heads in a Row:
Given:
Flipping a coin twice.
Required:
We need to find the likelihood of flipping heads twice in a row.
Explanation:
The sample space = All possible outcomes.
The sample space, S= {TT,TH,HT,HH}
[tex]n(S)=4[/tex]Let A be the event of flipping heads twice..
The favorable outcomes = flipping heads twice.
The favorable outcomes ={HH}
[tex]n(A)=1[/tex]Consider the probability formula.
[tex]P(A)=\frac{n(A)}{n(S)}[/tex][tex]P(A)=\frac{1}{4}[/tex][tex]P(A)=0.25[/tex]The probability of flipping heads twice in a row is 0.25 which is a close value to the number 0.
This event happens least likely.
Final answer:
Flipping heads twice in a row is the least likely.
The probability of flipping heads twice in a row is 0.25.
What is the answer and how do I solve this
A parent absolute value function f(x) = |x| is plotted as
We can change the appearance of this absolute value function based on what we add to the absolute value function and the constant accompanied by it.
Let's start with shifting the plot from |x| to |x+1|. If we add +1 to x inside an absolute value function, the parent absolute value function will shift one unit to the left. This shifting is represented by the red dotted plot on the figure below.
We now multiply a constant -3 on the absolute value function |x+1|. Multiplying a negative number to the absolute value function results in mirroring the absolute value function via the x-axis. Then, the plot will be compressed by a factor of 1/3. We now have
Hence, the final plot for the given absolute value function y = -3|x+1| is
Number 14. Need help finding the area of the shaded area. Forgot how to solve it. Please help.
To find the area of the shaded region we need to calculate the area of the square and subtract to it the area of the circle.
The area of a square is calculated as follows:
[tex]A=b^2[/tex]where b is the length of each side.
Substituting with b = 16 cm (given that the radius of the circle is 8 cm, then the length of the square's side is 2x8 = 16 cm):
[tex]\begin{gathered} A_1=16^2 \\ A_1=256\operatorname{cm}^2 \end{gathered}[/tex]The area of a circle is calculated as follows:
[tex]A=\pi r^2[/tex]where r is the radius of the circle.
Substituting with r = 8 cm, we get:
[tex]\begin{gathered} A_2=\pi\cdot8^2 \\ A_2=\pi\cdot64 \\ A_2\approx201\operatorname{cm}^2 \end{gathered}[/tex]Finally, the area of the shaded region is:
[tex]\begin{gathered} A_3=A_1-A_2 \\ A_3=256-201 \\ A_3=55\operatorname{cm}^2 \end{gathered}[/tex]A scale drawing of a rectangular park is 4 inches wide and 8 inches long. The actual park is 320 yards long. What is the perimeter of the actual park, in square yards?
Given:
• Width of scale drawing = 4 inches
,• Length of scale drawing = 8 inches
,• Length of actual park = 320 yards
Let's find the perimeter of the actual park.
Let's first find the width of the actual park.
To find the width of the actual park, we have:
[tex]\begin{gathered} \text{ width of actual = }\frac{\text{ length of actual}}{\text{ length of scale}}*\text{ width of scale} \\ \\ \\ \text{ width of actual = }\frac{320}{8}*4 \\ \\ \text{ width of actual = 40 * 4 = 160 yards} \end{gathered}[/tex]The width of the actual park is 160 yards.
Now, to find the perimeter of the actual park, apply the formula do perimeter of a rectangle:
P = 2(L + W)
Where:
P is the perimeter
L is the length = 320 yards
W is the width = 160 yards
Thus, we have:
P = 2(320 + 160)
P = 2(480)
P = 960 yards
Therefore, the perimeter of the actual park is 960 yards.
ANSWER:
960 yards
A tornado siren begins blaring from the center of town 9.5 seconds after a tornado was spotted. The siren is located 490 meters north of a school. If the siren’s sound wave travels at a constant velocity of 350 meters per second south, how long will it take the sound wave to travel from the siren to the school?
The relationship between distance, time and velocity is:
[tex]v=\frac{d}{t}[/tex]The question ask us for the time, we can solve for t:
[tex]v=\frac{d}{t}\Rightarrow t=\frac{d}{v}[/tex]To find the time that it will take the sound wave travelling at 350 m/s to reach the school at 490m is the distance divided the velocity:
[tex]\begin{gathered} t=\frac{490m}{350\frac{m}{s}} \\ \end{gathered}[/tex][tex]t=1.4s[/tex]The answer is 1.4s
GRAPH each triangle and CLASSIFY the triangle according to its sides and angles.
Answer:
[tex]\Delta CAT\text{ is an ISOSCELES triangle}[/tex]Explanation:
To properly classify the traingle, we need to get the length of the sides
To get the length of the sides, we need to get the distance between each two points using the distance between two points formula
Mathematically,we have the formula as:
[tex]D\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where (x1,y1) refers to the coordiantes of the first point while (x2,y2) refers to the coordinates of the second point
let us get the coordinates of the individual points as seen from the plot shown
C (1,8)
A (5,10)
T (7,6)
So, let us find the distance between each two points
For AC, we have:
[tex]D\text{ = }\sqrt[]{(5-1)^2+(10-8)^2}\text{ = }\sqrt[]{20}[/tex]For AT, we have:
[tex]D=\sqrt[]{(7-5)^2+(6-10)^2\text{ }}\text{ = }\sqrt[]{20}[/tex]Lastly, for CT, we have:
[tex]D\text{ = }\sqrt[]{(7-1)^2+(6-8)^2\text{ }}\text{ = }\sqrt[]{40}[/tex]From our calculations, we can see that AC = AT
If we have a triangle which has two of its sides equal in length (the angle facing these sides would be same too), we call this an isosceles triangle
So, the class of triangle CAT is isosceles triangle
What is the value of f(3) on the following graph?
Answer
f(3) = -2
Explanation
We are asked to find the value of f(3) from the graph.
This means we are looking for the value of f(x) or y on the graph, at a point where x = 3.
From the graph, we can see that at the point where x = 3, y = -2
Hence, f(3) = -2
Hope this Helps!!!
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The GCD of two numbers is 11 and their LMC is 220. One of the numbers is 55. find the other number.
If the GCD of two numbers is 11 and their LCM is 220 and one of the number is 55, then the second number is 44
The one number = 55
Consider the second number as x
GCD is the greatest common divisor
LCM is the least common multiple
The greatest common divisor of two numbers = 11
The least common multiple of two numbers = 220
We know
The product of two numbers= The product of GCD and LCM
55 × x = 11 × 220
55x = 2420
x = 44
Hence, If the GCD if two numbers is 11 and their LCM is 220 and one of the number is 55, then the second number is 44
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Identify the slope and y-intercept of equation 5x-3y=9
To identify the slope and y-intercept, we will take the given equation to its slope-intercept form:
[tex]y=mx+b,[/tex]where m is the slope and b is the y-intercept.
To take the equation to its slope-intercept form, we add 3y to the given equation:
[tex]\begin{gathered} 5x-3y+3y=9+3y, \\ 5x=9+3y\text{.} \end{gathered}[/tex]Now, we subtract 9, and get:
[tex]5x-9=3y\text{.}[/tex]Finally, dividing by 3, we get:
[tex]y=\frac{5}{3}x-3.[/tex]Therefore, the slope and y-intercept are:
[tex]\frac{5}{3},\text{ and -3 }[/tex]correspondingly.
Answer:
Slope:
[tex]\frac{5}{3}\text{.}[/tex]Y-intercept:
[tex]-3.[/tex]I need to find the equation of a circle I will include picture
Given,
The center of the circle is (6, -3).
The coordinates of the point, circle is passing through (6,6).
The general equation of the circle is,
[tex](x-h)^2+(y-k)^2=r^2[/tex]Here, x, y are the coordinates of the point.
h and k are the center of the circle.
r is the radius of the circle.
Substituting the value of h, k , x and y in the equation of circle then,
[tex]\begin{gathered} (6-6)^2+(6-(-3))^2=r^2 \\ 0+9^2=r^2 \\ r=9 \end{gathered}[/tex]So, the radius of the circle is 9.
Substituting the value of h, k and r in the general equation of circle.
[tex]\begin{gathered} (x-6)^2+(y-(-3))^2=9^2 \\ x^2+36-12x+y^2+9+6y=81 \\ x^2+y^2-12x+6y-36=0 \end{gathered}[/tex]Hence, the equation of circle is x^2+y^2-12x+6y-36=0
Solve for x and then give the m
x = 38
Step-by-step explanation:
(x + 6) + (3x - 16) + x = sum of angles in a triangle
(x + 6) + (3x - 16) + x = 180
(x + 3x + x ) + (6 - 16) = 180
5x +(-10) = 180
5x - 10 = 180
5x = 180 + 10
5x = 190
5x/5 = 190/5
x = 38
Answer:
x = 38 and m∠M = 98
Step-by-step explanation:
Angles in any triangle will always add up to 180 :
So angle O + Angle N + Angle M = 180
(x+6)+(3x-16)+(x) = 180
Simplify:
5x-10 = 180
Add 10 to both sides :
5x = 190
Divide both sides by 5 :
x = 38
Angle M will therefore
= 3(38) - 16
= 114 - 16
= 98
Hope this helped and have a good day
What is the domain, range, and function? {(-3, 3), (1, 1), (0, -2), (1,4), (5, -1)}
The domain are all the inputs, that is; the x-values
Domain = { -3, 0, 1, 5}
The range are all the output, that is the y-values
Range = { 3, 1, -2, 4, -1}
This is just a relation and not a function, as we have more than 2 same value of x
Find the time. Round to the nearest day given the following:Principal: $74,000Rate: 9.5%Interest: $2343.33
Explanation
Simple Interest is calculated using the following formula:
[tex]I=\text{PRT}[/tex]where P is the principal ( initial amount)
R is the rate ( in decimal)
T is the time ( in years)
so
Step 1
Let
[tex]\begin{gathered} P=74000 \\ \text{rate}=\text{ 9.5\% =9.5/100= 0.095} \\ T=t\text{ ( unknown)} \\ \text{Interest}=\text{ 2343.33} \end{gathered}[/tex]now, replace
[tex]\begin{gathered} I=\text{PRT} \\ 2343.33=74000\cdot0.095\cdot t \\ 2343.33=7030t \\ \text{divide both sides by 7030} \\ \frac{2343.33}{7030}=\frac{7030t}{7030} \\ 0.3333=t\text{ } \end{gathered}[/tex]so, the time is 0.333 years
Step 2
convert 0.333 years into days
[tex]1\text{ year }\Rightarrow365\text{ days}[/tex]so
[tex]\begin{gathered} 0.333years(\frac{365}{1\text{ year}})=121.66 \\ \text{rounded} \\ 122\text{ days} \end{gathered}[/tex]therefore, the answer is
122 days
In 2000, there were 750 cell phone subscribers in a small town. The number of subscribers increased by 80% per year after 2000. How many cell phone subscribers were in 2010? Round off the answer to the nearest whole number.
This is an exponential growth. We would apply the exponential growth formula which is expressed as
y = a(1 + r)^t
Where
a represents the imitial number of subscribers
r represents the growth rate
t represents the number of years
y represents the number of subscribers after t years
From the information given,
a = 750
r = 80/100 = 0.8
t = 9 (number of years between 2000 and 2010)
Thus,
y = 750(1 + 0.8)^9
y = 750(1.8)^9
y = 148769.48
Rounding to the nearest whole number, the number of cell phone subscribers in 2010 is
148769
Please give steps and explanations to how you get the correct answer I am confused
To find the area under a function in a given interval you need to find the definite integral of the function in that interval.
For the given function:
[tex]\begin{gathered} P=100(0.4)^t \\ \\ \int_0^8Pdt=\int_0^8100(0.4)^tdt \end{gathered}[/tex]Use the next properties to find the integral:
[tex]\begin{gathered} \int a\times f(x)dx=a\int f(x)dx \\ \\ \int a^xdx=\frac{a^x}{\ln(a)} \end{gathered}[/tex][tex]\int_0^8100(0.4)^tdt=100\int_0^80.4^tdt=100\times\frac{0.4^t}{\ln(0.4)}\lvert^8_0[/tex]Evaluate the result for the given interval:
[tex]\begin{gathered} (100\times\frac{0.4^8}{\ln(0.4)})-(100\times\frac{0.4^0}{\ln(0.4)}) \\ \\ =-0.07152-(-109.13566) \\ \\ =109.06 \end{gathered}[/tex]Then, the area under the given function in the interval (0,8) is 109.06Carl is sewing a quilt. The number of yards of green fabric in the quilt is proportional to the number of yards of bluefabric in the quilt. This equation represents the proportional relationship between the number of yards of greenfabric, g, and yards of blue fabric, b, in the quilt.6 2/3 b = 5 1/3 gEnter the number of yards of green fabric used for 1 yard of blue fabric
Answer:
1 1/4 yards of green fabric.
Explanation:
The equation representing the proportional relationship between the number of yards of green fabric, g, and yards of blue fabric, b, in the quilt is:
[tex]6\frac{2}{3}b=5\frac{1}{3}g[/tex]If 1 yard of blue fabric is used: b=1
[tex]\begin{gathered} 6\frac{2}{3}\times1=5\frac{1}{3}g \\ \frac{20}{3}=\frac{16}{3}g \\ \text{ Multiply both sides by }\frac{3}{16} \\ \frac{3}{16}\times\frac{20}{3}=\frac{16}{3}\times\frac{3}{16}g \\ g=\frac{20}{16} \\ g=1\frac{1}{4}\text{ yards} \end{gathered}[/tex]If 1 yard of blue fabric is used, then 1 1/4 yards of green fabric will be used.
please help me work through this, thank you! it specifies to round to 2 decimal places
Since they will collide the time taken for both to reach the intersection is the same.
Let the time taken by t.
Recall that for steady motion,
[tex]\begin{gathered} d=st \\ \text{ Where:} \\ d=\text{ the distance covered} \\ s=\text{ the speed} \\ t=\text{ the time} \end{gathered}[/tex]Substitute d = 4 and s = 442 into the equation:
[tex]\begin{gathered} 4=442t \\ \text{ Dividing both sides by }442,\text{ it follows that:} \\ t=\frac{4}{442} \end{gathered}[/tex]Therefore, the distance covered by the Coyote in this time is given by:
[tex]d=\frac{4}{442}\times481=\frac{74}{17}[/tex]Using the Pythagorean Rule, it follows that the distance between Road Runner and the Coyote along the diagonal is given by:
[tex]h=\sqrt{(\frac{74}{17})^2+4^2}[/tex]Since speed s for a body that travelled distance d in time t is given by:
[tex]s=\frac{d}{t}[/tex]it follows that the required speed is given by:
[tex]-\sqrt{(\frac{74}{17})^2+4^2}\times\frac{442}{4}=-65\sqrt{101}[/tex]Therefore, the required rate is -65√101 kph.
Which decimal represents 8 X 1,000 + 4 X 100 + 7 X7 16 +31,0001,0A 8,004.073C 8,400.703B 8,040.073D 8,400.730
The given expression:
[tex]8\times1000+4\times100+7\times\frac{1}{10}+3\times\frac{1}{1000}[/tex]Simplify the expression:
[tex]\begin{gathered} 8\times1000+4\times100+7\times\frac{1}{10}+3\times\frac{1}{1000}=8000+400+0.7+0.003 \\ 8\times1000+4\times100+7\times\frac{1}{10}+3\times\frac{1}{1000}=8400.703 \end{gathered}[/tex]Answer : c) 8400.703