Jimmy is paid $14.50 per hour for a regular forty-hour work week and 5 point time and a half for any hour worked over 40. This pas week, Jimmy earned $754.00 in total pay. How many hours of overtime did Jimmy work?
Let
x -----> the total hours worked
we have that
$14.50 --------> 40 hours
5.5($14.50) -------> > 40 hours
so
754=14.50*40+5.5(14.50)x
solve for x
754=580+79.75x
79.75x=754-580
79.75x=174
x=2.2 hours
Find the value of z such that 0.03 or f the area lies to the right of z Round your answer tom2 decimal places
ANSWER
z = 1.88
EXPLANATION
We have to find z such that the area under the normal curve to the right of that value is 0.03,
This is the same as finding z such that the area to the left of that value is 1 minus 0.03,
[tex]1-0.03=0.97[/tex]These are the values that z-score tables show. So, we have to find a z-score where the value in the table is 0.97,
The z-score whose area to its left is closest to 0.97 is z = 1.88.
Hence, for z = 1.88, the area under the curve to its right is 0.03.
Match each piece of the function with its domain.(6, oo)(-00, 1)(1,00)(-oo, -2)(-00, 6)(-2, 6)(3,00)(1, 4)
Explanation
The question wants us to select all the domains in the set of functions graphed.
The domain of a function is the set of all possible inputs for the function.
To do so, we have to be aware that there are 3 pieces of functions
These are shown below
These are
[tex]\begin{gathered} (-\infty,-2) \\ \\ (-2,6) \\ \\ (6,\infty) \end{gathered}[/tex]
The stock price for dgy was $38.21. In June. In July the stocked had in by 7 percent, but in August the price fell by 7 percent. What was the price of dgy stock in august . Round your answer to nearest cent , if necessary
The initial price is $38.21, and it got an increase of 7%, so the new price is the old one multiplied by 1.07:
[tex]38.21\cdot1.07=40.88[/tex]Then, the new price decreased by 7%, so let's multiply it by 0.93 (that is, 1 minus 0.07):
[tex]40.88\cdot0.93=38.02[/tex]So the price in August is $38.02.
The r value of -0.89 suggests that the independent variable ________, the dependent _________
We have that a correlation coefficient shows us how related is the dependent variable to the behavior of the independent variable.
MagnitudA correlation coefficient of ±1 means that the dependent variable moves as the independent variables moves too.
0 means that the dependent variable can move or not no matter how the independent variable changes.
As ±0.89 is near to ±1, we can say that in this case dependent and independent variable are related.
SignWhen the coeffitcient of correlation is negative it means that if the independent variable goes up, the dependent goes down, and visceversa.
In this case, while one decreases the other increases.
Answer: as the independent value increases, the dependent value decreases.
Add the complex numbers 3 + 11i and -3 - 11i.6 + 0i0 + 0i0 + 22i- 9 + 121i
SOLUTION
The given complex unbers are:
[tex]3+11i,-3-11i[/tex]Add the complex numbers:
[tex]3+11i+(-3-11i)[/tex]Simplify the expression:
[tex]\begin{gathered} 3+11i-3-11i \\ =3-3+11i-11i \\ =0+0i \end{gathered}[/tex]Therefore the required answer is: 0+0i
Transform AABC by the following transformations:• Reflect across the line y = -X• Translate 1 unit to the right and 2 units down.87BА )5421-B-7-6-5-4-301245678- 1-2.-3-5-6-7-8Identify the final coordinates of each vertex after both transformations:A"B"(C"
SOLUTION
A reflection on the line y = -x is gotten as
[tex]y=-x\colon(x,y)\rightarrow(-y,-x)[/tex]So, the coordinates of points A, B and C are
A(3, 6)
B(-2, 6)
C(3, -3)
Traslating this becomes
[tex]\begin{gathered} A\mleft(3,6\mright)\rightarrow A^{\prime}(-6,-3) \\ B(-2,6)\rightarrow B^{\prime}(-6,2) \\ C(3,-3)\rightarrow C^{\prime}(3,-3 \end{gathered}[/tex]Now translate 1 unit to the right and 2 units down becomes
[tex]\begin{gathered} A^{\prime}(-6,-3)\rightarrow A^{\doubleprime}(-5,-5) \\ B^{\prime}(-6,2)\rightarrow B^{\doubleprime}(-5,0) \\ C^{\prime}(3,-3\rightarrow C^{\doubleprime}(4,-5) \end{gathered}[/tex]So, I will attach an image now to show you the final translation.
find the unit price of a six pack of water for $6.90 fill in the amount per bottle of water
Given:
six pack of water = $6.90
To find:
Unit(one) price of water bottle(Price of one water bottle).
[tex]\frac{6.90}{6}=1.15[/tex]Therefore,
The price of one water bottle is $1.15.
Some fireworks are fired vertically into the air from the ground at an initial velocity of 80 feet per second. This motion can be modeled by the quadratic equation s(t) = -16t^2 + 80t. If a problem asks you to find how high the firework can go (this is the point where it explodes), what are they asking you for? (a) x coordinate of the vertex (b) y coordinate of the vertex (C) x coordinate of the roots (d) y coordinate of the roots
We are to know the highest point of the fireworks.
If we graph the quadratic, we will have a parabola with a maximum.
We basically want the maximum point. This occurs at the vertex.
• The x-coordinate of the vertex is at what time the maximum point occurs.
,• The y-coordinate of the vertex is the exact height (max).
Thus, when we are asked to find how high the firework can go, we will find the y-coordinate of the vertex.
Answer(b) y coordinate of the vertexKevin went to the nursery and bought a 5 ft tall tree. After planting the tree, Kevin made a table to record theheight, h, of the tree, t years after it was planted. Verbally describe the relationship between h and t.t 0 1 2 3 4h 5 6 7 8 9
As we can see inthe table foe every year that pass the thre grows 1 ft
As we can see inthe table foe every year that pass the thre grows 1 ft
I need help for my assignment I need to submit today
The general equation of a circle is expressed as
[tex]\begin{gathered} (x-a)^2+(y-b)^2=r^2\text{ ----- equation 1} \\ \text{where} \\ (a,\text{ b)}\Rightarrow\text{ center of the circle} \\ r\Rightarrow radius\text{ of the circle} \end{gathered}[/tex]Given that a circle having equation
[tex]\begin{gathered} (x-2)^2+(y-5)^2\text{ = 16} \\ \Rightarrow(x-2)^2+(y-5)^2\text{ = }4^2 \end{gathered}[/tex]is moved up 3 units and 1 unit to the left. Thus, we have
[tex]\begin{gathered} (x-2+1)^2+(y-5-3)^2\text{ = }4^2 \\ \end{gathered}[/tex]This gives
[tex](x-1)^2+(y-8)^2\text{ = }4^2\text{ ----- equation 2}[/tex]Comparing equations 1 and 2, we have
[tex]a\text{ = 1, b = 8, r = 4}[/tex]Hence,
the center (a, b) of the circle is (1, 8),
the radius r of the circle is 4,
the equation of the circle is
[tex](x-1)^2+(y-8)^2=4^2[/tex]how do i evaluate 8!4!/7!2!
Solution:
Consider the following expression:
[tex]\frac{8!4!}{7!2!}[/tex]Remember that The factorial function is defined by the product:
[tex]n!\text{ = }1\cdot2\cdot3\cdot\cdot\cdot\cdot\cdot\cdot(n-2)\cdot(n-1)\cdot n[/tex]thus, according to this definition, the given expression can be expressed as:
[tex]\frac{8!4!}{7!2!}\text{ = }\frac{(1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8)\text{ (}1\cdot2\cdot3\cdot4\text{)}}{(1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7)(1\cdot2)}[/tex]now, simplifying the previous expression we obtain:
[tex]\text{= }(8)\text{ (}3\cdot4\text{) = }96[/tex]we can conclude that the correct answer is:
[tex]\text{ }96[/tex]Find the perimeter of the isosceles triangle in simplest form. x2 + 20 units 2x units
The perimeter of an isosceles triangle is given by:
[tex]P\text{ = 2a + b}[/tex]From the question, b = 2x; a = x^2 + 20
[tex]P\text{ = 2a }+b=2(x^2+20)+2x=2x^2+40\text{ + 2x}[/tex][tex]P=2x^2\text{ + 2x + 40}[/tex]Spilt each number into its prime factors. Please enter the prime factors from smallest to largest.84 =
Let's make the table of the prime factors of 84:
then we have that 84=2x2x3x7, therefore, the prime factors are 2, 3 and 7
Select the correct answer.Consider this equation,tan(6)If 8 is an angle in quadrant II, what is the value of cos(8),OA.B._vOD.
Remember the definition of the tangent function:
[tex]\tan \theta=\frac{\sin \theta}{\cos \theta}[/tex]Then, we notice that:
[tex]\tan (\theta)=-\sqrt[]{\frac{19}{17}=}-\sqrt[]{\frac{\frac{19}{6}}{\frac{6}{17}}}=\frac{\sin \theta}{\cos \theta}[/tex]Then, we can conclude that:
[tex]\frac{\sin \theta}{\cos \theta}=-\frac{\sqrt[]{\frac{19}{6}}}{\sqrt[]{\frac{6}{17}}}[/tex]Something important to remember is that, in quadrant II, the value of sin(x) is positive, whereas the value of cos(x) is negative
So,
[tex]\begin{gathered} \sin (\theta)=\sqrt[]{\frac{19}{6}} \\ \Rightarrow\frac{1}{\cos \theta}=-\frac{1}{\sqrt[]{\frac{6}{17}}} \\ \Rightarrow\cos \theta=-\sqrt[]{\frac{17}{6}} \end{gathered}[/tex]Therefore, the answer to the question is option A
Samuel and Kathleen deposit $700.00 into a savings account which earns 4% interestcompounded monthly. They want to use the money in the account to go on a trip in 2 years.How much will they be able to spend?
To find how much they will be able to spend, we have to use the compoud interest formula, so:
[tex]\text{Amount}=700000\cdot(1+0.04)^{24}[/tex][tex]Amount=1794312.92[/tex]The surface area of a cell phone screen is 4900 mm². Use the fact that 10 mm = 1 cm to convert this area to cm². Round your answer to the nearest whole number. Do not type the units in the space below.
Answer:
49 cm²
Step-by-step explanation:
10 mm = 1 cm
1 mm = 1/10 cm
4900 mm² = 4900 × mm × mm
4900 mm² = 4900 × 1/10 cm × 1/10 cm = 49 cm²
Hello Just Want to make sure my answer is correct
So,
Let's remember that:
The three point postulate states that:
Through any three noncollinear points, there exists exactly one plane.
The Plane-Point Postulate states that:
A plane contains at least three noncollinear points.
As you can notice, the diagram illustrates that:
Given that a plane exists, then, there are three collinear points.
That's the three point postulate.
Ishaan started a toy car collection. His grandfather gave him 15 cars to start his collection. He can use his allowance to add 4 cars to his collection every month. Which equation can be used to find y, the total cars in his collection after x months?
The equation that he can use to find y, the total cars in his collection after x months is y = 15 + 4x.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the number of months be x.
Let the number of cars be y.
The equation will be:
y = 15 + (4 × x)
y = 15 + 4x
This illustrates the equation.
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
Please fill in the blanks so that the following statement is trues
x-intercepts
1) In a quadratic equation, the Real solutions correspond to the points in which the parabola intercepts the x-axis.
2) Note that when the roots are not real solutions, then we'd have complex numbers and the parabola wouldn't intercept the x-axis.
3) Therefore, the answer is: x-intercepts
If log a=4 log b= -16 and log c=19 find value of log a^2c (——-) /—— / B
We have the following
[tex]\begin{gathered} \log a=4 \\ \log b=-16 \\ \log c=19 \\ \log (\frac{a^2\cdot c}{\sqrt[]{b}}) \end{gathered}[/tex]Let's find a, b and c in order to solve the problem
a.
[tex]\begin{gathered} \log a=4 \\ a=10^4=10000 \end{gathered}[/tex]a = 10,000
b.
[tex]\begin{gathered} \log b=-16 \\ b=10^{-16}=\frac{1}{10^{16}} \end{gathered}[/tex]b=1.0E-16
c.
[tex]\begin{gathered} \log c=19 \\ c=10^{19} \end{gathered}[/tex]c=1.0E19
Thus, the value of log [ a^2c/sqrt(c) ] is :
replace:
[tex]\log (\frac{a^2\cdot c}{\sqrt[]{b}})=\log _{10}\mleft(\frac{\left(10^4\right)^2\cdot\:10^{19}}{\sqrt{10^{-16}}}\mright)[/tex]simplify:
[tex]\begin{gathered} \frac{\left(10^4\right)^2\cdot\:10^{19}}{\sqrt{10^{-16}}}=\frac{10^8\cdot10^{19}}{10^{-8}}=10^8\cdot10^8\cdot10^{19}=10^{8+8+19}=10^{35} \\ \Rightarrow\log 10^{35}=35 \end{gathered}[/tex]Therefore, the answer is 35
Determine whether or not the digits below are divisible by: 2,3,4,5,6,8,9,or, 10 a. 897 b. 12,000 c. 8190 d. 327
You have the following numbrs:
897
12,000
8190
327
In order to determine if the previous numbers are divisibles for numbers between 2 and 10, you take into account the following points:
- If last two digits are divisible by a number, and the part of the number without the last units is divisible too, you can consider that the complete number is divisible too.
- If the last digit is 0, then the number is divisible by 2 and 5 and 10.
- If the number is even, it is dividible by 2.
- In case a number ends in varios zeros you can consider if the digits before the zeros are divisible by a specific number.
- 897 is divisible by 3, because 97 is divisible by 3 and 800 too.
- 12,000 is divisible by 2, 3, 4, 5, 6, 8 and 10, because it is an even number, ends in 0 and the first digits are divisible by 3, 4, 6.
- 8190 is divisible by 2, 3, 5, 6, and 10, becaues it is even, ends in 0 and the number of last two digits is divisible by 3 and 6 and 8100 too.
- 327 is divisible by 3, because number of last two digits is divisible by 3 and 300 too.
you guess there are 80 marbles in a jar but there are actually 50. what is the percent of error
Calculate value = 80
Actual value = 50
[tex]\begin{gathered} \text{Percentage error = }\frac{Calculated\text{ value - Actual vale}}{\text{Actual value}}\text{ X 100\%} \\ =\text{ }\frac{80\text{ - 50}}{50}\text{ x 100} \\ =\text{ }\frac{30\text{ x 100}}{50} \\ =\text{ }\frac{3000}{50} \\ =\text{ 60\%} \end{gathered}[/tex]Given the matrices A and B shown below, find 4B – į A.3A=( 1215B5
Step 1 : To determine the matrices as shown below
What is the solution to the equation below?A.x = B.x = C.x = D.x =
Explanation
We are given the following equation:
[tex]\sqrt{5x-2}-1=3[/tex]We are required to determine the value of x.
This is achieved thus:
[tex]\begin{gathered} \sqrt{5x-2}-1=3 \\ \text{ Add 1 to both sides} \\ \sqrt{5x-2}-1+1=3+1 \\ \sqrt{5x-2}=4 \\ \text{ Square both sides } \\ (\sqrt{5x-2})^2=4^2 \\ 5x-2=16 \\ \text{ Collect like terms } \\ 5x=16+2 \\ 5x=18 \\ \text{ Divide both sides by 5} \\ \frac{5x}{5}=\frac{18}{5} \\ x=\frac{18}{5} \end{gathered}[/tex]Hence, the answer is:
[tex]x=\frac{18}{5}[/tex]Hi, could you help me figure out why I got 8 points off in this problem?
In triangle PQR
Construction: Draw PX perpendicular to QR where x lies on QR
Since:
PX perpendicular to QR
In the 2 triangles PXQ and PXR
given
proved up
PX = PX ------- common side in the 2 triangles
Triangle PXQ congruent to triangle PXR by the AAS theorem of congruency
As a result of congruency
PQ = PR ------- proved
i need help with my homework PLEASE CHECK WORK WHEN DONE
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given data
[tex]\begin{gathered} \mu=27 \\ \sigma=2 \\ x=25 \end{gathered}[/tex]STEP 2: Write the formula for calculating the z-score
[tex]z=\frac{x-\mu}{\sigma}[/tex]STEP 3: Calculate the z-score
[tex]z=\frac{25-27}{2}=-\frac{2}{2}=-1[/tex]STEP 4: Find the probability
Using the z-score calculator,
Be sure to include the correct unit in your answer
The fence required is:
[tex]388.3125ft^2[/tex]Explanation:For the farmer to build an accurate fence, he needs to know the area of the rose garden. The area is the sum of the area of the rectangle and the area of the semicircle.
The area of the rectangle is:
[tex]\begin{gathered} A=wl \\ =15ft\times20ft \\ =300ft^2 \end{gathered}[/tex]The area of the semicircle is:
[tex]\begin{gathered} A=\frac{\pi}{2}r^2 \\ \\ \text{Where r is the radius }=\frac{15}{2}=7.5ft,\pi=3.14 \\ \\ A=\frac{3.14}{2}(7.5)^2=88.3125ft^2 \end{gathered}[/tex]The area of the rose garden is:
[tex]300ft^2+88.3125ft^2=388.3125ft^2[/tex]A paper airplane contest is being held. The following results are found: 80% of the participants used a triangle shape. The triangle shaped planes only won their trials 16% of the time. The other shaped planes won their trials 36% of the time. Create a tree diagram for this situation: What is the probability that a triangle plane won overall?Out of 100 planes, which shape has the most winners?A winning plane is selected at random, what is the chance it is triangle shaped?
Given:
Percent of participants that used triangles shape = 80% = 0.80
The triangles shaped won their trials 16% of the time = 0.16
The other shaped plane won their trials 36% of the time = 0.36
Thus, we have:
Percent of participants who used other shapes = 100% - 80% = 20% = 0.20
Amount of time the triangle shaped plane lost = 100% - 16% =84% = 0.84
Amount of time the other shaped plane lost = 100% - 36% = 64% = 0.64
Let's solve for the following:
• (a) Create a tree diagram for this situation.
We have the tree diagram below:
• (b) What is the probability that a triangle plane won overall?
To find the probability that a triangle plane won overall, we have:
[tex]P(\text{triangle)}=\frac{0.8\times0.16}{(0.8\times0.16)+(0.2\times0.36)}=\frac{0.128}{0.128+0.072}=0.64[/tex]• (c) Out of 100 planes, which shape has the most winners?
Given that 80% used triangle, the number of planes with triangle shape will be:
0.8 x 100 = 80 planes
Number of planes with other shape:
0.2 x 100 = 20 planes
Number of winners for traingles:
0.16 x 80 = 12.8
Number of winners for other shape:
0.36 x 20 = 7.2
Therefore, the shape with the most winners is the triangle shape.
• (d),. A winning plane is selected at random, what is the chance it is triangle shaped?
To find the probability a winning plane selected at random is triangle shaped, wehave:
[tex]P(\text{triangle)}=\frac{12.8}{12.8+7.2}=\frac{12.8}{20}=0.64[/tex]ANSWER:
(b) 0.64
(c) Triangle shape
(d) 0.64
Which of the following represents the translation of R (-3, 4), along the vector <7, -6> <-1, 3>.
Solution
Step 1:
The translation is a term used in geometry to describe a function that moves an object a certain distance.
Step 2:
Pre-mage R = (-3,4)
Step 3:
When moved along (7, -6) the new coordinates become:
R' = (-3+7 , 4 - 6 ) = (4 , -2)
R' = ( 4 , -2 )
Step 4:
When moved along (-1, 3) the new coordinates become:
R'' = ( 4-1 , -2+3 ) = ( 3 , 1 )
R'' = (3 , 1)
Final answer
[tex]R(-3\text{ , 4\rparen }\rightarrow\text{ R'\lparen4 , -2\rparen }\rightarrow\text{ R''\lparen3 , 1\rparen}[/tex]Simplify. -(-6w + x - 3y)
Answer: 6w - x + 3y
Step-by-step explanation:
