Solve the quadratic equation by the square root method and write the solution in radical form. simplify the solution. 4y^2=80

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.

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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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.

Answer:

Step-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

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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Answer: Scalene Right

Step-by-step explanation:

None of the side lengths are equal and there's a 90 degree angle

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.

Answer: no exact answer

Step-by-step explanation:

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.

The y-coordinate for the solution to the system of equations is y = -3.

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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Answer:c

Step-by-step explanation:

The unknown in the similar triangles are as follows;

x = 15 units

x = 16 units

Two triangles are said to be similar when they have two corresponding angles congruent and the sides proportional to each other.

Let's solve for x in the triangles as follows:

using the proportion,

2.

9 / x = x / 25

cross multiply

25 × 9 = x²

x² = 225

x = √225

x = 15 units

3.

x / 12 = 12 / 9

cross multiply

9x = 144

x = 144 / 9

x = 16 units

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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.

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

Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.

Dilation is the increase or decrease in the size of a figure by a scale factor of k, thereby creating an image. Resizing an object is accomplished through the transformation of dilation. The objects can be enlarged or shrunk using dilation. The result of this transformation is an image that has the same shape as the original shape. The size of the shape varies, though. A dilation should either stretch or contract the original shape. The term "scale factor" describes this transformation.

From the diagram:

Scale factor = A'B' / AB = 6/3 = 2

Center = (6, -6)

Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.

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The Ohio Lottery has been based on the probability deriving with the correct derivation of the number with the highest chances.

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.

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]

Step-by-step explanation:

A=4πr²

A = 4× 22/7 ×8²

A = 4 ×22\7×64

A=804.6m²

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

Let 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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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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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

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

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%.

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.

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.

Answer:

Step-by-step explanation:

First you identify your variable, for our sake lets use x:

x= number in question

Next you write the equation given in the question:

2(x-5)= x+25

Next you use the distributive property and multiply 2 by both x and negative 5 to get:

2x-10=x+25

Now you want to get all of the x's to one side so you subtract the x on the right, fro the one on the left giving you:

x-10=25

Then you simply add 10 to 25 giving you the answer of x=35

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°.

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

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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The total value of $6800 compounded quarterly at 6% for 3 years is $8,123

From 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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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.

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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