The Bronx Zoo has a number of 4-legged mammals and 2-legged birds. Maggie visited the zoo and counted 200 animals that were either mammals or birds. Among these animals she counted a total of 522 legs. Write an algebraic equation that can be used to solve for the number of birds, and then solve the equation.

Answer:

\( \boxed{\sf Mass \ (M) \ of \ the \ round \ ball = 10 \ grams} \)

Given:

Volume (V) = 10 millilitres

Density (\( \sf \rho \)) = 1 gram/millilitre

To Find:

Mass (M) of the round ball

Step-by-step explanation:

Formula:

\( \boxed{ \bold{Density \: ( \rho) = \frac{Mass \ (M)}{Volume \ (V)} }}\)

\( \sf \implies Mass \ (M) = Density \ (\rho) \times Volume \ (V)\)

Substituting value of density (\( \sf \rho \)) & volume (V) in the equation:

\( \sf \implies M = 1 \times 10 \\ \\ \sf \implies M = 10 \: grams\)

\( \therefore\)

Mass (M) of the round ball = 10 grams

Answer:

A 2,3,6 :)

Step-by-step explanation:

thats answer corect me if im wrong hope it help

Answer:

x > - 16

Step-by-step explanation:

41- 3/4 x < 53

Subtract 41 from each side

41-41- 3/4 x < 53-41

-3/4x < 12

Multiply each side by -4/3, remembering to flip the inequality

-4/3 * -3/4x > 12 * -4/3

x > - 16

The given function is y = x ∫₁^(√9)  (t⁴ - 1) dt. Here, we need to find the length of the curve between x = 1 and x = 3.

Let us differentiate the function y = x ∫₁^(√9)  (t⁴ - 1) dt with respect to x using the Leibnitz rule:dy/dx = ∫₁^(√9)  (t⁴ - 1) dt + x d/dx (∫₁^(√9)  (t⁴ - 1) dt)Here, the first term is simply the given function. Let us evaluate the second term separately. Let u = ∫₁^(√9)  (t⁴ - 1) dt, then we have u = [t⁵/5 - t] from 1 to √9 which gives u = 16/5. Hence, d/dx (∫₁^(√9)  (t⁴ - 1) dt) = d/dx u = 0. Therefore, dy/dx = ∫₁^(√9)  (t⁴ - 1) dt.Length of curve between x = 1 and x = 3 is given byL = ∫₁³ √(1 + (dy/dx)²) dx= ∫₁³ √(1 + (∫₁^(√9)  (t⁴ - 1) dt)²) dx.

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Answer:

  -0.2

Step-by-step explanation:

Between the left marked point and the right one, the y-value changes by ...

  Δy = 2 -3.6 = -1.6

and the x-value changes by ...

  Δx = 5 -(-3) = 8

The rate of change of y with respect to x is the ratio of these:

  Δy/Δx = -1.6/8 = -0.2

The rate of change of y with respect to x is -0.2.

Answer:

Slope intercept: y = 0x + 2

Point slope: y - 2 = 0(x + 5)

Standard: 0x - y = 2

Answer:

(2n 2+5n−4)⋅(n+1)

Step-by-step explanation:

STEP

1:Equation at the end of step 1

 (((4•(n2))+3n)+((2•(n3))-4))+(3n2-2n)

STEP 2:Equation at the end of step 2

 (((4•(n2))+3n)+(2n3-4))+(3n2-2n)

STEP 3:Equation at the end of step 3:

 ((22n2 +  3n) +  (2n3 - 4)) +  (3n2 - 2n)

STEP 4:Checking for a perfect cube

4.1    2n3+7n2+n-4  is not a perfect cube

Answer:

total mass is 80

60% of 80 = 48

aka 24 (30%) x2

Answer:

y = 1/2x + 7

Step-by-step explanation:

Parallel lines have the same slope.

Therefore the new equation will have a slope(m) = 1/2

Substitute m = 1/2 and point (-2, 6) into y = mx + b to solve for "b"

y = mx + b

6 = 1/2(-2) + b

6 = -1 + b

7 = b

The new equation: y = mx + b

                                y = 1/2x + 7

Let's assume the first odd integer is x. Since the next odd integer would be consecutive, we can represent it as x + 2.

According to the problem, the product of these two consecutive odd integers is 399:

x * (x + 2) = 399

Expanding the equation:

x^2 + 2x = 399

Rearranging the equation into a quadratic form:

x^2 + 2x - 399 = 0

To solve this quadratic equation, we can either factor it or use the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = 2, and c = -399.

x = (-2 ± √(2^2 - 4 * 1 * -399)) / (2 * 1)

Simplifying:

x = (-2 ± √(4 + 1596)) / 2

x = (-2 ± √1600) / 2

x = (-2 ± 40) / 2

Now, we can calculate the two possible values for x:

x = (-2 + 40) / 2 = 38 / 2 = 19

x = (-2 - 40) / 2 = -42 / 2 = -21

Since we are looking for consecutive odd integers, we take the positive value of x, which is 19. The next consecutive odd integer would be 19 + 2 = 21.

Therefore, the two consecutive odd integers whose product is 399 are 19 and 21.

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Answer:

Just do 12x+7 and 5x-1 divide that answer by 57 that seems easy and i am in 6th grade

Step-by-step explanation:

if this is not right i dont know what is

Answer:

Angle WST = 91°

Step-by-step explanation:

The first step in this situation is to find Angle TSU. Then find x, which is 7, which can be put into the equation shown for Angle WST.

Answer: B.) x ≥ -6

Step-by-step explanation:

Minimization of  f(x) = |x+3| + x^3 at the endpoints (-2 and 6)  the minimum value of the function is approximately 3.84, which occurs at x= \sqrt{1/3}

within the given interval.

To minimize the function subject to the constraint f(x) = |x+3| + x^3 that x lies in the interval [-2, 6], we need to find the value of x that minimizes f(x) within that interval.

First, let's analyze the function f(x). The absolute value term |x+3| can be rewritten as:

|x+3| =

x+3 if x+3 >= 0

-(x+3) if x+3 < 0

Since the interval [-2, 6] includes both positive and negative values of x+3, we need to consider both cases.

Case 1: x+3 >= 0

In this case, f(x) = (x+3) + x^3 = 2x + x^3 + 3

Case 2: x+3 < 0

In this case, f(x) = -(x+3) + x^3 = -2x + x^3 - 3

Now, we can find the minimum of f(x) within the given interval by evaluating the function at the endpoints (-2 and 6) and at any critical points within the interval.

Calculating the values of f(x) at x = -2, 6, and the critical points, we can determine the minimum value of f(x) and the corresponding value of x.

Since the equation involves both absolute value and a cubic term, it is not possible to find a closed-form solution or an exact minimum value without numerical methods or approximation techniques.

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The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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Answer:

We know that the equation for the speed is:

Speed = Distance/time.

First, we know that he walks 2 miles in 15 minutes.

distance = 2miles

time = 15 minutes

Then his speed in that interval is:

Speed = (2 mi)/(15 min) = (2/15) miles per minute.

Now, at this same speed, he wants to walk 3 more miles. And we want to find the equation that represents how much time she needs to walk 5 miles (the 2 first miles plus the other 3 miles)

We use again the equation:

Speed = Distance/Time

But we isolate Time, to get:

Time = Distance/Speed

Where:

Distance = 5 miles

Speed = (2/15) miles per min

Time = (5 miles)/((2/15) miles per min) = 37.5 minutes

She needs 37.5 minutes to walk the 5 miles.

Answer:

The digits arranged in order from least to largest is 3.011, 3.09, 3.9, 9.3

Step-by-step explanation:

The arrangement of decimals in order from smallest to largest can be done by  taking note of the  digit in the unit portion, the tenths, hundredths and thousandths.

The numbers are;

9.3

3.09

3.9

3.011

The largest number is the 9.3

Of the three numbers with 3 as unit, the lowest hundredths is 0.011, therefore, we have;

Therefore, the least (lowest) number = 3.011

The next is the 3.09 as 0.09 is larger than 0.011

Then the second number is 3.9

The digits arranged in order from least to largest is then 3.011, 3.09, 3.9, 9.3.

Answer:

your answer will be A

Step-by-step explanation:

^_^

Answer:

189in²

Step-by-step explanation:

first you multiple the triangle width(6) time the triangle height(7).

Then  you divide that by 2

and times that times the prism length(9)

The values of p, q, and r are p = 2, q = 5, and r = 3, respectively.

Given that the lowest common multiple (LCM) of A and B is 2250, and the prime factorization of A is A = 2 × p × q¹, and the prime factorization of B is B = 2 × p² × q², we can compare the prime factorizations to determine the values of p, q, and r.

From the prime factorization of 2250 (2 × 3² × 5³), we can observe the following:

The prime factor 2 appears in both A and B.

The prime factor 3 appears in A.

The prime factor 5 appears in A.

Comparing this with the prime factorizations of A and B, we can deduce the following:

The prime factor p appears in both A and B, as it is present in the common factors 2 × p.

The prime factor q appears in both A and B, as it is present in the common factors q¹ × q² = q³.

From the above analysis, we can conclude:

p = 2

q = 5

r = 3.

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The p-value for this z test statistic is equal to 0.0287.

A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.

The z test statistic can be calculated by using this formula:

\(t=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }\)

Where:

In this scenario, the z test statistic for a one-tailed hypothesis test (lower tail) is equal to -1.9. Therefore, by using a t-distribution and z-score calculator for a normal distribution, the p-value for this test is given by:

P-value = P(t > -1.9)

P-value = 0.0287.

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The solution is Option C.

The L'Hopital's rule is applied to the equation lim x approaches 0 (1-cosx)/x

L'Hopital's rule then states that the slope of the curve when t = c is the limit of the slope of the tangent to the curve as the curve approaches the origin, provided that this is defined. The limit of a quotient of functions (i.e., an algebraic fraction) is equal to the limit of their derivatives.The tangent to the curve at the point [g(t), f(t)] is given by [g′(t), f′(t)]

And , lim x approches c  [ f ( x ) / g ( x ) ] = lim x approches c [ f' ( x ) / g' ( x ) ]

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

The equation is A = lim x approaches 0 (1/x)

On simplifying the equation , we get

The limit diverges as the function diverges and limit does not exist

And ,  lim x approaches 0₊ (1/x) ≠ lim x approaches 0₋ (1/x) = ∞

b)

The equation is A = lim x approaches 0 ( 2x² - 1 ) / ( 3x - 1 )

On simplifying the equation , we get

when x = 0 ,

Substitute the value of x = 0 in the limit , we get

A = ( 2 ( 0 )² - 1 ) / ( 3 ( 0 ) - 1 )

A = ( 0 - 1 ) / ( 0 - 1 )

A = 1

c)

The equation is A = lim x approaches 0 ( 1 - cosx ) / x

On simplifying the equation , we get

Applying L'Hopital's rule , we get

lim x approches c  [ f ( x ) / g ( x ) ] = lim x approches c [ f' ( x ) / g' ( x ) ]

f ( x ) = ( 1 - cos x )

g ( x ) = x

f' ( x ) = sin x

g' ( x ) = 1

So ,

lim x approches 0 [ f' ( x ) / g' ( x ) ] = lim x approches 0 ( sin x / 1 )

when x = 0

sin ( 0 ) = 0

Therefore , the value of lim x approaches 0 (1-cosx)/x = 0

d)

The equation is A = lim x approaches 0 ( cos 2x ) / 2

On simplifying the equation , we get

when x = 0 ,

A = cos ( 2 ( 0 ) / 2

A = cos ( 0 ) / 2

A = 1/2

Hence , the L'Hopital's rule is applied to lim x approaches 0 ( 1 - cosx ) / x

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Step-by-step explanation:

let kevein be x and daniel be y

x=4y (equation i)

x=6+y(equationii)

putting the value of x in equationii

4y=6+y

3x=6

x=2

Answer:

i don't know

Step-by-step explanation:

i am lower grade srry

Answer:

Step-by-step explanation:

3*2+3*8+2-2*5=6+24-10+2=22