The coordinates of point H' will be: H'(3, 9)
What is Translation ?We know that a translation is basically a transformation that occurs when an object is moved from one place to another place.
The original object's dimensions, orientation, or shape are unaffected by translation.
Translating a point P(x, y) 1 unit up means we need to add to use P'(x, y+1), that is adding 1 unit to the y-coordinate of the point P'(x, y).
Now we have to translate the triangle 1 unit up. So, use the formula
P(x, y) → P'(x, y + 1)
Thus, the coordinates of point H' will be:
H( 3, 8) → H'( 3, 8+1) → H'(3, 9)
Therefore, the coordinates of point H' will be: A'(3, 9).
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Determine if the points are solution points to the inequalities below. If the point is a solution, enter yes.
If the point is not a solution, enter no. Enter yes or no in lower case letters (no capital letters).
a. Is (2, 10) a solution to y < 12- x?
b. Is (3, 13) a solution to y ≤ 15 - x?
c. Is (4, 19) a solution to y > 19 - x?
d. Is (5, 13) a solution to y ≥ 12 - x?
The solution is;
a. (2, 10) is not a solution to y < 12- x.
b. (3, 13) is a solution to y ≤ 15 - x
c. (4, 19) is a solution to y > 19 - x
d. (5, 13) is not a solution to y ≥ 12 - x
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.
A Set of such values is called a solution set to the considered equation or inequality.
Substitute the values where the variables are, and simplify to the point where you can tell whether the statement is true.
Each ordered pair is (x, y), thus the first value gets substituted for x; the second value gets substituted for y.
a. (2, 10)
11 < 13 -2 = 11
no
b.(3, 13)
8 ≤ 16 -3 = 13
yes
c. (4, 19)
20 > 18 -4 = 14
yes
d. (5, 13)
9 ≥ 15 -5 = 10
no
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Answer question B please
I tried doing my own explanation but i i only received a mark not full, i would really appreciate it if you would help m,
thx, kind regards
Lisa
Step-by-step explanation:
The slashes through the lines indicate they're of the same length, which means this is an equilateral triangle. Therefore all three angles are 60 degrees.
The lines being parallel mean that angle x shares the same angle as the triangle in the bottom-right corner.
The parallel lines intersecting with the line segment that is consistent throughout the triangle makes the angle the same.
Step-by-step explanation:
We can see that the triangle in the picture is an equilateral triangle, because its sides are all marked with one dash, meaning they are equal lengths. We note that all the angles in an equilateral triangle are each 60°.
The little arrows on the top and bottom lines in the figure indicate that they are parallel, which means that the diagonal line between them creates a set of alternate angles (I've attached a pic of what alternate angles generally look like to make this clearer).
Alternate angles are equal, which means x is equal to the angle at the bottom right of the triangle, which is 60°.
According to Wikipedia, the following are the lengths of terms of the US Presidents that preceded Joe Biden. There is a total of 44. You may have expected to see a total of 45, as Biden is the 46th us President, but Grover Cleveland was considered the 22nd and the 24th President, but is only counted once in this list The 2922 is the length of two full terms and the 1461 is the length of one full term FDR, the 4422 in the table, had actually started his FOURTH term before dying in office The 31 is William Henry Harrison who became ill shortly after his inauguration. His death may have been due to pneumonia Number of US Presidents 12 1 1 Term in Days 4422 2922 2865 2.840 2.728 2.041 2.027 1.886 1,654 1.503 1,461 1.460 1.430 1.419 1 1 12 1 1 1.419 1.262 1,036 969 895 881 492 199 31 TOTAL: 1 1 1 1 1 1 1 1 1 44 Determine the mean, median and mode for this set of data Give each to the nearest whole day Mean = Median = Mode = and With one of the modes being a high value as well as the term of FDR being much higher than all others, was pulled up to a higher value than another of hte measures of central tendency the
The mean of the given data is 1744 days, median of the given data is 1460.5 days, mode of the given data is 1461 days & 4422 days.
To find the mean, median, and mode of the lengths of terms of the US Presidents that preceded Joe Biden:
Mean:
To find the mean, we add up all of the term lengths and divide by the total number of terms:
Mean = (4422 + 2922 + 2865 + 2840 + 2728 + 2041 + 2027 + 1886 + 1654 + 1503 + 1461 + 1460 + 1430 + 1419 + 1262 + 1036 + 969 + 895 + 881 + 492 + 199 + 31) / 44
Mean = 1743.77 days
Median:
To find the median, we need to arrange the term lengths in order from smallest to largest, and then find the middle term. In this case, since we have an even number of terms, we will take the average of the two middle terms:
31 199 492 881 895 969 1036 1262 1419 1430 1460 1461 1503 1654 1886 2027 2041 2728 2840 2865 2922 4422
Median = (1460 + 1461) / 2
Median = 1460.5 days
Mode:
The mode is the most frequently occurring term length. In this case, there are two modes: 1,461 days and 4,422 days.
Since the term length of FDR is much higher than all the other term lengths, it has pulled up the mean to a higher value than the other measures of central tendency. Additionally, the mode being a high value is likely due to the fact that FDR served for more than three terms, which is an outlier in the data set.
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A 80 kg monkey climbs a 15 meter tree in half a minute. What is the magnitude of power the monkey demonstrated?.
The demonstration of magnitude of power given by 80 kg monkey by climbing a 15 meter tree in half a minute is equal to option b. 392 J/S.
Weight 'm' of the monkey is equal to 80kilogram
Height 'h' of the tree is equal to 15 meter
Time 't' taken by monkey to climb a tree = half a minute
= 30 minutes
g = 9.8 m/s²
Magnitude of power = ( m × g × h )/ t
⇒ Magnitude of power = ( 80 × 9.8 × 15 )/ 30
⇒ Magnitude of power = 784 / 2
⇒ Magnitude of power = 392 J/S
Therefore, the magnitude of the power for the given weight , displacement and time is equal to option b. 392 J/S.
The above question is incomplete, the complete question is:
A 80 Kg monkey climbs a 15 meter tree in half a minute. What is the magnitude of power the monkey demonstrated?
a. 13.1 J/S
b. 392 J/S
c. 784 J/s
d. 11760 J/s
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4. [0/2 Points]. DETAILS
(b) g(g(3))
Use f(x) = 5x - 4 and g(x) = 2x2 to evaluate the expression.
(a) f(f(2))
how do i solve this?
Answer:
324
Step-by-step explanation:
To evaluate (a) f(f(2)), we first evaluate f(2) which is 52-4 = 6. Then, we evaluate f(6) which is 56-4 = 26. So, f(f(2)) = 26.
To evaluate (b) g(g(3)), we first evaluate g(3) which is 23^2 = 18. Then, we evaluate g(18) which is 218^2 = 324. So, g(g(3)) = 324
¿Que probabilidad hay de que al lanzar dos dados la suma sea 11 en la primera tirada y 5 en la segunda?
Answer:
Step-by-step explanation:
The probability of rolling a sum of 11 on the first roll of two dice is 1/36, as there is only one combination of dice that can add up to 11 (a 5 and a 6).
The probability of rolling a sum of 5 on the second roll of two dice is also 1/36, as there is only one combination of dice that can add up to 5 (a 1 and a 4).
The probability of two independent events occurring is equal to the product of their individual probabilities. So, the probability of rolling a sum of 11 on the first roll and a sum of 5 on the second roll is:
1/36 * 1/36 = 1/1296
So, the probability of rolling a sum of 11 on the first roll and a sum of 5 on the second roll is 1/1296.
Find the lengths of the sides of a triangle if two of the sides are equal, the third side is 1 1/3 cm longer than the others, and its perimeter is 5 2/5 cm. The two equal sides of the triangle are (blank)cm. The third side is (blank) cm.
Answer:
Step-by-step explanation:
Here's a step by step solution with more details:
Let's call the length of the two equal sides of the triangle as x.
The third side, which is 1 1/3 cm longer, will have a length of x + 1 1/3 cm.
The perimeter of the triangle is 5 2/5 cm, so we can write an equation using the lengths of the sides:
x + x + (x + 1 1/3) = 5 2/5
Simplifying the equation:
2x + 1 1/3 = 5 2/5
Subtracting 1 1/3 from both sides:
2x = 4 1/5
Dividing both sides by 2:
x = 2 2/5
So the two equal sides of the triangle are 2 2/5 cm and the third side is 2 2/5 + 1 1/3 = 3 7/15 cm.
Answer:
One equal side = [tex]1\frac{16}{45}[/tex]cm and third side is [tex]2\frac{31}{45}[/tex]cm
Step-by-step explanation:
This is describing an isosceles triangle
1[tex]\frac{1}{3}[/tex] = [tex]\frac{4}{3}[/tex]
5[tex]\frac{2}{5}[/tex] = [tex]\frac{27}{5}[/tex]
Let
x = one of the two equal sides of the triangle
∴ Third side of triangle = [tex]\frac{4}{3} + x[/tex]
Perimeter of a triangle = Sum of all three sides:
[tex]\frac{27}{5}[/tex] [tex]= x + x + (\frac{4}{3} + x)[/tex]
Expand the parenthesis using the Distributive Law and bring all the like terms together:
[tex]=\frac{27}{5} = 2x + \frac{4}{3} + x[/tex]
[tex]= \frac{27}{5} = 3x + \frac{4}{3}[/tex]
[tex]= \frac{27}{5} -\frac{4}{3} = 3x[/tex]
The two denominators of the two fractions have to be manipulated to be made the same:
[tex]= (\frac{3}{3})(\frac{27}{5}) - (\frac{5}{5})(\frac{4}{3}) = 3x[/tex]
[tex]= \frac{81}{15} - \frac{20}{15} = 3x[/tex]
[tex]= \frac{81 - 20}{15} = 3x[/tex]
[tex]= \frac{61}{15} = 3x[/tex]
Cross-multiplication is added:
[tex]= (61)(1) = (15)(3x)[/tex]
[tex]= 61 = 45x[/tex]
Isolate x and make it the subject of the formula:
x = [tex]\frac{61}{45}[/tex]
x = One of the two equal sides = [tex]1\frac{16}{45}[/tex]cm
∴Third side:
= [tex]\frac{61}{45} + \frac{4}{3}[/tex]
= [tex]\frac{61}{45} + (\frac{15}{15})(\frac{4}{3})[/tex]
= [tex]\frac{61}{45} + \frac{60}{45}[/tex]
= [tex]\frac{61 + 60}{45}[/tex]
= [tex]\frac{121}{45}[/tex]
= [tex]2\frac{31}{45}[/tex]cm
Mary invests £12000 into a savings account. The account 1.5% compound interest per year. Work out the value of her investment after 2 years.
Answer:
Step-by-step explanation:
To calculate the compound interest on Mary's savings account, we can use the formula:
A = P * (1 + r/n)^(nt)
Where:
A is the amount after t years
P is the initial principal (£12000)
r is the interest rate (1.5%)
n is the number of times the interest is compounded in a year (let's assume it's compounded annually)
t is the number of years (2)
So, plugging in the values, we get:
A = £12000 * (1 + 0.015/1)^(1 * 2)
A = £12000 * (1.015)^2
A = £12000 * 1.0302
A = £12363.84
So, after 2 years, Mary's £12000 investment would be worth £12363.84, including the compound interest.
It is important to know what the variables in interest-rate formulas represent.
Compound Interest: A = P(1 + F)nt
Continuously Compounded Interest: A = Pert
Write the variable in the blank next to its description.
Answer:
Step-by-step explanation:
In the compound interest formula: A = P(1 + r)^t
A represents the amount of money in the account at the end of the term t, including interest.
P represents the initial principal, or the amount of money invested.
r represents the interest rate, usually expressed as a decimal.
t represents the number of time periods over which the interest is compounded.
In the continuously compounded interest formula: A = Pe^(rt)
A represents the amount of money in the account at the end of the term t, including interest.
P represents the initial principal, or the amount of money invested.
r represents the interest rate, usually expressed as a decimal.
t represents the number of time periods over which the interest is compounded.
So the variables in the formulas and their descriptions are:
A: the amount of money in the account at the end of the term t, including interest
P: the initial principal, or the amount of money invested
r: the interest rate, usually expressed as a decimal
t: the number of time periods over which the interest is compounded.
Find the total value of $6800 compounded quarterly at 6% for 3 years.
The total value of $6800 compounded quarterly at 6% for 3 years is $8,123
How to determine the total valueFrom the question, we have
A = final amount
P = principal amount (initial investment) = $6800
r = annual interest rate = 0.06 ie. 6%
n = number of times interest is compounded per year = 4
t = time (in years) = 3
The total value is calculated as:
A = P(1 + r/n)^(nt)
substitute the known values in the above equation, so, we have the following representation
A = 6800(1 + 0.06/4)^(4*3)
Evaluate
A = 8130.2
Hence,, the value is $8130.2
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I will give brainliest and ratings if you get this correct
A. The indifference curve of a consumer is negatively sloped to the right because it represents the consumer's preference for one good over another. As the consumer's income increases, their willingness to substitute one good for the other increases.
B. The indifference curve is convex to the origin because it shows the diminishing marginal rate of substitution of the two goods. As the consumer reaches the optimal combination of goods, the marginal rate of substitution between the two goods decreases.
C. Using the Lagrange method, the optimum combination of goods can be determined as follows:
Let L(X,Y) be the Lagrangian of this problem:
L(X,Y) = √X² + Y² - λ(200 - 3X - 4Y)
Where λ is the Lagrange multiplier.
The optimal solution is obtained by setting the derivatives of L with respect to X and Y to 0 and solving the equations simultaneously.
∂L/∂X = 0 -> X = 11.85
∂L/∂Y = 0 -> Y = 8.57
Therefore, the optimum combination of goods is X = 11.85 and Y = 8.57.
D. The slope of the indifference curve is equal to the slope of the budget line. This can be shown by comparing their respective equations and noting that their slopes are the same. The equation for the indifference curve is Y/X = (-2/3) and the equation for the budget line is Y/X = (-3/4). Since these equations are the same, it follows that the slopes of the two lines are equal.
Six more than one-fifth of a number p is equal to a number k.
Step-by-step explanation:
We can start by using an equation to represent the given information. Let's call the number p, and the number k, then:
k = (1/5)p + 6
So, "six more than one-fifth of a number p is equal to a number k" can be represented mathematically as k = (1/5)p + 6. To find the value of p, we can solve for p:
p = 5k - 30
So, p is equal to 5 times the value of k minus 30.
Write as a product.
(5c-3d)²-9d²
Answer:
the answer is 25c²
Step-by-step explanation:
(5c-3d)²-9d²
5²c²+3²d²-9d²
25c²+9d²-9d²
25c²
Answer:
= 25c² - 30cd
Step-by-step explanation:
(5c-3d)²-9d²
[tex](5c - 3d)(5c - 3d) - 9 {d}^{2} \\ 5c(5c - 3d) - 3d(5c - 3d) - 9{d}^{2} \ \\ 25 {c}^{2} - 15cd - 15cd + 9 {d}^{2} - 9 {d}^{2} \\25 {c}^{2} - 30cd[/tex]
Can someone do all of this and explain each one
Answer: no exact answer
Step-by-step explanation:
8m
6m
10m
5m what is the area of this shape
Answer:
68 m²Step-by-step explanation:
we have two rectangles side by side, the larger one measures 8m by 6m, the smaller one 5m by 4m, the 4 meters is the difference between the base (10m) and the 6m side, so we find the areas and add them using the formula A = L x W, the result is not in the choices but it is right.
6 * 8 + 4 * 5 = remember PEMDAS
48 + 20 =
68 m²
Of the apps on Juan’s tablet, 3/4 are gaming apps,and 5/7 of the gaming apps are action games.what fraction of the apps on Juan’s tablet are action games?
On solving the provided question, we can say that By fraction, 3/4 times 5/7 is 15/28 and Action games are 15/28 of the apps.
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
By fraction,
3/4 times 5/7 is 15/28.
Action games are 15/28 of the apps.
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Given the following observation for ortime serie X
t=1,2,3,4,5,6,7,8,9,10
Xt=47,64,23,71,38,64,55,41,59,48
Find
r(2)
Answer:t he autocorrelation of the time series X at lag 2 is approximately -0.018.
Step-by-step explanation:
To find the autocorrelation of the time series X at lag 2, we need to calculate the covariance between X(t) and X(t-2). This can be done using the following formula:
r(2) = cov(X(t), X(t-2)) / var(X(t))
where cov(X(t), X(t-2)) is the covariance between X(t) and X(t-2), and var(X(t)) is the variance of X(t).
To calculate the covariance, we'll use the following formula:
cov(X(t), X(t-2)) = sum((X(t) - mean(X(t))) * (X(t-2) - mean(X(t-2)))) / (n - 1)
where n is the number of observations in the time series. To calculate the variance, we'll use the following formula:
var(X(t)) = sum((X(t) - mean(X(t)))^2) / (n - 1)
First, let's calculate the mean of X(t):
mean(X(t)) = (47 + 64 + 23 + 71 + 38 + 64 + 55 + 41 + 59 + 48) / 10 = 51
Next, let's calculate the covariance between X(t) and X(t-2):
cov(X(t), X(t-2)) = sum((X(t) - 51) * (X(t-2) - 49)) / (10 - 1) = -10.3
Finally, let's calculate the variance of X(t):
var(X(t)) = sum((X(t) - 51)^2) / (10 - 1) = 563.7
Plugging in these values, we can find the autocorrelation at lag 2:
r(2) = cov(X(t), X(t-2)) / var(X(t)) = -10.3 / 563.7 = -0.018
So the autocorrelation of the time series X at lag 2 is approximately -0.018.
Omg please someone help me
Answer:
Planes
Step-by-step explanation:
You can think of a plane as a sheet of paper that goes on in all directions.
Answer:
B. planes
Step-by-step explanation:
The grammer makes sense
Determine the type of triangle that is drawn below.
Answer: Scalene Right
Step-by-step explanation:
None of the side lengths are equal and there's a 90 degree angle
Theta -90 90 Cosine (theta) ? 0 a. 1 c. 2 b. -1 d. 0
Answer:
b. -1.
Step-by-step explanation:
The cosine function is periodic with period 2π, and for angles in the range [-90°, 90°], it takes on values in the range [-1, 1].
For the angle θ = -90°, the cosine is given by:
cos(-90°) = cos(270°) = -1
the answer is b. -1.
Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 70 miles per hour, with a standard deviation of 3 miles per hour. Estimate the percent of vehicles whose speeds are between 64 miles per hour and 76 miles per hour.
Answer:
The Empirical Rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean, and approximately 99.7% of the data falls within three standard deviations of the mean.
In this case, the mean speed is 70 mph and the standard deviation is 3 mph. So, we can estimate the percent of vehicles whose speeds are between 64 mph and 76 mph as follows:
64 mph = 70 mph - 3 mph * 1
76 mph = 70 mph + 3 mph * 1
Since the speeds are within one standard deviation of the mean, we can use the Empirical Rule to estimate that approximately 68% of the vehicles have speeds between 64 mph and 76 mph.
So, the answer is approximately 68%.
{y=1/2x−4
{ y=−2x+1
What is the y-
coordinate for the solution to the system of equations?
The y-coordinate for the solution to the system of equations is y = -3.
What is substitution method?The substitution method is typically used in mathematics to solve an equation system. In this approach, you solve the equation for one variable first, then you enter its value into the other equation.
Simultaneous equations may usually be solved easily using the substitution method. There are direct ways that can give you the value of the unknown variables, such as cross-multiplication techniques. However, this method can be chosen over other algebraic methods for straightforward equations that don't require complicated calculations.
The system of equation is given as:
y = 1/2x - 4
y = -2x + 1
Substituting the value of y in equation 1 we have:
-2x + 1 = 1/2x - 4
-2x + 1 = x - 8 / 2
(-2x + 1)(2) = x - 8
-4x + 2 = x - 8
2 + 8 = x + 4x
10 = 5x
x = 2
Substituting the value of x in the second equation:
y = -2(2) + 1
y = -4 + 1
y = -3
Hence, the y-coordinate for the solution to the system of equations is y = -3.
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Math Essay on probability of the Ohio lottery
The Ohio Lottery has been based on the probability deriving with the correct derivation of the number with the highest chances.
What is probability?Probability has been defined as the mathematical description of learning the chances of an event to occur. The probability ranges from 0 to 1, with 1 being complete probability, and 0 means no chances of event to occur.
The Ohio lottery has been given as the game of lottery operated by the Ohio Lottery Commission. The purpose initiated by the Ohio Lottery has been to raise the funds for the education.
The lottery has been based on the probability of the common outcomes that delivers the formation of the numbers with the highest chances of getting resulted.
The games such as Bucket 5, Super Lotto, Ohio Lotto has been based on the probability of the drawing the numbers, and the correct probability won the lottery.
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Your question is probably incomplete, and most probably the complete question is:
Create a Math Essay on probability of the Ohio lottery.
A football has a radius of 8 cm. What is the surface area of the football?
Step-by-step explanation:
A=4πr²
A = 4× 22/7 ×8²
A = 4 ×22\7×64
A=804.6m²
Find the total area of the shaded region. Ay 1.5- 14 x=5y3 (5,1) * = 5y? 0.5- х 07 0 2.5 5 7.5 Find the area of the region enclosed by the curves x= x = 7y?, x=0, and y=1. The area of the region enclosed by the curves is (Type a simplified fraction.)
The total area of the shaded region for the region x = 5y³ , x = 5y² in the interval ( 5, 1 ) is equal to ( 5 / 12 ).
From the attached graph :
The area of the shaded region :
x = 5y³ , x = 5y² for the interval ( 5, 1 ) is equal to :
= [tex]\int\limits^1_0 {( 5y^{2 } - 5y^{3 }}) \, dy[/tex]
= [ ( 5y³/3 ) - ( 5y⁴ / 4 ) ][tex]| \limits^1_0[/tex]
Substitute the lower limit and upper limit we get,
= (5 /3 )( 1 )³ - 0 - ( 5 / 4 )( 1⁴) + 0
= ( 5 / 3 ) - ( 5 / 4 )
= ( 20 - 15 ) / 12
= 5 / 12
Therefore, the total area of the shaded region in the given graph for the lower and upper limit is equal to ( 5 / 12 ) .
The given question is incomplete, I answer the question in general according to my knowledge:
Find the total area of the shaded region x = 5y³ , x = 5y² for the interval
( 5, 1 ).
Graph is attached.
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The hypotenuse of a right triangle measures 7cm and one of its legs measures 2m. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer: 6.7
Step-by-step explanation: 7^2-2^2=45
square 45 =6.7
By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 299 mg of cholesterol. If the child eats 3 cupcakes and 4 slices of pizza, he or she takes in 90 mg of cholesterol. By eating 3 eggs and 1 cupcake, a child consumes 834 mg of cholesterol. How much cholesterol is in each item? The quantity of cholesterol in an egg is.....mg, the quantity of cholesterol in a cupcake is.....mg, and the quantity of cholesterol in a slice of pizza is.....mg. (Simplify your answers. Type mixed numerals, if possible. Otherwise, type integers or fractions.)
The quantity of cholesterol in an egg is 272 mg
The quantity of cholesterol in a cupcake is 18 mg
The quantity of cholesterol in a slice of pizza is 9 mg
How to find the amount of cholesterol in each itemLet the amount of egg be e
Let the amount of cupcake be c
Let the amount of pizza be p
By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 299 mg of cholesterol
e + c + p = 299
The child eats 3 cupcakes and 4 slices of pizza, he or she takes in 90 mg of cholesterol
3c + 4p = 90
By eating 3 eggs and 1 cupcake, a child consumes 834 mg of cholesterol
3e + c = 834
e + c + p = 299
3c + 4p = 90
3e + c = 834
solving the simultaneous equation gives
e = 270
c = 18
p = 9
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Suppose ABC Inc Can Produce 20 Units of Output Using any of the 4 Techniques Below TECHNIQUE TI 12 13 Т4 LAND LABOR CAPITAL 10 18 12 10 20 8 10 22 6 10 24 3 Further Suppose That The Output sells for $20 Per Unit In The Market. And the prices of land, labor, And capital are $8, $6, & $4, respectively.
11. Which technique should this firm use to maximize profit?
12. This firm will earn a profit equal to ________ dollars.
13. This firm will earn a Revenue equal to _____ dollars.
14. The profit associated with T1 is equal to _______ dollars.
15. If the price of labor falls to $2, ceteris paribus, this firm will earn a profit of
______dollars.
A baseball coach purchased bats and batting helmets. The coach purchased 19 items in all. Each bat cost $18.25 and each batting helmet cost $24.50. If the coach spent a total of $396.75, how many bats did the coach purchase?
Answer:
11 bat and 8 helmets.
Step-by-step explanation:
Let x = the number of bats
Let y = the number of batting helmets
x + y = 19 Rewrite as y = 19 - x
18.25x + 24.50y = 369.75 Multiply by 100
1825x + 2450y = 36975 Substitute 19 - x for y
1825x + 2450(19 -x) = 39675 Distribute the 2450
1825x + 46550 - 2450x = 39675 combine like terms
-625x + 46550 = 39675 subtract 46550 from both sides
-625x = -6875 Divide both sides by -625
x = 11
He bought 11 bats
x + y = 19 Substitute 11 for x to solve for y
11 + y = 19 Subtract 11 from both sides
y = 8
He bought 8 helmets.
Miri and Sara are collecting bags of aluminum cans for a recycling drive. Miri collects 3 times as many bags of
cans as Sara. Miri collects 123 bags of cans. Which equation and solution represent the number of bags of cans,
s, Sara collects?
The equation and solution that represents the number of bags of cans of aluminum cans for recycling that Sara collects, given that Miri collects 3x cans as Sara, is x = 123/3, which is 41.
What is an equation?An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.
Mathematical expressions contain variables, constants, numbers, and values using mathematical operands.
Equations differ from mathematical expressions based on the use of the equation symbol (=).
The number of bags of aluminum cans collected by Sara = x
The number of bags of aluminum cans collected by Miri = 3x
3x = 123 bags
The equation representing the number of bags of cans Sara collects x = 123/3
x = 41 (123/3)
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