What is the solution to the equation?

Answer:

Each Brownie should sell for $ 1.27.

Step-by-step explanation:

Since Mike's Bakery makes brownies that cost $ .80 each, of which 15 percent will spoil and thus are not salable, and Mike wants a 35 percent markup based on cost, producing 500 brownies, to determine the price at which each brownie should sell for the following calculation must be performed:

500 x 0.80 = 400

500 x 0.85 = 425

400 x 1.35 = 540

540/425 = 1.27

Therefore, each Brownie should sell for $ 1.27.

Answer:

Step-by-step explanation:

Cost = 500 * .80 = $400

35% markup = $400*.35 = $140

$400 (cost) + $140 (profit) = $540

500 brownies w/15% waste = 500 * .15 = 75 bad brownies

500 brownies minus 75 brownies = 425 brownies

$540 total cost + profit divided by 425 brownies = $1.27 price per brownie.

Out of 69 students in the art class, around 23 are expected to fail the mathematics test, assuming the probability of passing given is 2/3.

To determine how many students are likely to fail mathematics in the art class, we need to use the given probability of passing the mathematics test, which is 2/3.

First, let's find the probability of failing the mathematics test. Since passing and failing are complementary events (i.e., if the probability of passing is p, then the probability of failing is 1 - p), we can calculate the probability of failing as 1 - 2/3, which simplifies to 1/3.

Now, let's consider the art class, which has a total of 69 students. If the probability of failing mathematics is 1/3, then approximately 1/3 of the students in the art class are likely to fail the mathematics test.

To find the number of students likely to fail, we multiply the probability of failing (1/3) by the total number of students in the art class (69).

(1/3) * 69 ≈ 23

Therefore, approximately 23 students are likely to fail mathematics in the art class of 69 students based on the given probability of passing the mathematics test.

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The area of the triangle is 47.91 units²

When all three sides of the triangle are known we can use Heron's formula. Consider the triangle ABC with sides a, b, and c has shown in the image.

Heron’s formula is:

Area =√s(s−a)(s−b)(s−c)

where,

a, b, c are the side length of the triangle

s is the semi-perimeter. s = (a+b+c)/2

In this case:

Using the knowledge of the radius of a circle. We can say:

a = BC = 3 + 9 = 12 units

b = AC = 5 + 3 = 8 units

c = AB = 5 + 9 = 14 units

s = (a+b+c)/2

s = (12+8+14)/2

s = 34/2

s = 17 units

Area = √s(s−a)(s−b)(s−c)

Area = √17(17−12)(17−8)(17−14)

Area = √17(5)(9)(3)

Area = √2295

Area = 47.91 units²

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The true statements about the figure are:

C) It is not a polyhedron

F) it is a sphere.

G) it has no edges.

Well, clearly we can see that we have a "ball".

The geometric name of that figure is "sphere", so F is a correct option.

Now, spheres have only one curved surface, so it does not have any edges, with that in mind, we can see that the true options are:

C) It is not a polyhedron (it does not have parallel faces)

F) it is a sphere.

G) it has no edges.

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Answer:

35/42 = b/7    and b= 35/6

Step-by-step explanation:

Our base is unkhown so it will be the variable in our equation :

so b is 35/6 cm

Answer:

x=3 ,y=6

Step-by-step explanation:

4x+6y=44 eqni

4x+2y=28 eqn ii

now subtract it eqn i and ii

4x+6y=44

-4x+2y=28

or, 0 +4y=24

or, 4y=24

or , y=24/4

or,y=6

putting value of y in eqn i

4x+6y=44

4x+6×6=44

4x=44-36

4x=12

x=12/4

x=3

Answer:

the first one is (23)

number 7 is ( 34.069)

Step-by-step explanation:

multiply the numbers

Answer:

8700kg

Step-by-step explanation:

b = mass of bricks

l = mass of lorry

b+l = total mass = 11600kg

b = 3l  ==>  l = b/3

substitute: b + b/3 = 11600

multiply every term by 3 to get rid of denominator: 3b + b = 34800

simplify and solve:  4b = 34800  ==>  b = 8700

check:  l = 8700/3 = 2900

2900 + 8700 = 11600?  YES

Answer:

a = 0.9

Step-by-step explanation:

For the quadratic equation \(\boxed{ax^2 + bx + c = 0}\) to have exactly one real root, the value of its discriminant, \(\boxed{b^2 - 4ac}\), must be zero.

For the given equation:

\(y = ax^2 - 6x + 10\),

• a = a

• b = -6

• c = 10.

Substituting these values into the formula for discriminant, we get:

\((-6)^2 - 4(a)(10) = 0\)

⇒ \(36 - 40a = 0\)

⇒ \(36 = 40a\)

⇒ \(a = \frac{36}{40}\)

⇒ \(a = \bf 0.9\)

Therefore the value of a is 0.9 when the given quadratic has exactly one root.

Answer: 1256.63706

Step-by-step explanation: A=(π20)2

The approximate area of the circle segment bounded by arc DE and chord DE is approximately 17.72 square units.

To approximate the area of the circle segment bounded by arc DE and chord DE, you can use the following formula:

Area = (1/2) * r^2 * (θ - sinθ)

Where:

r is the radius of the circle (r = 20 in your case).

θ is the central angle in radians (47° converted to radians is approximately 0.8203 radians).

Let's calculate it:

θ = 47° * (π / 180) ≈ 0.8203 radians

Now, plug these values into the formula:

Area = (1/2) * (20^2) * (0.8203 - sin(0.8203))

Area ≈ (1/2) * 400 * (0.8203 - 0.7317)

Area ≈ (1/2) * 400 * 0.0886

Area ≈ 17.72 square units

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Yes, we can verify using subtraction:

If we subtract 5 from 5.5 and the result is positive we can conclude 5.5 is greater than 5, if the result is negative, we can conclude 5.5 is less than 5, so:

Since 0.5 > 0, the result is positive, therefore 5.5 is greater than 5. Therefore Ella will get a bag.

The graph of the image of the polygon after a reflection in the line y = -x is (2, 2), (-2, -3), (1, -1), and (1, 4).

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

We are given that;

Points of polygon A(-3,2),B(1,-1),C(-2,-2) and D(-4,-1)

Now,

To reflect a polygon in a line, we reflect each of its vertices in the line and then connect the reflected points to form the reflected polygon.

The line y = -x is the line passing through the origin with slope -1, which means that any point (x, y) reflected in this line will be transformed to the point (-y, -x).

Let's reflect each of the vertices in the line and connect the reflected points to form the reflected polygon:

Reflecting point A(-3, 2): (-2, -3)

Reflecting point B(1, -1): (1, -1)

Reflecting point C(-2, -2): (2, 2)

Reflecting point D(-4, -1): (1, 4)

Now we can plot these points and connect them to form the reflected polygon.

So, the reflected polygon with given slope of line is ACBD, with vertices at (2, 2), (-2, -3), (1, -1), and (1, 4).

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Answer:

60,480 is the correct answer.

Step-by-step explanation:

First of all, let us have a look at the formula of factorial of a number 'n':

\(n! = n \times (n-1) \times (n-2) \times ...... \times 1\)

i.e. multiply n with (n-1) then by (n-2) upto 1.

Keep on subtracting 1 from the number and keep on multiplying until we reach to 1.

So, \(9!\) can be written as: \(9 \times 8 \times 7 \times ...... \times 1\)

Similarly \(3!\) can be written as: \(3 \times 2 \times 1\)

Re-writing \(9 !\) :

\(9 \times 8 \times 7 \times ...... 3 \times 2 \times 1\\\Rightarrow 9 \times 8 \times 7 \times ...... 3 !\)

Now, the expression to be evaluated:

\(\dfrac{9!}{3!} = \dfrac{9 \times 8 \times 7 \times ..... \times 3!}{3!}\\\Rightarrow 9 \times 8 \times 7 \times 6 \times 5 \times 4\\\Rightarrow 60480\)

Answer:

60480

Step-by-step explanation:

Answer:

mode = no mode. median = 133, mean = 133

Step-by-step explanation:

mode = most common value. all of the values appear once. so there is no mode.

median = arranging the data in numerical order, then finding middle value.

there are 8 values. we have 4 on one side (124, 126, 128, 130) and 4 on the other (136, 137, 140, 143).

median is halfway between 130 and 136. that is 133.

mean = add up the values/ how many there are

adding them up, you get 1064. there are 8 values.

mean = 1064/8 = 133

The length of the zip wire is approximately 25.42 meters.

To calculate the length of the zip wire, we can use trigonometry and the given information about the angle and the distance between the two posts.

Given:

Distance between the two posts: 25m

Angle of the zip wire to the horizontal: 10°

We can use the trigonometric function cosine (cos) to find the length of the zip wire. Cosine relates the adjacent side to the hypotenuse of a right triangle.

In this case, the adjacent side is the distance between the two posts (25m) and the hypotenuse is the length of the zip wire that we want to calculate.

Using the cosine function:

cos(angle) = adjacent/hypotenuse

cos(10°) = 25m/hypotenuse

To find the hypotenuse (length of the zip wire), we can rearrange the equation:

hypotenuse = 25m / cos(10°)

Using a calculator or trigonometric tables, we can find the value of cos(10°) to be approximately 0.9848.

Therefore, the length of the zip wire is:

hypotenuse = 25m / 0.9848 ≈ 25.42m

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On solving the provided questions, we can say that Probability, P( -1.6 \(\leq\) Z \(\leq\) 1.6 ) = 89.04%

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

he diameter of the ball bearings varies according to a distribution that is approximately Normal

mean 11.5 mm and standard deviation 0.05 mm

the probability that the difference in the diameters of the two ball bearings is less than 0.06 mm

Probability, P( -1.6 \(\leq\) Z \(\leq\) 1.6 ) = 89.04%

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Division is opposite of multiplication. If 3 groups of 4 make 12 in the multiplication, 12 divided into the 3 equal groups give 4 in each group in division. The main goal of dividing is to see how many equal groups are formed or how many are in the each group when sharing fairly.

In divisions involving fractions, numerator is called the dividend while the denominator is called the divisor while the answer is called the quotient.

Now, when Dividing decimal by a whole number, it means the decimal is the numerator while the whole number is the denominator.

The first step is to estimate quotient by approximating the dividend and divisor to the nearest compatible numbers. For example; 6.5/9

The nearest compatible number for numerator is 6 while for the denominator it is 10. Thus, we have;

7/10 = 0.7

Second step is to perform division with original numbers. This gives us;

6.5/9 = 0.722

Third step is to compare the both answers to see if our estimate makes sense.

Using compatible numbers gave us quotient of 0.7 while the normal division gave us a quotient of 0.722

Since both the quotient are very close, then it means our estimated quotient is okay.

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So, Gina's farm produced approximately 471.8 tons of sweet potatoes this year. Rounded to the nearest whole number, this is 472 tons.

When we talk about an increase, we are referring to a change in quantity or value that is greater than the original amount. In other words, an increase means that something has gotten bigger, larger, or more than it was before.

Given by the question.

To find out how much sweet potatoes Gina's farm produced this year, we need to add 40% of last year's production to the amount produced last year:

40% of 337 tons = 0.4 x 337 = 134.8 tons

Adding this to last year's production gives:

337 + 134.8 = 471.8 tons

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Each person get 4/5 of the e leftover bag of beads.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

From the question,

The total number of leftover beads is 1/5

4 people are to share the leftover beads

so,

the ratio will be 1/5 ÷ 1/4

1/5 x 4

=4/5

Hence, each person will get 4/5 of the beads

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Answer:

19

Step-by-step explanation:

because it not it

Answer:

See below:

Step-by-step explanation:

So first, we can find out the cost for one meter of cloth by dividing 25 by 337.5 Rupees:

\(\frac{337.50}{25} = 13.50\)

We now divide 810 by 13.50

\(\frac{810}{13.50} = 60\)

We now get our answer of 60 meters!

Cheers!

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To solve -7y > 161, we divide both sides by -7 and we get y < -23. The inequality sign flipped because we divided both sides by a negative number.

To solve 7y > -161, we divide both sides by 7 and it leads to y > -23. The inequality sign does not flip in this case, because we are not dividing both sides by a negative number.

The similarities is that we end up with -23 on the right side, but the inequality signs are different.

Answer: (10 - 3x)(10 + 3x)

Step-by-step explanation:

Answer:

Everyone has financial a plan, but not everyone knows what to do to make the plan work. Planning is different from putting it into action.

Answer:r=2 cos^4(theta)

Step-by-step explanation:To find the values of theta where the maximum r-values occur on the graph of the polar equation r = 2 cos^4(theta), we need to find where the derivative of r with respect to theta is equal to zero, since the maximum r-values occur at these points.

First, we can simplify the equation by using the identity cos(2theta) = 2cos^2(theta) - 1 and substituting cos^2(theta) = (1 + cos(2theta))/2. This gives:

r = 2 cos^4(theta) = 2(1/2 + 1/2 cos(2theta))^2 = 1 + cos(2theta) + cos^2(2theta)/2.

Next, we can take the derivative of r with respect to theta, using the chain rule:

dr/dtheta = -sin(2theta) - 2cos(2theta)sin(2theta).

Setting this equal to zero and factoring out sin(2theta), we get:

sin(2theta)(-1 - 2cos(2theta)) = 0.

This equation is satisfied when sin(2theta) = 0 or cos(2theta) = -1/2.

When sin(2theta) = 0, we have 2theta = k*pi for some integer k. Therefore, theta = k*pi/2.

When cos(2theta) = -1/2, we have 2theta = 2*pi/3 + 2*k*pi or 2theta = 4*pi/3 + 2*k*pi for some integer k. Therefore, theta = pi/3 + k*pi or theta = 2*pi/3 + k*pi.

These are the values of theta where the maximum r-values occur on the graph of the polar equation r = 2 cos^4(theta).

Answer:

22° + m<C = 90°

Step-by-step explanation:

We are given that <A (which is equal to 22°) and <B are vertical angles, and that <B is complementary to <C.

We want to write an equation that will help us solve <C.

Recall that vertical angles are congruent by vertical angles theorem.

This means that <A ≅ <B; it also means that the measure of <B is also 22°.

Also recall that complementary angles add up to 90°.

This means that m<B + m<C = 90°.

Since we deduced that m<B is 22°, we can substitute that value into the equation.

Hence, an equation that can be used to solve for <C is:

22° + m<C = 90°