Let's assume the following variables.
x = number of units produced
It is stated in the problem that for every unit produced, there is an additional wage of $0.34. Hence, on top of $11.06 per hour wage, there will be an additional of $0.34x per hour. In equation, we have wage per hour:
[tex]W=11.06+0.34x[/tex]If Mike was able to produce 17 units, our x here is 17. Let's plug this value to the formula.
[tex]W=11.06+0.34(17)[/tex]Then, solve.
[tex]\begin{gathered} W=11.06+5.78 \\ W=16.84 \end{gathered}[/tex]Therefore, Mike's hourly wage is $16.84.
A triangle is graphed in this coordinate plane. what is the area of this triangle in square units A.9B.12C.18D.36
Answer
Option C is correct.
The area of the triangle = 18 square units
Explanation
The area of a triangle is given as
Area of the triangle = ½ × B × H
where
B = Base of the triangle = 6 units (From -3 t
4. -X2 + 10 5x + 3 5x+3 6r 4x2 + 2x - 7 I need the perimeter.
The perimeter is the sum of all sides, therefore:
[tex]\begin{gathered} P=(5x+3)+(4x^2+2x-7)+(-x^2+10)+(5x+3) \\ add_{\text{ }}like_{\text{ }}terms\colon \\ (5x+5x+2x)+(4x^2-x^2)+(3+3+10-7) \\ 3x^2+12x+9 \end{gathered}[/tex][tex]\begin{gathered} 3x^2+12x+9 \\ \frac{1}{3}(3x^2+12x+9)=x^2+4x+3 \end{gathered}[/tex]The factors of 3 that sum to 4 are 3 and 1. So:
[tex]x^2+4x+3=(x+3)(x+1)[/tex]Determine which of the lines are parallel and which of the lines are perpendicular. Select all of the statements that are true.
Line a passes through (-1, -17) and (3, 11).
Line b passes through (0,4) and (7,-5).
Line c passes through (7, 1) and (0, 2).
Line d passes through (-1,-6) and (1, 8).
Answers:
Line A is parallel to line D.
Line A is perpendicular to line C.
Line C is perpendicular to line D.
=====================================================
Explanation:
Let's use the slope formula to calculate the slope of the line through (-1,-17) and (3,11)
[tex](x_1,y_1) = (-1,-17) \text{ and } (x_2,y_2) = (3,11)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{11 - (-17)}{3 - (-1)}\\\\m = \frac{11 + 17}{3 + 1}\\\\m = \frac{28}{4}\\\\m = 7\\\\[/tex]
The slope of line A is 7
-------------
Now let's find the slope of line B.
[tex](x_1,y_1) = (0,4) \text{ and } (x_2,y_2) = (7,-5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-5 - 4}{7 - 0}\\\\m = -\frac{9}{7}\\\\[/tex]
-------------
Now onto line C.
[tex](x_1,y_1) = (7,1) \text{ and } (x_2,y_2) = (0,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - 1}{0 - 7}\\\\m = \frac{1}{-7}\\\\m = -\frac{1}{7}\\\\[/tex]
-------------
Lastly we have line D.
[tex](x_1,y_1) = (-1,-6) \text{ and } (x_2,y_2) = (1,8)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{8 - (-6)}{1 - (-1)}\\\\m = \frac{8 + 6}{1 + 1}\\\\m = \frac{14}{2}\\\\m = 7\\\\[/tex]
------------------------------
Here's a summary of the slopes we found
[tex]\begin{array}{|c|c|} \cline{1-2}\text{Line} & \text{Slope}\\\cline{1-2}\text{A} & 7\\\cline{1-2}\text{B} & -9/7\\\cline{1-2}\text{C} & -1/7\\\cline{1-2}\text{D} & 7\\\cline{1-2}\end{array}[/tex]
Recall that parallel lines have equal slopes, but different y intercepts. This fact makes Line A parallel to line D.
Lines A and C are perpendicular to one another, because the slopes 7 and -1/7 multiply to -1. In other words, -1/7 is the negative reciprocal of 7, and vice versa. These two lines form a 90 degree angle.
Lines C and D are perpendicular for the same reasoning as the previous paragraph.
Line B unfortunately is neither parallel nor perpendicular to any of the other lines mentioned.
You can use a graphing tool like Desmos or GeoGebra to verify these answers.
product of the equationa^4•a^6
Okay, here we have this:
Considering the provided operation, we are going to perform it, so we obtain the following:
Let us remember that when two terms with the same base are multiplied, then the base is preserved and the exponents are added, in this case we have:
[tex]\begin{gathered} a^4\cdot a^6 \\ =a^{(4+6)} \\ =a^{10} \end{gathered}[/tex]Finally we obtain that the operation is equal to a^10.
ABC with coordinates (1.3), B.4.5), and C15,2), what are the coordinates of ABC after the glide reflection described by t (-1,1) R y-axis?
Answer:
A'(0,4)
B'(-3,6)
C(-4,3)
Step-by-step explanation:
A glide reflection is the combination of a translation with a rotation.
In this question:
T(-1,1): This means that the translation is given by:
(x,y) -> (x-1,y+1)
Rotation: Around the y-axis. This means that:
(x,y) -> (-x,y)
The triangle has the following coordinates:
A(1,3), B(4,5), C(5,2)
Applying the translation:
(x,y) -> (x-1,y+1)
A(1,3) -> (1-1,3+1) = (0,4)
B(4,5) -> (4-1,5+1) = (3,6)
C(5,2) -> (5-1, 2+1) = (4,3)
Rotation over the y-axis:
(x,y)->(-x,y)
A'(0,4)
B'(-3,6)
C(-4,3)
Determine the value of b.
b3 = 343
b = ±114.3
b = ±7
b = 114.3
b = 7
Answer:
(d) b = 7
Step-by-step explanation:
You want the solution to b³ = 343.
SolutionThe equation can be written in standard form and factored according to the factoring of the difference of cubes:
b³ -343 = 0
(b -7)(b² +7b +49) = 0
The solutions to this are the values of b that make the factors 0.
b -7 = 0 ⇒ b = 7
b² +7b +49 = 0 ⇒ b = -3.5 ± i√36.75 . . . . . complex solutions
The one real solution to the equation is b = 7.
__
Additional comment
Every cubic has 3 solutions. Here, two of them are complex. When the only terms in the equation are the cubic term and the constant, there will always be only one real root.
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The equation b^3 = 343 has two valid real solutions: b = 7 and b = -7. Both values satisfy the equation and meet the given condition. Option B.
To determine the value of b, we can solve the equation b^3 = 343.
Taking the cube root of both sides, we get:
b = ∛343
The cube root of 343 is 7, since 7 * 7 * 7 = 343. Therefore, one solution to the equation is b = 7.
However, it's important to note that the cube root function has a real and complex solution. In this case, b = 7 is the real solution, but there are two additional complex solutions.
Using complex numbers, we can express the other two solutions as follows:
b = -∛343
b = -7
So the complete set of solutions for b is b = 7, -7.
In summary, the equation b^3 = 343 has two real solutions: b = 7 and b = -7. These solutions satisfy the equation and fulfill the condition. So Option B is correct.
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Daniel's family raises honey bees and sells the honey at the farmers' market. To get ready for market day, Daniel fills 24 equal sized jars with honey. He brings a total of 16 cups of honey to sell at the farmers' market.
Use an equation to find the amount of honey each jar holds.
To write a fraction, use a slash ( / ) to separate the numerator and denominator.
The fraction for the amount of honey each jar holds is 2/3.
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.
From the information, Daniel fills 24 equal sized jars with honey and he brings a total of 16 cups of honey to sell at the farmers' market.
The amount of honey will be:
= Number of cups / Number of jars
= 16 / 24
= 2/3
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. . Read the problem and write your answer for each part. Make sure to label each part: , , .jasmine is tracking the growth of a specific bacteria bacteria for a science experiment. She assumes that there are bacteria () in a Perti dish at 12:00 midnight. Jamie observes that the number of bacteria increases by 25 every hour . write an equation that describes the relationship between total number of bacteria () and time () in hours, assuming there are () bacteria in the perti dish at = 0. . if Jamie starts with bacteria in the perti dish, how many bacteria will be present after 6 hours? . if Jamie starts with bacteria in the perti dish, draw a graph that displays the total number of bacteria with respect to time from 12:00 midnight ( = ) to 8:00 am. ( = ). Label each axis and label points on your graph at times = , , , .use the coordinate plane below to draw your graph.
Part A:
Let:
T(h)= Total Number of bacterias as a function of time
h = Number of hours
B = Initial number of bacterias
Since the number of bacteria increases by 25 every hour, we can defined the equation as:
[tex]T(h)=25h+B[/tex]Part B:
B = 5
h = 6
Evaluate the previous equation for those values:
[tex]\begin{gathered} T(6)=25(6)+5 \\ T(6)=150+5 \\ T(6)=155 \end{gathered}[/tex]there will be 155 baterias after 6 hours
Part C
Let's graph the equation:
[tex]T(h)=25h+5[/tex]2) (3 pt) Write the function from the table and graph.хf(x)-10004122130.52) f(x) =
(x - h)^2 = 4p(y - k)
(-1 - 3)^2 = 4p(8 - 0.5)
(-4)^2 = 4p(7.5)
16 = 30p
p = 16/30
p = 8/15
(x - 3)^2 = 16/15(y - 0.5)
15(x^2 - 6x + 9) = 16y - 8
15x^2 - 90x + 135 = 16y - 8
16y = 15x^2 - 90x + 135 + 8
y = 15/16 x^2 - 90/16 x + 143/16
f(x) = 15/16 x^2 - 90/16x + 143/16
Graph the line with the given slope m and y-intercept b
Answer:
draw a line from the top left to the bottom right going through the centre
Step-by-step explanation:
because m=-1 (gradient)
and b=0 (y intercept)
The probability of a certain brand of battery going dead within 15 hours is 1/3. Noah has a toy that requires 4 of these batteries. He wants to simulate the situation to estimate the probability that at least one battery will die before 15 hours are up. 1. Noah will simulate the situation by putting marbles in a bag. Drawing one marble from the bag will represent the outcome of one of the batteries in the toy after 15 hours. Red marbles represent a battery that dies before 15 hours are up, and green marbles represent a battery that lasts longer. How many marbles of each color should he put in the bag? Explain your reasoning. *
a.
Noah put marbles on a bag, each color marble represents that the battery of the toy died before 15 hours (red marbles) or that the battery lasted after 15 hours (green marbles)
There are 4 batteries on the toy, for each battery there are two possible outcomes, each one represented by a red and green marble.
So, for each battery, he has to put two marbles. There will be 4 red marbles and 4 green marbles in the bag.
b.
To estimate the probability that at least one battery will die within 15 hours, you have to calculate the expected value.
3: A Bunch of SystemsSolve each system of equations without graphing and show your reasoning. Then, check yoursolutions,
Use the elimination method to solve the given system of equations.
To do so, multiply the first equation by -3 so that the coefficient of x in the first equation becomes the additive inverse of the coefficient of x in the second equation:
[tex]\begin{gathered} -3(2x+3y)=-3(16) \\ \Rightarrow-6x-9y=-48 \end{gathered}[/tex]Then, the system is equivalent to:
[tex]\begin{gathered} -6x-9y=-48 \\ 6x-5y=20 \end{gathered}[/tex]Add both equations to eliminate the variable x and to obtain an equation in terms of the variable y only:
[tex]\begin{gathered} (-6x-9y)+(6x-5y)=-48+20 \\ \Rightarrow-6x-9y+6x-5y=-28 \\ \Rightarrow-14y=-28 \\ \Rightarrow y=\frac{-28}{-14} \\ \therefore y=2 \end{gathered}[/tex]Replace y=2 into the first equation to find the value of x:
[tex]\begin{gathered} 2x+3y=16 \\ \Rightarrow2x+3(2)=16 \\ \Rightarrow2x+6=16 \\ \Rightarrow2x=16-6 \\ \Rightarrow2x=10 \\ \Rightarrow x=\frac{10}{2} \\ \therefore x=5 \end{gathered}[/tex]Replace y=2 and x=5 into the second equation to confirm the answer:
[tex]\begin{gathered} 6x-5y=20 \\ \Rightarrow6(5)-5(2)=20 \\ \Rightarrow30-10=20 \\ \Rightarrow20=20 \end{gathered}[/tex]Therefore, the solution to the system of equations is x=5, y=2.
A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 81 m long and 60 m wide. Find the area of the training field. Use the value 3.14 for n, and do not round your answer. Be sure to include the correct unit in your answer.
ANSWER:
EXPLANATION:
Given:
To find:
The area of the training field
We can see that the two semicircles will form a circle with a diameter(d) of 60 m, so the radius(r) of the circle will be;
r = d/2 = 60/2 = 30 m
Given pi as 3.14, we can go ahead and determine the area of the circle as seen below;
[tex]\begin{gathered} Area\text{ of the circle}=\pi r^2 \\ \\ =3.14*30^2 \\ \\ =3.14*900 \\ \\ =2826\text{ m}^2 \end{gathered}[/tex]a digital music player is marked down from its list price of $249.99 to a sale price of $194.99. What is the discount rate?
The discount rate of the digital player is 22%
How to determine the digital player's discount rate?From the question, we have the given parameters:
List price = $249.99
Sales price = $194.99
Start by calculating the change in the price.
This is calculated as follows
Change = List price - Sales price
So, we have
Change = $249.99 - $194.99
Evaluate the difference
Change = $55
The discount rate of the digital player is then calculated as
Discount = Change/List price x 100%
This gives
Discount = 55/249.99 x 100%
Evaluate
Discount = 22%
Hence, the discount rate is 22%
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1. Tyra bought a lolli-pop with a diameter of 2 inches. What is the circumference of the lolli-pop to the nearest tenth of an inch? A. 3.9 inches B. 15.7 inches C. 6.3 inches D. 7.9 inches
A lollypop have a circular shape
Diameter D is the line in a circumference that divides it in half
then calculate directly π• D
to the nearest tenth
π•D = 3.14 x 2 = 6.28
then nearest number is 6.3 , or 6.30. Option C)
You got 84 of 100 questions on the test correct. What percent did you get correct?Answer: 84%100%16%8.4%11/100 is equal to what percent?Answer: 110%10%89%11%3 out of 4 students in your class are girls. What percent of the class are girls?Answer: 3%4%75%25%
18. The weights of four puppies are shown in pounds. 9.5 9 9.125 9 Which list shows these weights in order from greatest to least F. 99.5 9 9.125 w 9.5 9 9.125 9.125 9 9.5 9 + J. 9 9 9.5 9.125
The correct list is
[tex]9\frac{3}{4},\text{ 9.5, 9}\frac{3}{8},9.125[/tex]This is option F
I need help on a problem
Those are similar triangles, which means, they are related by a ratio
For example in this case,
7: 10
to find x
10 / 7 = x/3
x= 10*3 /7
x= 30/ 7
x= 4.29
____________
Q.Using triangle congruency theorems, justify why the triangles are similar.
4a)
Looking at the figure,
AD and BE are parallel lines
AE and BD are transversals
Thus,
angle DAE is congruent to angle BEA because they are alternate angles(They lie in similar positions but on alternate sides of the transversal
Also,
angle ADB is congruent to angle EBD because they are alternate angles(They lie in similar positions but on alternate sides of the transversal.
Angle ACD is congruent to angle BCE
Recall, 2 triangles are similar if at least, 2 of their corresponding angles are congruent. In this case, 3 corresponding triangles are congruent. Thus,
triangle ADC is similar to triangle EBC by AA(angle angle) postulate
4b) If 2 triangles are similar, it means that the ratio of their corresponding sides is equal. Thus,
AD/EB = DC/BC = AC/ CE
From the information given,
AD = 2
AC = 4
EB = 5
Thus,
2/5 = 4/CE
By cross multiplying,
2 * CE = 5 * 4
2CE = 20
CE = 20/2
CE = 10
Can someone explain how I would know the difference between a 2:7 ratio and 7:2 ratio when a point partitions the line? Thank you!
Solution
For this case we can do the following:
We can understand 7/2 as the reciprocal of 2/7 and we can create the following diagram
Factor 6z^2 + 31z + 18
Cecilia is making a punch that uses 3 quarts of fruit juice for every quart of citrus soda. How many quarts of each does she need to make 16 quarts of punch?
The number of quarts of each constituent she needs to produce 16 quarts of punch is; 12 quarts of fruit juice and 4 quarts of citrus soda.
What quantity of each constituent is needed to produce 16 quarts of punch?It follows from the task content that the quantity of each constituent that is required to make 16 quarts of punch are to be determined.
Since it follows that 3 quarts of fruit juice are required to mix with every quart of citrus soda, it follows that the amount of punch made in this scenario is; 4 quarts of punch.
Hence, since there are 4 partitions of 4 quarts punch is 16 quarts punch, the amount of.each constituent needed by proportion are as follows;
3 quarts of fruit juice × 4 = 12 quarts of fruit juice.1 quarts of fruit juice × 4 = 4 quarts of citrus soda.Read more on proportion;
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Calculate the degree of the angles in the triangles below.
the sum of the internal angles of a triangle is equal to 180, then
[tex]\begin{gathered} 2x+7+5x+12=180 \\ 7x+19=180 \\ 7x+19-19=180-19 \\ 7x=161 \\ \frac{7x}{7}=\frac{161}{7} \\ x=23 \end{gathered}[/tex]so
answer:
angle 1 = 2x + 7 = 2(23) + 7 = 46 + 7 = 53°
angle 2 = 5x = 5(23) = 115°
angle 3 = 12°
The answer for the bottom question need a fast quick answer
Area of a circle is
[tex]A=\pi\cdot r^2[/tex][tex]\begin{gathered} d=2r \\ d=22 \\ r=\frac{22}{2} \\ r=11 \end{gathered}[/tex][tex]\begin{gathered} A=\pi(11)^2 \\ A=380.133ft^2 \end{gathered}[/tex]The area of the garder is 380.13 square footsIf a square foot cost $ 1.25
[tex]\begin{gathered} 1ft^2\to1.25\text{dollars} \\ 380.13ft^2\to x \\ x=\frac{380.13ft^2\cdot(1.25dollar)}{1ft^2} \\ x=475.16\text{dollar} \end{gathered}[/tex]To cover the garden they need to buy $475 in mulchf(x) = x^3- 9x^2 + 10.c ) list the x values of all the inflection points of F
To find the inflection points the first step we have to follow is to find the second and third derivatives of the function:
[tex]\begin{gathered} f\mleft(x\mright)=x^3-9x^2+10 \\ f^{\prime}\left(x\right)=3x^2-18x \\ f^{\prime}^{\prime}\left(x\right)=6x-18 \\ f^{\prime}^{\prime}^{\prime}\left(x\right)=6 \end{gathered}[/tex]Now, find the values of x for which the second derivative is 0:
[tex]\begin{gathered} 0=6x-18 \\ 18=6x \\ x=\frac{18}{6} \\ x=3 \end{gathered}[/tex]Evaluate the third derivative at this values of x, if the third derivative is different from 0, then that value is an inflection point:
[tex]f^{\prime}^{\prime}^{\prime}\left(3\right)=6[/tex]It means that there is an inflection point at x=3.
Tye mapping diagram below matches the points on the graph next to it.find the value of X
Given,
The coordinates of the points shown in the graph is:
[tex](-6,2),\text{ \lparen6,2\rparen, \lparen6,1\rparen and \lparen3,1\rparen}[/tex]Here, the given mapping is:
[tex](-6,2),\text{ \lparen6,2\rparen, \lparen x,1\rparen and \lparen3,1\rparen}[/tex]On comparing the coordinates then x = 6.
Hence, the value of x is 6.
Can someone please help me with this drag and drop? I would appreciate It a lot! Please explain :) I’ll give brainliest
Answer:
move B to true then everything is right ✅
Which of the following size measures will form a right triangle
From the given side lengths, let's find the measures that will form a right triangle.
Apply Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]Where:
• a ,and ,b, are lengths of the legs
,• c is the length of the hypotenuse.
Now, let's start from the first measures in option a.
• 48m, 64m, and 85m
[tex]\begin{gathered} 48^2+64^2=85^2 \\ \\ 2304+4096=7225 \\ \\ 6400\ne7225 \end{gathered}[/tex]The measures in option a will NOT form a right triangle since the left side of the equation does not equal the right side.
• 27 yd, 36 yd, 45 yd
[tex]\begin{gathered} 27^2+36^2=45^2 \\ \\ 729+1296=2025 \\ \\ 2025=2025 \end{gathered}[/tex]The measures in option B will form a right triangle because the Equation is true.
ANSWE
What’s the total of all the present values of the payments? $320,640 $787,116 $878,611 $987,116
The total of all the present values of the payments is $2,973,483.
What is the present value?The present value is the future cash flows discounted to the present day's values.
The present value can be determined using an online finance calculator that inputs the future cash flows, the interest rate, and the period.
How is the total present value determined?The total present value is a function of the summation of the four present values.
Since the present values are given, computing the total involves the mathematical operation of addition.
Present Values:1st payment $320,640
2nd payment $787,116
3rd payment $878,611
4th payment $987,116
Total PV $2,973,483
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Answer:
The correct answer is $878,611 for plato users
Step-by-step explanation:
Tickets numbered 1 - 10 are drawn at random and placed back in the pile. Find the probability that at least one ticketnumbered with a 6 is drawn if there are 4 drawings that occur. Round your answer to two decimal places.
The probability of a 6 being drawn in one pick is
[tex]\frac{1}{10}[/tex]For 4 drawings, the probability would be
[tex]\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}=\frac{4}{10}=\frac{2}{5}=0.40[/tex]