1/\(\sqrt{3}\) is the exact trigonometric ratios for the angle x whose radian measure is given.
What are trigonometric ratios?Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to sides and angles.
Trigonometric ratios, which contain the values of all trigonometric functions, are based on the ratio of sides of a right-angled triangle. The ratios of a right-angled triangle's sides with regard to a certain acute angle are known as its trigonometric ratios.
The right triangle's three sides are as follows:
Hypotenuse (the longest side)Perpendicular (opposite side to the angle)Base (Adjacent side to the angle)sin(4π/3) = sin(π + π/3)
= - sin(π/3)
= - \(\sqrt{3}\)/2
CSC(4π )/3) = csc(π + π /3)
= - csc(π /3)
= - 2/\(\sqrt{3\\\)
cos(4π /3) = cos(π + π /3)
= - cos(π /3) = - 1/2
sec(4 π /3) = sec(π + π/3)
= - sec(π /3) = - 2
tan(4π )/3) = tan(π + π /3)
= tan(π/3) = \(\sqrt{3}\)
Cot (4π/3 )= cot(π + π/3)
= Cot π/3 = 1/\(\sqrt{3}\)
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please help! i will mark you as brainliest :) (worth 30 points)
Answer:
Step-by-step explanation:
The reason why we perform an analysis of variance for comparing means rather than conducting multiple two-mean comparisons is Multiple choice question. because multiple two-mean comparisons increase the Type I error probability. simply because ANOVA has simpler calculations but otherwise offers no benefit over the multiple t-tests. power is compromised when using t-tests.
Instead of performing repeated two-mean comparisons, we conduct an analysis of variance to compare means because doing so reduces the likelihood of Type I errors. Here option A is the correct answer.
ANOVA is preferred over multiple two-mean comparisons because it reduces the Type I error probability and offers several benefits over conducting multiple t-tests.
When conducting multiple two-mean comparisons, the likelihood of making a Type I error (i.e., rejecting a true null hypothesis) increases with each comparison made. This is known as the multiple comparison problem, and it can lead to an inflated false positive rate.
In contrast, ANOVA uses a single test to compare multiple means simultaneously, reducing the likelihood of making a Type I error. ANOVA achieves this by partitioning the total variation in the data into different sources of variation and estimating the amount of variation due to random chance.
Additionally, ANOVA offers several benefits over multiple t-tests. One advantage is that it provides a statistical significance test for the overall difference among the groups, not just for pairwise comparisons. ANOVA also allows for the testing of interactions between factors that influence the mean differences. Furthermore, ANOVA calculations can be more efficient than conducting multiple t-tests, especially when the number of groups is large.
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Complete question:
The reason why we perform an analysis of variance for comparing means rather than conducting multiple two-mean comparisons is
A. Because multiple two-mean comparisons increase the Type I error probability.
B. Simply because ANOVA has simpler calculations but otherwise offers no benefit over the multiple t-tests.
C. Power is compromised when using t-tests.
Kendall went to the candy store and bought 2 pounds of candy. If 1/5 of Kendall's candy was chocolate, how many pounds of chocolate candy did Kendall buy?
The answer is 1/10
This is simple division
The equation is (1/5÷2)
I did my work on a sheet of paper so i know i did this correctly
My explanation of my work:
Keep change flip is the operation used here
So you keep 1/5 ,change the division sign to multiplication and flip the 2/1 into 1/2 so the new equation is (1/5x1/2) the answer to that is 1/10
Have an amazing day :)
-yO mAmA
Diego deposited $ 1000 for 4 years at a simple interest rate of 6%. Find the interest and the total balance of
Diego's account after 4 years
Answer:36380
Step-by-step explanation:
Please help me solve this question asap I have a test 12 hours from now!!!! I need solution with steps and how you solved it.
The missing number from the diagram is 26. Option D
How to determine the valueFirst, we need to know that square of a number is the number times itself
From the diagram shown, we have that;
a. 2² = 4
4² = 16
Add the values
4 + 16 = 20
Also, we have that;
3² = 9
9² = 81
Add the values
= 81 + 9 = 90
Then,
1² = 1
5² =25
Add the values
25 + 1 = 26
Thus, to determine the value, we need to find the square of the other two and add them.
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HELP ASAP! PLEASE!
What relationship between the population of Ohio and the number of years displayed in the scatter plot
Answer:
The number line has to be shown in a picture if you want more specific instructions from others.
Step-by-step explanation:
Show a picture
can someone PLS HELPPPP ????
Answer:-
\(\frac{1}{3}\)
Step-by-step explanation:
Delta y / Delta x (delta = difference of)
\(\frac{1}{3}\).
What is the unit rate when 4 pizzas cost $36.52?
Each pizza costs $ -
Answer:
yeah I think is 9.13
Step-by-step explanation:
if 180 liters of fluid enter the kidneys each day, about how much fluid will be reabsorbed? 178 liters 100 liters 50 liters 2 liters
If 180 liters of fluid enter the kidneys each day, about 178 liters of fluid will be reabsorbed by the kidneys each day.
The kidneys play a crucial role in filtering and regulating fluid balance in the body. On average, approximately 180 liters of fluid enter the kidneys each day through the process of filtration. However, not all of this fluid is excreted as urine. The majority of it, around 99%, is reabsorbed back into the bloodstream.
The reabsorption process occurs in the renal tubules, where essential substances such as water, electrolytes, and nutrients are selectively transported back into the bloodstream while waste products and excess substances are removed for eventual excretion.
Therefore, out of the initial 180 liters that enter the kidneys, around 178 liters are reabsorbed, leaving only a small amount (approximately 2 liters) to be excreted as urine.
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Two square based pyramids are joined, total volume is 2700mm, perpendicular height 16mm on top pyramid and 20mm on the other, joint base has length and width of x, find x. Please help me..
Answer:
15 mm
Step-by-step explanation:
Since both pyramids are joined together, this means that the base of the pyramid which is a square have the same dimensions.
Let the length and width of the base be x, hence the dimension of the base is x mm by x mm.
For the first pyramid, the volume is:
V₁ = a²h₁/3; where a is the length of the square base, h₁ is the height.
Since the pyramid has a height of 16 mm, hence:
V₁ = 16x²/3
the second pyramid, the volume is:
V₂ = a²h₂/3; where a is the length of the square base, h₂ is the height.
Since the pyramid has a height of 20 mm, hence:
V₂ = 20x²/3
Since the total volume (V) of the pyramid is 2700 mm³, hence:
V = V₁ + V₂
V = 16x²/3 + 20x²/3
2700 = 16x²/3 + 20x²/3
2700 = 36x²/3
36x² = 8100
x² = 225
x = 15 mm
PLEASE PLEASE HELP ME AND GIVE THE CORRECT SSNWT ANSWER!!!
Answer:
47
Step-by-step explanation:
I dont know
let x[t] be a parametric motion and denote speed v[t]=|V[t]|=√[√[t] . V[t]], where velocity is V[t]=X'[t].
The speed v[t] is always a positive value, since it's the magnitude of the velocity vector.
The velocity of the motion at time t is given by V[t] = x'[t], which is the derivative of the position function x[t] with respect to time.
To compute v[t], you take the square root of the magnitude of V[t], which is given by:
v[t] = |V[t]| = sqrt(|x'[t]|) = sqrt(sqrt[t] * |V[t]|)
Here, the square root of t is taken as a weighting factor for the velocity, which means that the speed increases with time. The speed v[t] is always a positive value, since it's the magnitude of the velocity vector.
Note that this formula assumes that the motion x[t] is differentiable, which means that the velocity V[t] is well-defined and continuous. If x[t] is not differentiable, then the velocity V[t] may not exist, and this formula wouldn't apply.T
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Find an approximate value of m such that the equation cos x = mx has exactly two solutions. (round your answers to four decimal places.)
The answer is , an approx. value of m such that the equation cos(x) = mx has exactly two solutions is m = 1 and m = -0.3183
To find an approximate value of m such that the equation cos(x) = mx has exactly two solutions, we can use the fact that the graph of y = cos(x) intersects the line y = mx at exactly two points.
The graph of y = cos(x) is a periodic function with a maximum value of 1 and a minimum value of -1.
Since we want the line y = mx to intersect the graph of y = cos(x) at exactly two points, the slope m must satisfy the condition -1 ≤ m ≤ 1.
Furthermore, for the line y = mx to intersect the graph of y = cos(x) at exactly two points, the line must pass through the maximum and minimum points of the graph of y = cos(x).
These occur at x = 0 and x = π.
At x = 0, we have cos(0) = 1 and the equation cos(x) = mx becomes 1 = m(0), which simplifies to m = 1.
At x = π, we have cos(π) = -1 and the equation cos(x) = mx becomes -1 = m(π), which simplifies to m = -1/π.
Therefore, an approx. value of m such that the equation cos(x) = mx has exactly two solutions is m ≈ 1 and m ≈ -0.3183 (rounded to four decimal places).
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x=12-1//3x
can anyone tell me the full answer
Answer:
x=9 is the answer......
Two gamblers play a version of roulette with a wheel as shown in the file P05_63.xlsx. Each gambler places four bets, but their strategies are different, as explained below. For each gambler, use the rules of probability to find the distribution of their net winnings after four bets. Then find the mean and standard deviation of their net winnings. The file gets you started.
a. Player 1 always bets on red. On each bet, he either wins or loses what he bets. His first bet is for $10. From then on, he bets $10 following a win, and he doubles his bet after a loss. (This is called a martingale strategy and is used frequently at casinos.) For example, if he spins red, red, not red, and not red, his bets are for $10, $10, $10, and $20, and he has a net loss of $10. Or if he spins not red, not red, not red, and red, then his bets are for $10, $20, $40, and $80, and he has a net gain of $10.
b. Player 2 always bets on black and green. On each bet, he places $10 on black and $2 on green. If red occurs, he loses all $12. If black occurs, he wins a net $8 ($10 gain on black, $2 loss on green). If green occurs, he wins a net $50 ($10 loss on black, $60 gain on green).
The mean is 65.0646 and standard deviation is 39.082 when we can see the complete form of the table in the picture.
Given that,
As seen in the spreadsheet file P05 63.xlsx, two gamblers engage in a game of wheel-based roulette. Each gambler lays four bets, but each uses a different strategy, as will be seen later. Use the probabilities to determine the distribution of each gambler's net earnings after four bets. Then calculate their net wins' mean and standard deviation. You can get going with the file.
We have to find the mean and standard deviation.
We know that,
In the picture we can see the complete table.
Here, we calculated probability as,
For example take a first row
P(red=4, black=0, green=0) = (18/37)⁴ + 0 + 0 = 0.056
So the mean is 65.0646 and standard deviation is 39.082.
Therefore, The mean is 65.0646 and standard deviation is 39.082 when we can see the complete form of the table in the picture.
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\(Find \: H.C.F \: of \: \\ 900 \: , 270 \\ using \: e.d.l \: \\ ( \: Euclid's \: division \: lemma \: )\)
H.C.F of 900 & 270
Answer:
90Step-by-step explanation:
Factorize both numbers:
900 = 2*2*3*3*5*5270 = 2*3*3*3*5Common factors are:
2*3*3*5So HCF is:
HCF(900, 270) = 2*3*3*5 = 90\(\Large \red \mid \: \underline {\rm {{{\color{blue}{Explanation...}}}}} \: \red \mid\)
We know that ,As per Euclid Division Algorithm.
\( \longrightarrow \: \Large\underbrace {\rm {{{\color{red}{ \: a \: = \: bq \: + \: r \: }}}}} \)
a denotes dividendb denotes divisorq denotes quotientr denotes remainder◆━━━━━▣✦▣━━━━━◆Using Euclid Division Algorithm\(\large\bf{\purple{ \hookrightarrow \: }} \tt \: \: 900 \: = \: 270 \: \times \: 3 \: + \: 90\)
Here ,\(\large\bf{\orange{ \implies \: }} \: \:r \: \neq \: 0\)
Again Applying Euclid Division Algorithm
\(\large\bf{\purple{ \hookrightarrow \: }} \tt \: 270 \: = \: 90 \: \times \: 3 \: + \: 0\)
Here ,\(\large\bf{\orange{ \implies \: }} \: \:r \: = \: 0\)
As the reminder is 0 , 90 will be the greatest common divisor for the two given numbers.
So,\({\boxed{ \Large{ \blue{ \bf{ \underline{ HCF \: = \: 90}}}}}}\)
◆━━━━━▣✦▣━━━━━◆Which of the following groups of numbers is in order from least to greatest?
0.54, , 40%
, 0.8, 94%
67%, , 0.8
0.54, 67%
Answer:
3/4, 0.8, 94%
Step-by-step explanation:
on average, an individual's bmr decreases approximately 3 to 5 percent per decade after what age? a. 20 b. 50 c. 30 d. 70
An individual's BMR decreases approximately 3 to 5 percent per decade on an average after the age of option C. 30.
BMR is known as basal metabolic rate which decreases when the age of a person increases.As metabolism factor slow down with the increase in age.After the age of 30 metabolism rate decreases which effect basal metabolic rate every decade by round about 3 to 5 percent.At the young age expenditure of the daily energy is quiet more compare to older age.On an average after the age of 30 BMR is decreases approximately by 3 to 5 percent.
Therefore, on an average individuals BMR is approximately decreases by round about 3 to 5 percent per decade after the age of option c. 30.
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Al released his balloon from the 10-yard line, and it landed at the 16-yard line. If the ball reached a height of 27 yards, what equation represents the path of his toss?
The equation of the path of the parabola is y = a(x - 13)² + 27
Given data ,
To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.
The equation of a parabola in vertex form is given by:
y = a(x - h)² + k
where (h, k) represents the vertex of the parabola
Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.
The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:
h = (10 + 16) / 2 = 13
Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)
Now, let's substitute the vertex coordinates (h, k) into the general equation:
y = a(x - 13)² + k
Substituting the vertex coordinates (13, 27)
y = a(x - 13)² + 27
To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).
This means that the highest point (13, 27) lies on the parabola
Substituting the vertex coordinates (13, 27) into the equation
27 = a(13 - 13)² + 27
27 = a(0) + 27
27 = 27
Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number
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0.9 x 100=
13.79 x 100=
29.894 x 100=
Answer:
multiplying by 100 "shifts" decimal point to the right by 2
90
1379
2989.4
Step-by-step explanation:
Answer:
0.9 x 100=90
13.79 x 100=1379
29.894 x 100=2989.4
Step-by-step explanation:
A sequence of transformations is applied to ACDE to create AC'D'E'.
Select all of the sequences of transformations that could be applied to ACDE so that ACDE = AC'D'E'.
A clockwise rotation of 90 degrees and then a dilation by a scale factor of 2.
A dilation by a scale factor of 2 and then a reflection across the y-axis.
A clockwise rotation of 90 degrees and then a reflection across the y-axis.
A translation 5 units down and then a dilation by a scale factor of 2.
A translation 5 units down and then a clockwise rotation of 90 degrees.
A reflection across the y-axis and then a translation 5 units down.
The option 1 "A clockwise rotation of 90 degrees and then a dilation by a scale factor of 2", option 3 "A clockwise rotation of 90 degrees and then a reflection across the y-axis." and option 5 "A translation 5 units down and then a clockwise rotation of 90 degrees." are correct.
In the given question,
A sequence of transformations is applied to ACDE to create AC'D'E'.
We have to select all of the sequences of transformations that could be applied to ACDE so that ACDE = AC'D'E'.
Firstly we learn about Transformation
A point, line, or geometric object can be changed in four different ways that are all collectively referred to as transformations. The pre-image is the shape of the object as it was originally, and the transformed shape of the object is termed the image.
We can transform an object by translation, rotation, reflection, and enlargement.
So according to explanation we can see that
Option 1 is correct because in this option we transform the ABCD by rotation of 90 degrees and then a dilation by a scale factor of 2. In this option only shape is changing.
Option 2 is not correct because in this option we used both dilation by a scale factor of 2 and then a reflection across the y-axis. In this option shape and size both changes.
Option 3 is also correct because in this option we rotate 90 degree in clockwise direction and then a reflection across the y-axis. So there only change the position.
Option 4 is not correct because there is a translation by 5 units down and then a dilation by a scale factor of 2. It will change the shape and direction both.
Option 5 is correct because there is a translation by 5 units down and then a clockwise rotation of 90 degrees. It will change only shape.
Option 6 is not correct because there is reflection across the y-axis and then a translation 5 units down.
Hence, the option 1,3 and 5 are correct.
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9. Let H be the set of all vectors of the form 3s. Find a 2s vector v in R3 such that H that H is a subspace of IR 3? Span {v). Why does this show 2t 10. Let H be the set of all vectors of the form 0.Show that H is a subspace of R3. (U'se the method of Exercise 9.) 11. Let W be the set of ali vectors of the formb where b and c are arbitrary. Find vectors u and v such that W Span (u, v. Why does this show that W is a subspace of R3? St 2s-t 4t 12 Let W be the set of all vectors of the form Show that W is a subspace of R4. (Use the method/of Exercise 11.)
9. H is a subspace of R3 as it contains a 2s vector [0, 2s, 0].
10. H is a subspace of R3 as it consists of the zero vector [0, 0, 0].
11. W is a subspace of R3 as it is spanned by the vectors [1,0,0] and [1,1,0].
12.W is a subspace of R4 as it is spanned by the vectors [1,2,0,0] and [0,-1,4,0].
9. To find a 2s vector v in R3 such that H is a subspace of R3, we can choose v = [0, 2s, 0]. This vector satisfies the condition of H being a subspace since it is of the form 2s, and any scalar multiple of v will also be of the form 2s, which is within H. Therefore, H is a subspace of R3.
0. Let H be the set of all vectors of the form [0, 0, 0]. To show that H is a subspace of R3, we can use the method from Exercise 9. By choosing v = [0, 0, 0],
we can see that H is closed under scalar multiplication and addition, as any scalar multiple or sum of the zero vector will still result in the zero vector. Therefore, H is a subspace of R3.
11. Let W be the set of all vectors of the form [b, c, 0], where b and c are arbitrary. To show that W is a subspace of R3, we need to find vectors u and v such that W is spanned by (u, v).
We can choose u = [1, 0, 0] and v = [0, 1, 0]. Any vector in W can be expressed as a linear combination of u and v, and therefore W is spanned by (u, v). This shows that W is a subspace of R3.
12. Let W be the set of all vectors of the form [s, 2s - t, 4t] in R4. To show that W is a subspace of R4, we can use the method from Exercise 11. By choosing u = [1, 2, 0, 0] and v = [0, -1, 4, 0],
we can observe that any vector in W can be expressed as a linear combination of u and v. Hence, W is spanned by (u, v), indicating that W is a subspace of R4.
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Graph the numbers on a numberline that are solutions to x+7>9 and 8x≤64.
The solution to both inequalities is where the two solutions overlap, which is where x is greater than 2 but also less than or equal to 8.
What is Graph?
In mathematics, a graph is a visual representation of a set of data, usually involving two or more variables. A graph can be used to show the relationship between the variables, and it can help to illustrate patterns, trends, or correlations that might not be apparent from a table of data alone.
To solve the inequalities x+7 > 9 and 8x ≤ 64, we first simplify them:
x+7 > 9
x > 2
8x ≤ 64
x ≤ 8
To graph this on a number line, we can draw a line with an open circle at 2 to indicate that x is greater than 2, and a closed circle at 8 to indicate that x is less than or equal to 8. Then we shade in the area between the two points to show the range of values that satisfy both inequalities.
Therefore, the solution to both inequalities is where the two solutions overlap, which is where x is greater than 2 but also less than or equal to 8.
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In Exercises 17-20, describe the possible lengths of the
third side of the triangle given the lengths of the other
two sides. (See Example 5.)
17. Sinches, 12 inches 18. 12 feet, 18 feet
Private commen
Add comment to Lau
19. 2 feet, 40 inches
20. 25 meters 25 meters
In Exercises 21-24, is it possible to construct a triangle
with the given side lengths? If not, explain why not.
21. 6. 7. 11
22. 3, 6, 9
23. 28. 17. 46
24. 35, 120, 125
17. the sum of the lengths of any two sides of a triangle is always greater than the length of the third side
T=the third side
12+18>T
12+T>18
18+T>12
the first equation says that T<30
the second equation says that T>6
putting these together...
6<T<30
(Credit: Arthur D)
a right cylindrical tank is full of water. the tank has a radius of 10 inches. how fast is the height of water in the tank changing if the water is being drained at 34 cubic inches per hour?
The answer is 3/25π m/h.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
With related rates, we need a function to relate the 2 variables, in this case it is clearly volume and height. The formula is:
v=πr²hThere is radius in the formula, but in this problem, radius is constant so it is not a variable. We can substitute the value in:V=π(5m)2hby solving the equation with the given valueshence,The answer is 3/25π m/h.
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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
Answer:
The perimeter is the sum of the lengths of all the sides of a polygon. Thus, the perimeter of this quadrilateral is:
(10a-6) + (7a+4) + (7a+4) + (10a-6)
Simplifying the expression:
= 34a - 4
Therefore, the perimeter of the quadrilateral is 34a - 4.
PLEASE HELP ME SOMEONE I NEEDDDDDDD HELP PLEASE QUICK!!!!!!!!
Answer:
2/60 = 1/30 = 3.3%
Step-by-step explanation:
canbon-14 is used to determite the age of artificats in carbon sating. it has a half-life of 5730 years. write the exponential decay function for a 24-mg sample. find the amount of carbon-14 remaining after 20 millennia
The amount of carbon-14 remaining after 20 millennia is 0.912 mg.
The exponential decay function for a 24-mg sample of carbon-14 can be represented by the equation:
y = 24e^(-kt)
where:
y is the amount of carbon-14 remaining
e is the base of the natural logarithm
k is the decay constant, calculated by dividing the natural logarithm of 2 by the half-life of carbon-14 (5730 years)
t is the time elapsed
So, k = ln(2)/5730
To find the amount of carbon-14 remaining after 20 millennia (20,000 years), we can plug in the values:
t = 20,000 years
y = 24e^(-k * 20,000)
Substituting the value of k:
y = 24e^(-ln(2)/5730 * 20,000)
y = 24 * e^(-0.000011 * 20,000)
y = 24 * 0.038
y = 0.912 mg
So, the amount of carbon-14 remaining after 20 millennia is 0.912 mg.
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PLZ dont ignore me! I need help on this :(
Answer: should be the last answer! to the right.
Step-by-step explanation:
You have 30 coins and the d are dimes and q are quarters
John is a mechanic with a technical license. He has worked 40 hours at minimum wage
this week. How much is his gross wage for the week?
Answer:
$290
Step-by-step explanation:
if minimum wage is $7.25
7.25×40= 290