Sydney bought 3 bottles of glitter each bottle of glitter cost $6 how much did Sydney spend on the bottles of glitter

Answer:

x=0

Step by step explanation:

cos (a+b) = cos(a) cos(b) -sin (a) sin (b)

Same identity forms in question.

L.H.S -cos (x+60)

Now write it in the form of sin .

sin [90-(60+x)]

Equal to RHS

R.H.S - 30

90-(60+x)=30

30-x=30

x=0

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The answer to the equation cos195°cos285° is -1/4.

An equation is a mathematical statement that asserts the equality of two expressions. Equations are used to describe relationships between different quantities and can be used to solve for unknown values. Equations are typically written as symbols, but can also be written in words. Simple equations might involve addition, subtraction, multiplication, and division, while more complex equations may involve exponents, logarithms, and trigonometric functions. Equations can be used to model and understand real-world phenomena, such as calculating projectile motion, or predicting the behavior of a chemical reaction.

This is derived from the trigonometric identity cos{60°−x}cosx – sin(60°−x)sinx. This identity states that the cosine of the sum of two angles is equal to the product of the cosines of each angle minus the product of the sines of each angle.

By substituting the angles 195° and 285° into the identity, we get cos{60°−195°}cos195° – sin(60°−195°)sinx. When we use the values of the angles, we get cos{-135°}cos195° – sin(135°)sinx. We can then simplify this to -1/4cos195° – 0sinx. As the sine of the angle is 0, this simplifies to –1/4cos195°. As the cosine of 195° is -1/4, the answer to the equation cos195°cos285° is -1/4.

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The answers are:

a) The z-score for a light bulb that lasts 500 hours is -10.

b) For a sample of 20 light bulbs, the probability that the average lifespan will be less than 980 hours is approximately 0.0367, or 3.67%.

c) The z-score for a light bulb that lasts 400 hours is -12. This is even more unusual than a lifespan of 500 hours.

d) Given the lifespan follows a normal distribution with a mean of 1000 hours, 50% of the light bulbs will have a lifespan less than 1000 hours.

a) The z-score is calculated as:

z = (X - μ) / σ

Where X is the data point, μ is the mean, and σ is the standard deviation. Here, X = 500 hours, μ = 1000 hours, and σ = 50 hours. So,

z = (500 - 1000) / 50 = -10.

The z-score for a bulb that lasts 500 hours is -10. This is far from the mean, indicating that a bulb lasting only 500 hours is very unusual for this brand of bulbs.

b) If a customer buys 20 of these light bulbs, we're now interested in the average lifespan of these bulbs. . In this case, n = 20, so the standard error is

50/√20

≈ 11.18 hours.

z = (980 - 1000) / 11.18 ≈ -1.79.

The probability that z is less than -1.79 is approximately 0.0367, or 3.67%.

c) The z-score for a bulb with a lifespan of 400 hours can be calculated as:

z = (400 - 1000) / 50 = -12.

The probability associated with z = -12 is virtually zero. So the probability of getting a bulb with a mean lifespan of 400 hours is virtually zero.

d) The mean lifespan is 1000 hours, so half of the light bulbs will have a lifespan less than 1000 hours. Since the lifespan follows a normal distribution, the mean, median, and mode are the same. So, 50% of light bulbs will have a lifespan less than 1000 hours.

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Answer:

The probability that the individual has the disease is 1/500

Step-by-step explanation:

i found the fraction of 1 in 500 which is 1/500, hope this helps :)

Step-by-step explanation:

Hey there!

The sides of a square; 3cm.

Area = l^2

\(area = {3}^{2} \)

\(a = 9\)

Therefore, the area is 9cm^2.

Hope it helps...

Step-by-step explanation:

Volume of Barrel : [pi x h(r² + 2R²)] / 3

Barrel A : 2pi(r² + 2R²)]/ 3

Barrel B : 5pi(r² + 2R²)]/ 3

Barrel A + Barrel B = 532

5pi(r² + 2R²)/3 + 2pi(r² + 2R²)/3 = 532

5pi(r² + 2R²) + 2pi(r² + 2R²) = 1596

7pi(r² + 2R²) = 1596

pi(r² + 2R²) = 228

Barrel A = 2 x 228/3 = 76 ft³ SMALLER

Barrel B = 5 x 228/3 = 380 ft³

hope it's helpful, I'm not sure if (r) and (R) are the same if the two barrels has a similar shape. but if they're the same, then the answer is correct

The 3 rules that we need to use to simplify the expression are:

As I understand, the expression that we have is:

\(\frac{((-8)^4)^{-5}}{(-8)^6}\)

The first rule we need to use, is the exponent of an exponent rule, it says that:

\((a^n)^m = a^{n*m}\)

If we apply that to the denominator, we get:

\(\frac{((-8)^4)^{-5}}{(-8)^6} = \frac{(-8)^{-20}}{(-8)^6}\)

Now we need to use the quotient of powers:

\(\frac{a^m}{a^n} = a^{m - n}\)

Using that we get:

\(\frac{((-8)^4)^{-5}}{(-8)^6} = \frac{(-8)^{-20}}{(-8)^6} = (-8)^{-20 - 6} = (-8)^{-26}\)

Finally, we use the rule for a negative exponent:

\(a^{-n} = \frac{1}{a^n}\)

So we get the simplified form:

\(\frac{((-8)^4)^{-5}}{(-8)^6} = \frac{(-8)^{-20}}{(-8)^6} = (-8)^{-26} = \frac{1}{(-8)^{26}}\)

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Answer:

B, C, and E

Step-by-step explanation:

Answer:

I would pick a, the estimated total to the nearest dollar is 38

Step-by-step explanation:

13.95 rounded is 14

23.50 rounded is 24

24+14=38

Answer:

\(16x^4y^2 a^6\)

Step-by-step explanation:

\((-4x^2ya^3)^2=(-4)^2(x^2)^2(y)^2(a^3)^2 \\ \\ =16x^4y^2 a^6\)

The total ways are there for her to select the schedule for the week =  \(\frac{22!}{15!}} \\\\\)  

Given, She makes 22 different dishes for each of the seven days of the week.

Total ways are there for her to select the schedule for the week = \($ ^{22}P_7\)

As We know,

\($ ^nP_k=\frac{n!}{(n-k)!}} \\\)

\($ ^{22}P_7=\frac{22!}{(22-7)!}} \\\\\)

\(\ $ ^{22}P_7=\frac{22!}{15!}} \\\\\)

Hence, The total ways are there for her to select the schedule for the week =  \(\frac{22!}{15!}} \\\\\)  

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Answer:

One Solution

Step-by-step explanation:

p+9=2p-3

subtract 9 from both sides

p+9=2p-3

-9 -9

simplify

p=2p-12

subtract 2p from both sides

p=2p-12

-2 -2

simplify

-p= -12

divide both sides by -1

p=1

Answer:

2x + 25

Step-by-step explanation:

Let that number be x.

Step 1 : Multiply x and 2.

x * 2 = 2x

Step 2 : Add 25 and 2x.

2x + 25

Hence,

25 is added to the product of a number and 2 is 2x + 25.

Part A: In this situation, a Type II error would take place if the council failed to reject the null hypothesis even if it was untrue (i.e., less than 40% of children under the age of 5 could pass a swim test).

If the researcher does not reject a null hypothesis that is actually wrong in the population, this is known as a type II error (false-negative). Notwithstanding the fact that type I and type II mistakes cannot be completely prevented, the researcher can lessen their risk by increasing the sample size.

from the question:

Part A: In this situation, a Type II error would take place if the council failed to reject the null hypothesis even if it was untrue (i.e., less than 40% of children under the age of 5 could pass a swim test). This would result in a lost chance to provide these kids with more swim safety training, perhaps placing them in danger of drowning or other swimming-related mishaps.

Part B: We are unable to reject the null hypothesis since the p-value (0.8438) exceeds the significance level (0.05). This indicates that there is insufficient information to draw the conclusion that less than 40% of children under the age of five can pass a swim test. But, since the test only looked at the alternative hypothesis that the fraction is less than 40%, we cannot draw the conclusion that it is exactly 40%.

Part C: One possible defect in the study is the use of a volunteer sample. The children who volunteered to take the swimming test may not be representative of the entire population of children under 5 in Bloomburg City. For example, parents who are more concerned about their children's swimming abilities may be more likely to volunteer their children for the test, leading to a biased sample. To obtain a more representative sample, a random sample of children under 5 could be selected from the population and asked to take the swimming test.

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PT = Line

RP = Segment

SR = Ray

∠2 and ∠3 = adjacent angles

∠2 and ∠4 = Vertical angles.

A line segment is a section of a straight line that is bounded by two different end points and contains every point on the line between them. The Euclidean distance between the ends of a line segment determines its length.

A line segment is a finite-length section of a line with two endpoints. A ray is a line segment that stretches in one direction endlessly.

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Answer:

1

Step-by-step explanation:

assuming your points are (0,3) and (-3,0) you would "rise" 3 and "run" 3 to get from one point to the next on a graph, making your rise over run (aka slope) 3/3 which is equal to 1.

Answer: \(4\sqrt{26}\)

Step-by-step explanation:

This is a rather tricky question at first, but it's easy when you figure out the trick.

The key here is using the Pythagorean theorem twice.

We see that the big triangle is divided by its height into two smaller ones.

First, use the Pythagorean theorem on the triangle on the left to find the height.

height = \(\sqrt{80-64}=\sqrt{16} =4\)

Now that we know the height is 4, we can use the Pythagorean theorem on the triangle on the right to find x.

x = \(\sqrt{20^{2}+4^{2} } =\sqrt{416} = 4\sqrt{26}\)

And there we have our final answer.

\((\stackrel{x_1}{8}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ \cfrac{1}{4}}(x-\stackrel{x_1}{8}) \\\\\\ y-6=\cfrac{1}{4}x-2\implies y=\cfrac{1}{4}x+4\)

Answer:

5/6 hours

Step-by-step explanation:

Create a proportion where x is the number of hours it will take to walk 1/6 of a mile:

\(\frac{1/5}{1}\) = \(\frac{1/6}{x}\)

Cross multiply and solve for x:

1/5x = 1/6

x = 5/6

So, it will take the tortoise 5/6 hours to walk 1/6 of a mile

Answer:

A≈314.16

Step-by-step explanation:

The formula to find the area of a circle when you have a diameter is,

A=1/4πd2.

Hope this helps!~

Counting from right to left, find the 68th digit of n is 10.

An integer, is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.

The largest integer with exactly 100 digits is the integer that consists of 100 copies of the digit 9.

This integer is equal to 10100 = 10

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The differential equation that describes the cell phone sales, where y(t) is the number of cell phones sold after t months is

dy/dt=0.159(1-y/90).

Given that the maximum that the manufacturer can sell is 90000 cell phones and after 27000 cell phones have been sold the sales are increasing by 7000 phones per month.

We are required to form a differential equation that shows the cell phone sales.

dy/dt=ry(1-y/90)-------1

D3=27r(1-27/90)

3=27r(7/10)

r=3*10/27*7

r=0.1583

Using the value of r in 1 to get the equation

dy/dt=0.159y(1-y/90)

Hence the differential equation that describes the cell phone sales, where y(t) is the number of cell phones sold after t months is dy/dt=0.159(1-y/90).

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Sensitivity analysis is performed in order to see how certain changes affect the optimal solution.

It is a tool used to analyze how variations in inputs to a mathematical model will impact the output or outcome. This helps decision-makers to better understand the robustness of their solutions, and identify the most critical inputs or parameters that affect the solution. In other words, sensitivity analysis helps to evaluate the impact of uncertainty or changes in the model on the optimal solution. It can also help to identify the range of values that the input variables can take without significantly affecting the optimal solution.
This analysis method involves adjusting key variables or parameters within a model to understand their impact on the final outcome. By conducting sensitivity analysis, decision-makers can identify the most critical factors in a problem and better understand the robustness of the optimal solution. By exploring the effects of varying inputs, it helps in assessing the risks and making informed decisions, ensuring the model's reliability and stability even when faced with uncertain or changing conditions.

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Answer:

D

Explanition:

The given probability of having six girls in a six-child family is 0.015625. To determine the method used to compute this probability, we need to analyze the information provided.

The Classical method is based on theoretical assumptions and probabilities calculated using mathematical principles. It assumes equally likely outcomes and relies on counting favorable outcomes over the total number of possible outcomes.

The Empirical method involves gathering data from observations or experiments to estimate probabilities. It relies on observed frequencies and relative frequencies to compute probabilities. However, the given probability does not suggest a sample or data collection, making it unlikely that the Empirical method was used.

The Subjective method involves assigning probabilities based on personal judgment or opinions. Individuals subjectively evaluate the likelihood of an event based on their own beliefs or knowledge.

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Answer
Y. Answer:

y=30

Step-by-step explanation:

(3)^2 equals 9, so the first blank is 9.

You then multiply it by the 2, so second blank is 18.

18+15=33

33-3=30=y

Answer:

30

Step-by-step explanation:

first space should be 9 since 3² is 9

second space should be 18 since 2×9=18

final space should be 30 since 18+15 is 33-3=30

A plot that will present the information that will highlight how many trees are in a range of heights, such as 60–64, 65–69, etc. : histogram

In this question, we have been given the tree heights recorded on a school campus.

A science teacher wants to choose a data display that will highlight how many trees are in a range of heights, such as 60–64, 65–69, etc.

We need to find a correct plot that will present the information in this way.

We know that in bar charts, each bar represents one value(category). And  in a histogram, each bar will represent a continuous data

Therefore, a plot that will present the information that will highlight how many trees are in a range of heights, such as 60–64, 65–69, etc. : histogram

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Answer:

Step-by-step explanation:

A plot that will display information highlighting the number of trees in a range of heights, such as 60-64, 65-69, and so on: histogram

We were provided the tree heights reported on a school grounds in this question. A science instructor needs to select a data presentation that will show how many trees are in a given height range, such as 60-64, 65-69, and so on. We must find a suitable plot to portray the data in this manner. We know that each bar on a bar chart represents one value (category). And each bar in a histogram represents continuous data.

The value of x is 2.6 cm.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that y=8cm and  θ is 19 degrees.

We need to find the value of x.

We know that sinθ = opposite side/ hypotenuse

sin19 = x/y

Substitute the value of y

sin19 =x/8

8 sin 19 =x

8×0.325=x

x=2.6 cm

Hence, the value of x is 2.6 cm.

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Answer:

24 blocks

Step-by-step explanation:

2(5) + 2(7) = 10 + 14

Answer:

What does it even say? Plus i'm 5th grade sooo, me OUT!

Step-by-step explanation:

Answer:

Slope=1.000/2.000=0.500

b-i

q-i

b-(2*q+6)=0

Step-by-step explanation:

1.1     Solve   b-2q-6  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  b-2q-6  = 0 and calculate its properties

Notice that when b = 0 the value of q is 3/-1 so this line "cuts" the q axis at q=-3.00000

 q-intercept = 6/-2 = 3/-1  = -3.00000

When q = 0 the value of b is 6/1 Our line therefore "cuts" the b axis at b= 6.00000

 b-intercept = 6/1  =  6.00000

Slope is defined as the change in q divided by the change in b. We note that for b=0, the value of q is -3.000 and for b=2.000, the value of q is -2.000. So, for a change of 2.000 in b (The change in b is sometimes referred to as "RUN") we get a change of -2.000 - (-3.000) = 1.000 in q. (The change in q is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  1.000/2.000 =  0.500

 Slope = 1.000/2.000 = 0.500

 b-intercept = 6/1 = 6.00000

 q-intercept = 6/-2 = 3/-1 = -3.00000

Answer:

The coefficient of x is 22.