A twizzler factory makes regular 8in, king size 10in, extra long 16in, and snack size 3in twizzlers. Before packaging the candy, the size is checked and any pieces that have a percent error of 1.5% or more are rejected. Would every size of twizzler be rejected for being 0.14in too short? Why or why not?

Assuming normal distribution, we can calculate the probability of a woman having a diastolic blood pressure less than 60 mm Hg using a z-score and standard normal distribution table. The probability is approximately 0.04%.

The probability that a randomly selected woman has a diastolic blood pressure less than 60 mm Hg depends on the distribution of the diastolic blood pressure in the population.

Assuming that the diastolic blood pressure in women follows a normal distribution with mean µ and standard deviation σ, we can use the standard normal distribution to calculate the probability.

Let Z be the standard normal random variable, given by:

Z = (X - µ) / σ

where X is the diastolic blood pressure, µ is the mean diastolic blood pressure for women, and σ is the standard deviation of the diastolic blood pressure for women.

To find the probability that a randomly selected woman has a diastolic blood pressure less than 60 mm Hg, we need to calculate the corresponding z-score and then look up its probability in the standard normal distribution table.

The z-score can be calculated as:

Z = (60 - µ) / σ

Once we have the z-score, we can use a standard normal distribution table or software to find the probability. For example, using a table, we can find that the probability of a randomly selected woman having a diastolic blood pressure less than 60 mm Hg is approximately 0.0004, or 0.04%.

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The domain of the relation in the graph is:

{-2, -1, 0, 2, 5}

A relation maps elements from one set (the domain) into elements from another set (the range).

Such that the domain is represented in the horizontal axis.

In the graph, we can see the points:

{(-2, -3), (-1, -1), (0, 3), (2, 1), (5, 2)}

The domain is the set of the first values of these points, then the domain is:

{-2, -1, 0, 2, 5}

The correct option is the first one.

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Answer:

125x - 33x⁴

Pull out like factors :

125x - 27x⁴ = -x • (27x3 - 125)

Factoring: 27x³- 125

Theory : A difference of two perfect cubes, a³ - b³ can be factored into

(a-b) • (a² +ab +b²)

(a-b)•(a²+ab+b²) =

a³+a²b+ab²-ba²-b²a-b³ =

a³+(a2b-ba²)+(ab²-b²a)-b³ =

a³+0+0+b³ =

a³+b³

Check : 27 is the cube of 3

Check : 125 is the cube of 5

Check : x³ is the cube of x¹

Factorization is :

(3x - 5) • (9x² + 15x + 25)

\( \)

The quadrilateral ABCD is a trapezoid because it has one pair of parallel sides.The slopes of sides AB and CD are equal to 2 and -2 respectively. Therefore, AB is parallel to CD, making quadrilateral ABCD a trapezoid.

1. To determine if a quadrilateral is a trapezoid, we need to check if it has one pair of parallel sides.
2. We can find the slopes of the sides AB, BC, CD, and AD using the slope formula: slope = (change in y) / (change in x).
3. If the slopes of any two sides are equal, then those sides are parallel. In this case, the slopes of AB and CD are equal, making AB parallel to CD.
More than 100 words:
To check if quadrilateral ABCD is a trapezoid, we need to determine if it has one pair of parallel sides.

Using the slope formula, we can find the slopes of the sides AB, BC, CD, and AD. The slope formula is given by slope = (change in y) / (change in x).

For side AB:
slope AB = (3 - (-1)) / (-2 - (-4))
slope AB = 4 / 2
slope AB = 2

For side BC:
slope BC = (3 - 3) / (-2 - 3)
slope BC = 0 / (-5)
slope BC = 0

For side CD:
slope CD = (-1 - 3) / (5 - 3)
slope CD = -4 / 2
slope CD = -2

For side AD:
slope AD = (-1 - (-1)) / (5 - (-4))
slope AD = 0 / 9
slope AD = 0

We can see that the slopes of sides AB and CD are equal to 2 and -2 respectively. Therefore, AB is parallel to CD, making quadrilateral ABCD a trapezoid.

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Answer:

64 lb

Step-by-step explanation:

you can solve this problem by using a proportion, then cross multiply and divide. (better explained in yt videos).

Given data:

The amount Rosa earned per hour is 12.25$.

The expression for the given statement is,

Multiply the above expression by 19 1/2 on both sides.

Thus, the amount earned by Rosa in 19 1/2 hours is $238.87.

Round the approximate value however you need to

Units are in square centimeters.

===================================================

Work Shown:

You have the 160 portions correct since 20*8 = 160.

The other pieces are equilateral triangles, in which we use the formula

\(A = \frac{\sqrt{3}}{4}x^2\)

where x is the side length of the triangle. Plug in x = 8 to get

\(A = \frac{\sqrt{3}}{4}x^2\\\\A = \frac{\sqrt{3}}{4}8^2\\\\A = \sqrt{3}*\frac{1}{4}*64\\\\A = \sqrt{3}*16\\\\A = 16\sqrt{3}\\\\\)

That's the exact area of one triangle, but we have two of them. Double the result to get \(2*16*\sqrt{3} = 32\sqrt{3}\)

The total surface area is the sum of all the smaller areas

\(160+160+160+32\sqrt{3} = 480+32\sqrt{3}\)

--------------------------

The exact surface area is \(480+32\sqrt{3}\) square cm.

Using a calculator, you should get \(480+32\sqrt{3} \approx 535.425625842204\)

Round this however you need to.

Answer:

C

Step-by-step explanation:

There are 3 pairs of corresponding sides with proportional lengths.

The ratios of the lengths of corresponding sides are equal AB/XY = BC/YZ = AC/XZ, then ΔABC and ΔXYZ  proven similar through SSS .

To prove two triangles similar using the SSS (Side-Side-Side) similarity criterion, all three pairs of corresponding sides of the two triangles must be proportional .

The SSS similarity criterion states that if the ratio of the lengths of corresponding sides in two triangles is equal, then the triangles are similar.

Given that we have a list of triangles,  to compare the ratios of their corresponding sides to see if any pairs satisfy the SSS similarity criterion.

The three pairs of corresponding sides in the triangles are denoted as follows:

Side A: Sides that are corresponding in length between the two triangles.

Side B: Sides that are corresponding in length between the two triangles.

Side C: Sides that are corresponding in length between the two triangles.

Since the specific list of triangles is not provided, I cannot give you the exact pairs that  proven similar through SSS similarity. However, I provide with an example:

Example:

Consider two triangles, ΔABC and ΔXYZ, where the corresponding sides are as follows:

ΔABC: AB, BC, and AC

ΔXYZ: XY, YZ, and XZ

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The magnitude of the gravitational force exerted on the 5.9-kg rock and the 5.8 x 10^-4-kg pebble near the surface of the Earth is 57.9 N and 0.0579 N, respectively.

To calculate the gravitational force exerted on an object near the Earth's surface, we can use the formula: F = mg, where F is the gravitational force, m is the mass of the object, and g is the acceleration due to gravity. Near the surface of the Earth, the standard value for g is approximately 9.8 m/s^2.

For the rock with a mass of 5.9 kg, the gravitational force can be calculated as follows:

F_rock = (5.9 kg) * (9.8 m/s^2) = 57.9 N.

For the pebble with a mass of 5.8 x 10^-4 kg, the gravitational force can be calculated as follows:

F_pebble = (5.8 x 10^-4 kg) * (9.8 m/s^2) = 0.0579 N.

Therefore, the rock experiences a gravitational force of 57.9 N, while the pebble experiences a gravitational force of 0.0579 N.

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The amount invested in each company is :

Using the simple interest relation:

Simple interest = principal × rate × time

Total amount = 10000

Let :

principal invested in PP = r

HENCE, amount invested in TT = 10000 - r

Total interest earned on both investments = $620

PP investment return + TT investment return = 620

(r × 10% × 1) + (10000 - r × 5% × 1) = 620

0.1r + 500 - 0.05r = 620

0.05r = 620 - 500

0.05r = 120

r = 120 / 0.05

r = 2400

Hence,

Amount invested in PP = $2400

Amount invested in TT = $(10000 - 2400) = $7600

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The slope of the rounded to the nearest hundredth radian, the is -1.00 radians.

To find the slope of the line passing through the origin at an angle of 3π/4 radians, we'll use the tangent function, which relates the angle to the slope of the line.

The angle given is 3π/4 radians.

The slope (m) of the line can be found using the tangent of the angle: m = tan(θ), where θ is the angle.

Calculate the slope
m = tan(3π/4)

Round to the nearest hundredth
Using a calculator, tan(3π/4) ≈ -1.00

So, the slope of the line passing through the origin at an angle of 3π/4 radians is approximately -1.00.

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Answer:

Please type it out for me, sorry!

Step-by-step explanation:

Answer:

Step-by-step explanation:

if the angles form a linear pair, that means their sum=180

10x-63+8x=180

18x=180+63

x=243/18=13.5  choice c

Answer:

Here is the sample space:

(1, 1), (1, 2) (1, 3), (2, 1), (2, 2), (2, 3), (3, 1),

(3, 2), (3, 3)

Answer:

2c^2

Step-by-step explanation:

Simplify: 8c^3d^2/4cd^2.

The d^2 cancels out leaving 8c^3/4c. 8/4 = 2. c^3/c = c^2.

Therefore, your answer is 2c^2

Answer:

2c^2

Step-by-step explanation:

8c^3d^2 / 4cd^2= 2c^2

If you invest $500 for a year at an interest rate of 8% each year, you will end up with $540 in your account at the end of that year.

This is further explained below.

Generally,  A present asset's future value, abbreviated as FV, is the value that asset is expected to have at some point in the future, based on a projected rate of growth. Because investors and financial planners use it to predict how much money an investment made now will be worth in the future, the future value is very significant to these professions.

Interest for the year = 8/100 *500

Interest for the year = 40

therefore,

future value = 500+40

future value = $540

In conclusion, the future value of $500 deposited for one year earning a 8 percent interest rate annually is

$ 540.00

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The numbers 2, -2, and -2 can replace the letters A, B, and C respectively in the table of values.

We use table of values when we have to graph out a linear equation. We can make use of the table of values to map out the corresponding values of x and y for a given line equation.

For y = x² - 3x - 2:

when x = -1;

y = (-1)² - 3(-1) -2

y = 1 + 3 - 2

y = 4 - 2

y = 2

when x = 0;

y = (0)² - 3(0) -2

y = 0 - 0 - 2

y = -2

when x = 3;

y = (3)² - 3(3) - 2

y= 9 - 9 - 2

y = 0 - 2

y = -2

Therefore, the values 2, -2, and -2 replace letters A, B, and C respectively in the table of values for y = x² - 3x - 2.

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Answer:

25.13

Step-by-step explanation:

Answer:

C ≈ 25.13 feet

Step-by-step explanation:

A = πr²

16π = πr²

divide by π

16 = r²

r = 4

plug r into circumference equation:

C = 2πr

C = 2π(4)

C ≈ 25.13

hope this helps :)

Answer:

225 adult tickets 530 student tickets

Answer:

$5.37

Step-by-step explanation:

Given the information, it will be easier to start with the pennies, dimes, and nickels and end with the quarters.

50 * 0.14 = P

50 * 0.14 = 7 pennies

50 * 0.38 = D

50 * 0.38 = 19 dimes

6 + P = N

6 + 7 = 13 nickels

50 - (P + D + N) = Q

50 - (7 + 19 + 13) = 11 quarters

(7 * 0.01) + (19 * 0.1) + (13 * 0.05) + (11 * 0.25) = 5.37

The value of the variable y is 9 given that BDJ=7y+2  and angle JDR=2y+7

From the attached diagram, we can see that the sum of m<BDJ and m<JDR is complementary (i.e. sums up to 90degrees)

Given the following

m<BDJ = 7y + 2

m<JDR = 2y + 7

Summing up to 90

m<BDJ + m<JDR = 90

7y + 2 + 2y + 7 = 90

7y+2y+2+7 = 90

9y + 9 = 90

9y = 90-9

9y = 81

y = 81/9

y = 9

Hence the value of the variable y is 9

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The lowest extreme or smallest value among the supplied possibilities is A. \(120\) because it has the absolute lowest.

The set of integer arithmetic ranges from -1 to negative infinity, with -1 being the biggest negative number and negative infinity being the lowest. As a result, there is no such thing as the smallest negative number.

The largest negative value is 1, or -1. From then, the numbers increase until they reach zero. When they approach negative infinity, there exists an unlimited amount of negative numbers. Hence, there are no negative integers with the lowest value.

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In classification analysis, we are determining the probability of an observation belonging to a specific class.

Classification analysis is a machine learning technique used to predict the class or category to which an observation belongs. The goal is to assign a probability to each possible class, indicating the likelihood of the observation belonging to that class. This is typically done by training a classification model on a labeled dataset, where the classes are known for a set of observations. The model learns patterns and relationships from the training data and then uses that knowledge to predict the class of new, unseen observations. The predicted probabilities can be used to make informed decisions, such as determining the most likely class for a given observation or setting a threshold for making binary decisions.

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Answer:

250 ft

Step-by-step explanation:

circumference of a circle = πD

D = diameter

to find diameter divide by pi

d = 250

The total revenue from the production and sale of 80 units, based on the given marginal revenue function, is $17,950.

To find the total revenue, we need to integrate the marginal revenue function over the range of units produced and sold. In this case, the marginal revenue function is given by MR = -0.5x + 450, where x represents the number of units.

To integrate the marginal revenue function, we need to find the antiderivative of -0.5x + 450 with respect to x. The antiderivative of -0.5x is -0.25x^2, and the antiderivative of 450 is 450x. Therefore, the antiderivative of -0.5x + 450 is -0.25x^2 + 450x.

Next, we evaluate the antiderivative at the upper and lower limits of the range of units, which are 80 and 0, respectively. Plugging in these values, we get:

Total Revenue = (-0.25 * 80^2 + 450 * 80) - (-0.25 * 0^2 + 450 * 0)

             = (-0.25 * 6400 + 36000) - 0

             = -1600 + 36000

             = 34,400

Therefore, the total revenue from the production and sale of 80 units is $34,400.

Marginal revenue: Marginal revenue is the additional revenue generated from producing and selling one additional unit of a commodity. It can be calculated by taking the derivative of the total revenue function with respect to the number of units. In this case, the marginal revenue function was given as MR = -0.5x + 450.

Revenue optimization: Revenue optimization involves finding the optimal number of units to produce and sell in order to maximize revenue. This is typically done by analyzing the marginal revenue and marginal cost functions. The optimal production level occurs when marginal revenue equals marginal cost.

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The probability that the next call will involve a question about the location of an ATM is 2/15.

We know that the probability of an event is equal to the ratio between the desired outcome and the total number of favorable outcomes.

Hence we can say that probability = desired outcome / total number of outcomes

Now here, to find the probability that the next call will involve a question about the location of an ATM, we need to determine the proportion of ATM-related calls out of the total number of calls.

Out of the last 45 telephone calls, 6 involved questions about ATM location. Therefore, the probability can be calculated as:

Probability = Number of ATM-related calls / Total number of calls

Probability = 6 / 45

Simplifying the fraction, we get:

Probability = 2 / 15

Therefore, the probability that the next call will involve a question about the location of an ATM is 2/15.

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Domain is all the values that go into a function, and the range is all the values that come out.

Answer:

Step-by-step explanation:

15-(-5) = 20 and 35-15=20  so d=20

\(a_n=a_1+d(n-1)\\\\a_1=-5\\d=20\\\\a_{84}=-5+20(84-1)=-5+20\cdot83=-5+1660=1655\)

\(\mathbb{FINAL\;ANSWER:}\)

\(\huge\boxed{\sf{y-1=4(x+2)}}\)

\(\mathbb{SOLUTION\;WITH\;STEPS:}\)

Hi! Hope you are having a nice day!

We are given:

Can we write the equation of the line in Point-Slope Form? Sure!

y-y₁=m(x-x₁)

y-1=-4(x-(-2)

y-1=-4(x+2)

Hope you could understand everything.

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