Nolan ordered a set of beads. He received 86 beads in all. 43 of the beads were orange. What percentage of the beads were orange?

When the height is 38 cm and the base is 32 cm, the rate at which the area of the triangle changes is 10 cm²/min.

The rate at which the area of a triangle changes can be found by multiplying the rate at which the base is shrinking by the rate at which the height is increasing.

Given:

Rate of shrinking of the base = -2 cm/min

Rate of increasing of the height = 3 cm/min

Height of the triangle = 38 cm

Base of the triangle = 32 cm

To find the rate at which the area of the triangle changes, we use the formula for the area of a triangle:

Area = (1/2) * base * height

Differentiating the area formula with respect to time gives us:

dA/dt = (1/2) * (db/dt) * height + (1/2) * base * (dh/dt)

Substituting the given values, we have:

dA/dt = (1/2) * (-2) * 38 + (1/2) * 32 * 3

Simplifying, we get:

dA/dt = -38 + 48

dA/dt = 10 cm²/min

Therefore, when the height is 38 cm and the base is 32 cm, the rate at which the area of the triangle changes is 10 cm²/min.

To know more about triangle refer here:

https://brainly.com/question/2773823

#SPJ11

To find the domain of the logarithmic function f(x) = -log3(x + 3), we first need to identify the values of x for which the function is defined. Logarithmic functions are defined only for positive arguments, meaning that we need x + 3 > 0.

Step 1: Solve the inequality x + 3 > 0.
x > -3

The domain of the function is all x values greater than -3. In interval notation, this is written as (-3, ∞).

Now, let's find the x-intercept of the function, which is the point where the function crosses the x-axis (y = 0). To do this, we need to solve the equation f(x) = 0 for x.

Step 2: Set f(x) = 0 and solve for x.
0 = -log3(x + 3)
-log3(x + 3) = 0

Step 3: Solve for the logarithmic equation.
log3(x + 3) = 1

Step 4: Rewrite the logarithmic equation in exponential form.
3^1 = x + 3
3 = x + 3

Step 5: Solve for x.
x = 3 - 3
x = 0

The x-intercept is (0, 0).

Lastly, let's find the vertical asymptote of the function. This is the line that the function approaches but never actually reaches. For logarithmic functions, the vertical asymptote is located at the point where the argument of the log is zero.

Step 6: Set x + 3 = 0 and solve for x.
x = -3

The vertical asymptote is x = -3.

To summarize:
- Domain: (-3, ∞)
- X-intercept: (0, 0)
- Vertical asymptote: x = -3

To learn more about ''domain of the logarithmic function'' visit : https://brainly.com/question/16444481

#SPJ11

Answer:

130^2 or 130 meters squared

Step-by-step explanation:

I decomposed the figure, then found the area of the decomposed figures then found the sum of them.

FIGURE A:

3 x 3 = 9

= 9^2

FIGURE B:

11 x 11 = 121

= 121 meters^2

So 121 + 9 = 130

= 130 meters^2

REMEMBER!!!!

THE FORMULA FOR AREA IS LENGTH * WIDTH = AREA

The entropy of the data set can be calculated using the formula: -p(log2p) - (1-p)(log2(1-p)), where p is the proportion of positive outcomes.

Plugging in the values, we get: -12/20(log2(12/20)) - (1-12/20)(log2(1-12/20)) = -0.971. Rounded to the nearest thousandths place, the entropy is -0.971.
The entropy of a dataset is a measure of its impurity or randomness. In your case, you have a dataset with 20 training outcomes, with 12 positive and 8 negative (since 20-12=8). To calculate the entropy, we use the formula:
Entropy = -p(positive) * log2(p(positive)) - p(negative) * log2(p(negative))
First, find the probabilities of positive and negative outcomes:
p(positive) = 12/20 = 0.6
p(negative) = 8/20 = 0.4
Next, plug these probabilities into the entropy formula:
Entropy = -0.6 * log2(0.6) - 0.4 * log2(0.4)
Entropy ≈ 0.971
Thus, the entropy of your dataset, rounded to the nearest thousandth, is 0.971.

To know more about entropy visit:

https://brainly.com/question/20166134

#SPJ11

Work Shown:

\(A = P*(1+r/n)^{n*t}\\\\2P = P*(1+r/1)^{1*3}\\\\2 = (1+r)^{3}\\\\(1+r)^{3} = 2\\\\1+r = \sqrt[3]{2}\\\\r = -1+\sqrt[3]{2}\\\\r \approx 0.25992\\\\\)

That converts to 25.992% after moving the decimal point two spots to the right. Round this value however your teacher instructs.

The solutions for each one are:

1) Two real

2) Two complex

3) One real.

For a quadratic of the form:

ax² + bx + c = 0

The discriminant is:

D = b² - 4ac

if D > 0, there are two real solutions.

if D=  0 there is one real solution.

if D < 0 the solutions are complex.

The first quadratic equation is:

2x² + 4x + 3 = 0

The discriminant is:

D = 4² - 4*2*3

  = 16 - 24 = -8

So this equation has no real solutions.

The second is:

3x² - 5x + 1 = 0

The discriminant is:

D = (-5)² - 4*3*1

  = 25 - 12 = 13

Two real solutions.

The last one is:

x² + 4x + 4  =0

We have:

D = 4² - 4*4*1

  = 16 - 16  =0

One real solution.

Learn more about quadratic equations at:

https://brainly.com/question/1214333

#SPJ1

Answer

CIAD

Step-by-step explanation

The Pythagorean theorem states:

where a and b are the legs and c is the hypotenuse of a right triangle.

Applying this theorem to triangle 1:

Then, the first letter is C.

Applying the theorem to triangle 2:

Then, the second letter is I.

Applying the theorem to triangle 3:

Then, the third letter is A.

Applying the theorem to triangle 4:

Then, the fourth letter is D.

Answer:

Step-by-step explanation:544

Answer:

total weight of wheat and rice is 8 kg

Step-by-step explanation:

rice = \(3\frac{3}{2}\)

=3*2+3/2

=9/2

wheat = \(2\frac{1}{2}\)

=2*2+1/2

=5/2

total weight of wheat and rice = \(\frac{7}{2} + \frac{9}{2}\)

since their denominator are same u can add numerators.

=7 +9/2

=16/2

=8

14 / 6 = 7/3.

Therefore, 7/3 is the scale factor used in this dilation.

The scale factor is the ratio of the new measurement to the old measurement. The scale factor that was used in the dilation is 7/3.

Suppose the initial measurement of a figure was x units.

And let the figure is scaled and the new measurement is of y units.

Since the scaling is done by multiplication of some constant, that constant is called the scale factor. Let that constant be 's'.

Then we have:

\(s \times x = y\\s = \dfrac{y}{x}\)

Thus, the scale factor is the ratio of the new measurement to the old measurement.

Scale factor

= Dimension of the new shape ÷ Dimension of the original shape

= 14ft / 6ft

= 7ft / 3ft

Hence, the scale factor that was used in the dilation is 7/3.

Learn more about Scale Factor here:

https://brainly.com/question/22312172

#SPJ5

If Lucinda used a random selection method, made an effort to ensure that the sample is representative, and the sample size is large enough, then it's possible that the sample is indeed random.

what are perpendicular lines?

Perpendicular lines are two lines that intersect at a 90-degree angle, forming four right angles at the point of intersection. In other words, if you were to draw a perpendicular line from one of the lines to the other at their point of intersection, it would form a right angle with each of the original lines.

Without having access to more information about how Lucinda selected the sample of students, it's difficult to determine whether or not the sample is truly random.

However, there are a few things that we can consider when trying to determine whether or not the sample is random. For example:

Did Lucinda use a random selection method to choose the students? If she simply surveyed her friends or classmates, for example, the sample would not be random.

Did Lucinda make any effort to ensure that the sample is representative of the larger population of students? For example, did she make sure to include students from a variety of grades, genders, and ethnic backgrounds.

Therefore, if Lucinda used a random selection method, and made an effort to ensure that the sample is representative, and the sample size is large enough, then it's possible that the sample is indeed random.

To learn more about perpendicular lines here is the given link -

https://brainly.com/question/18271653

#SPJ1

We are given a vector field F and we need to determine if it is conservative vector. If it is, we need to find the potential function f. Additionally, we need to find the work done by F along certain paths.

To determine if the vector field F is conservative, we need to check if its curl is zero. Computing the curl of F, we find that it is zero, indicating that F is indeed a conservative vector field. To find the potential function f, we can integrate the components of F with respect to their respective variables. Integrating (3x² + y) with respect to x gives us x³ + xy + g(y), where g(y) is the constant of integration. Similarly, integrating (x - y) with respect to y gives us xy - y² + h(x), where h(x) is the constant of integration. The potential function f is the sum of these integrals, f(x, y) = x³ + xy + g(y) + xy - y² + h(x). To find the work done by F along a path, we need to evaluate the line integral ∫ F · dr, where dr represents the differential displacement along the path. We would need more information about the specific paths mentioned in order to calculate the work done.

To know more about conservative vector here: brainly.com/question/32064186

#SPJ11

Answer:

60%

Step-by-step explanation:

convert to hundreds:

30 out of 50 is the same as 60 out of 100, aka 60%.

Answer:

60 percent

Step-by-step explanation:

50 total

50 is 10 percent

30/50 r boys

60/100 = 60 percent boys

Step-by-step explanation:

To determine if a system of two equations with two unknowns has infinite solutions using matrices, you can perform Gaussian elimination or row reduction on the augmented matrix of the system. If the reduced form of the matrix is the identity matrix, then the system has a unique solution. If the reduced form is a row of zeros except for the last column, then the system has no solution. If the reduced form has a row with all zeros except for the last column being non-zero, then the system has an infinite number of solutions.

In other words, the system has infinite solutions if the row reduced form of the augmented matrix has a row of the form [0 0 c], where c is a non-zero scalar. This means that there is a non-trivial solution that satisfies the equation, indicating that there are infinitely many solutions.

The constant of variation based on the information is one half.

From the information given, when x is 2, y is 1, when x is 4, y is 2, etc. It should be noted that this is a direct variation.

This will be illustrated as:

y = kx

when y = 1, x = 2.

1 = 2k

Divide both side by 2.

k = 1/2

Therefore, the constant of variation is 1/2.

Learn more about constant of variation on:

brainly.com/question/25215474

#SPJ1

Answer:

The answer you're looking for is 1470.

Step-by-step explanation:

The method I used was PEMDAS

Since there was no parenthesis, I simplified the exponents.

2.130 x 10³ - 6.6 x 10² = ?
2.130 x 1000 - 6.6 x 100 = ?

After that, I multiplied all terms next to each other.

2.130 x 1000 - 6.6 x 100 = ?
2130 - 660 = ?

The final step I did was to subtract the two final terms and ended up with 1470 as my final answer.

1470 = ?

I hope this was helpful!

Answer:

C \(\displaystyle x = 15\)

Step-by-step explanation:

Use the Pythagorean Theorem to define the hypotenuse:

\(\displaystyle a^2 + b^2 = c^2 \\ \\ 12^2 + 9^2 = x^2 \hookrightarrow 144 + 81 = x^2 \hookrightarrow \sqrt{225} = \sqrt{x^2} \\ \\ \boxed{15 = x}\)

I am joyous to assist you at any time.

\( \huge \underline\text{ Hello There}\)

\( \text{We know, Pythagoras Theorem}\)

\(\implies \text{ (Hypotenuse)²= (Base)² + (Altitude)²}\)

\( \text{Here, \red{Hypotenuse}= x, \red{Base}= 9, \red{Altitude}= 12}\)

\( \underline \text{To Find, } \text{Value of'x'}\)

\( \huge \underline\text \red {Solution}\)

\((x) {}^{2} = (9) {}^{2} + ({12})^{2} \\ \implies (x) { }^{2} = 81 + 144 \\ \implies (x) {}^{2} = 225 \\ \implies x = \sqrt{225} \\ \implies x = 15\)

\( \tt{So \: The \: Value \: of'x'= 15}\)

\( \bold{\therefore Hypotenuse= 15}\)

\( \text{Correct Opt. C= x =15}\)

y

=

1

6

x

+

19

3

←

equation in slope-intercept form

Step-by-step explanation:

Answer:

y = -x/6 + 19/3

Step-by-step explanation:

\((y - 7)( - 2 - 4) = (x - 4)(6 - 7) \\ - 6y + 42 = 4 - x \\ x - 6y = - 38 \\ or \\ y = (38 - x) \div 6\)

Negative one sixth times the quantity 3 minus 15 times the quantity one third squared end quantity end quantity will be C. negative two ninths

Based on the information given, the expression will be:

= 1/6 ×( 3 - 15 ) × (1/3)²

= -1/6 × -12 × 1/9

= -2 × 1/9

= -2/9

In conclusion, the correct option is D.

Learn more about expressions on:

brainly.com/question/723406

#SPJ1

To determine the number of miles David drove the truck, we need to subtract the base fee and divide the remaining amount by the additional charge per mile.

Let's denote the number of miles driven by 'm'. The equation can be set up as follows:

$209.57 - $14.99 = $0.94 * m

Simplifying the equation:

$194.58 = $0.94 * m

To solve for 'm', we divide both sides of the equation by $0.94:

m = $194.58 / $0.94

m ≈ 206.7

Therefore, David drove the truck for approximately 206.7 miles. Since it's not possible to drive a fraction of a mile, we can assume that David drove either 206 or 207 miles, depending on the rounding convention used.

To learn more about equation : brainly.com/question/29657983

#SPJ11

Answer:

112.5in²

Step-by-step explanation:

Answer

\(225in^{2}\)

Step-by-step explanation:

hope this helped :-)

Answer:

180-132

Step-by-step explanation:

the entire angle should sum to 180

Answer:

48 °

Step-by-step explanation:

132° + x° = 180°        (Linear pair)

∴ x° = 180° - 132°

∴ x° = 48°

Hope this helps :)  !!!

Answer:

14.12 × 2 + 5.93 = 34.17

40$ - 34.17 = 5.83$

Answer:

$14.12+$14.12=$28.24+$5.93=$34.17

Change is $6.83

Answer:

\(3x^2+4x+8\)

Step-by-step explanation:

To find the value of \(7x^2+6x+9-4x^2-2x-1\)

We need to combine like terms by grouping

\(7x^2-4x^2+6x-2x+9-1\)

= \(3x^2+4x+8\)

Hope this helps :)

Have a great day!

Answer:

22. first multiply two with the digits and signs then add

So using order of operations (parentheses, exponents, multiplication & division, addition & subtraction), you have to do 4+7 inside the parentheses first, then multiply that by 2.

4+7=11

11×2=22

2(4+7)=22

♡ Hope this helps! ♡

❀ 0ranges ❀

Answer:

3/9=3

3*18=54

you can buy 54 packages

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

3/9=x/18

3/9=1/3

so 1/3=x/18

cross product

3*x=1*18

3x=18

x=18/3

x=6

Answer:

BALLZ

Step-by-step explanation:

T3ST1CALZ

Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

Interior angles of a triangle sum to 180°. Therefore:

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)

Let's first find the union and intersection for B.

1. For the collection B:

Recall that Bn = N - {1, 2, 3, ..., n} and B = {Bn: n ∈ N}.

a) Union of B:

To find the union of B, we need to consider all elements in any Bn. Since Bn excludes the first n natural numbers, the union will include all natural numbers greater than n for all n. In other words, the union will contain all natural numbers.

Union(B) = N

b) Intersection of B:

To find the intersection of B, we need to consider elements common to all Bn. Observe that, as n increases, Bn excludes more natural numbers. Therefore, there will be no natural numbers common to all Bn.

Intersection(B) = ∅

2. For the collection M:

Recall that Mn = {..., -3n, -2n, -n, 0, n, 2n, 3n, ...} and M = {Mn: n ∈ N}.

a) Union of M:

To find the union of M, we need to consider all elements in any Mn. Since every Mn contains multiples of n, the union will contain all multiples of natural numbers.

Union(M) = {k * n: k ∈ Z, n ∈ N}

b) Intersection of M:

To find the intersection of M, we need to consider elements common to all Mn. Observe that the only element common to all Mn is 0, as it is a multiple of every natural number.

Intersection(M) = {0}

So, for the indexed collections B and M, we found:

- Union(B) = N
- Intersection(B) = ∅

- Union(M) = {k * n: k ∈ Z, n ∈ N}
- Intersection(M) = {0}

To know more about unions and intersections refer here:

https://brainly.com/question/28337869?#

#SPJ11