Janelys leans a 16-foot ladder against a wall so that it forms an angle of 61^{\circ} ∘ with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary.

To display formulas, one way is to press the key combination [Ctrl]+[] (grave accent).

The key combination [Ctrl]+[] is used to display formulas.

This is a useful feature for checking and editing formulas without altering the calculated values.

By pressing [Ctrl]+[], users can easily view the underlying formulas and ensure their accuracy.

This key combination provides a convenient way to switch between the formula view and the results view, enabling efficient editing and troubleshooting of complex calculations.

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Answer:

6.5%

Step-by-step explanation:

Percentage decrease

\( = \frac{2.30 - 2.15}{2.30} \times 100 \\ \\ = \frac{0.15}{2.30} \times 100 \\ \\ = \frac{15}{2.30}\\ \\ = \frac{150}{23}\\ \\ = 6.52173913 \\ \\ \approx \: 6.5\%\)

Step-by-step explanation:

Hope this helps, happy learning

Answer:

Option D

Step-by-step explanation:

By using geometric mean theorem in the given right triangle ABC,

\(\frac{AD}{BD}= \frac{BD}{DC}\)

BD² = AD × DC

h² = (AC - CD) × DC

h² = (25 - 16) × 16

h² = 9 × 16

h = \(\sqrt{144}\)

h = 12

Therefore, measure of side h = 12 units.

Option D will be the correct option.

Answer:

12 is correct via a p e x

Answer:

\(5 \times ( - 1)3 + 2 \\ \\ 5 - 3 + 2 \\ \\ = 4\)

Step-by-step explanation:

\(5 {x}^{3} + 2 \\ x = - 1 \\ 5 \times {( - 1)}^{3} + 2 \\ = - 5 + 2 \\ = - 3 \\ or \: 5x3 + 2 \\ = 5 \times - 1 \times 3 + 2 \\ = - 1 5 + 2 \\ = - 13 \\ thank \: you\)

The distance from the playground to the road along the other path is 1.3 miles.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

Angle= 50

The two paths intersect at an angle of 50.

Using Trigonometry

cos 50 = B/ H

0.6428 = B / 2

B = 1.2856

B= 1.3 miles

So, the other path is 1.3 miles away.

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Solving problems involving normal proportions requires careful attention to detail, as well as a good understanding of statistical concepts such as standardization and probability.

When solving a problem where you want to find normal proportions, you can follow the following steps:

Define the problem: Clearly define the problem you are trying to solve, including any relevant details such as the population, sample size, and the variable of interest.

Check assumptions: Check if the conditions for using normal distributions are met. The data should be continuous, the sample size should be large enough, and the distribution should be approximately normal.

Calculate the sample mean and standard deviation: If you are working with a sample, calculate the sample mean and standard deviation.

Standardize the data: Convert the data into standard normal distribution, by subtracting the mean from each observation and dividing by the standard deviation.

Determine the probability: Once the data has been standardized, you can use a standard normal distribution table or a calculator to determine the probability of the variable falling within a certain range or above/below a certain value.

Interpret the results: After determining the probability, interpret the results in the context of the problem. For example, you might conclude that there is a 95% chance that a randomly selected observation falls within a certain range, or that the variable of interest is higher than a certain value in 5% of cases.

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Answer:

1:6

Step-by-step explanation:

1500:9000

=150:900 (divide by ten)

=15:90 (divide by ten)

= 1:6. (divide each number by 15)

Answer:

x^2 - 4x + 5 = 0

Step-by-step explanation:

:)

x = (2 + i) and (2 - i) are the roots of the quadratic equation f(x) = x² - 4x + 5.

The values of variables satisfying the given quadratic equation are called its roots.

Given  (2 + i) and (2 - i) are roots of the quadratic equation.

Let the quadratic equation be f(x).

(x - (2 + i)) and (x - (2 -i)) are the factors of f(x).

Since, f(x) is a quadratic equation, it has only two roots.

f(x) = (x - (2 + i))(x - (2 - i))

f(x) = x² - (2 - i)x - (2 + i)x + (2 - i)(2 + i)

f(x) = x² - 2x + ix - 2x - ix + 4 - i²

f(x) = x² - 4x + 4 + 1

f(x) = x² - 4x + 5

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(a). O The entire student body (the 17,000 students) and (b). O the 200 students interviewed are the answers to the above-asked question. This is a multiple-choice question about statistics sampling and population. The inquiry inquires about the problem's population of interest and sample.

The answers to the above statistics-based questions can be stated as,

(a) O The population of interest in this topic is the whole student body of the institution, which has 17,000 students because the student senate wants to know what percentage of all students support changing the grading system.

(b) O The sample in this problem consists of the 200 students who were questioned to determine their attitudes toward the proposed change in the grading system. They represent a subset of the overall student body and are used to estimate the percentage of all students who support the change.

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Based on the information given, the old oak tree is 1 order of magnitude or ten times bigger in comparison to the younger oak tree.

In mathematics and related areas, the orders of magnitude compare two items or variables using 10 as a reference. In this way, if the value is 10 times bigger than another the order of magnitude is 1 (one zero), but if one value is 100 times bigger then the order of magnitude is 2(100 or 2 zeros).

1012 / 92 = 11 which means the order of magnitude is 1

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The vector v in 2-space of length 3 pointing up at an angle of π/4 measured from the positive x-axis is: (3/√2, 3√2) and The vector w in 3-space of length 1 lying in the yz-plane pointing upward at an angle of 2π/3 measured from the positive y-axis is: (0, -1/2, √3/2).

a. Vector (v)

Vector (v)=v (cos Ф, sin Ф)

V=1 while the counterclockwise angle that is measured from positive x=Ф=π/4

Hence:

Vector=3(cos π/4, sinπ/4)

Vector=(3/√2, 3√2)

b. Vector w:

Vector w=1(0, cos 2π/3, sin2π/3)

Vector w=(0, -1/2, √3/2)

Therefore the vector v in 2-space of length 3 pointing up at an angle of π/4 measured from the positive x-axis is: (3/√2, 3√2) and The vector ws: (0, -1/2, √3/2).

The complete question is:

Resolve the following vectors into components:

a. The vector v in 2-space of length 3 pointing up at an angle of π/4 measured from the positive x-axis.

(b) The vector w in 3-space of length 1 lying in the yz-plane pointing upward at an angle of 2π/3 measured from the positive y-axis.

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The total cost of the engagement ring is $10,975. The sales tax is calculated as follows: $10,000 x 0.0975 = $975.

A sales tax is a type of consumption tax that local or state governments apply on the sale of products or services that consumers pay for when they make a purchase. When a company has a link to the jurisdiction in some way, it is responsible for collecting sales tax and remitting payment to the government.

It is only imposed and paid when the taxable supply is produced while engaging in a "taxable activity". Taxes should be based on the value of the goods or service. Because of the way the sales tax is structured, consumers are required to bear the majority of the tax burden. Because sales tax is an indirect tax, this is true.

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The volume of the right cone is 7 units.

The radius of a cone can be found as follows:

The volume of the right cone is 245π unit³. The height of the right cone is 15 units.

Therefore,

volume of a right cone = 1 / 3 πr²h

where

Hence,

volume of the right cone = 245π

h = 15 units

Hence,

245π = 1 / 3 × π × r²  × 15

divide both sides by π

245 = 15 / 3 r²

245 = 5r²

r² = 245 / 5

r = √49

r = 7 units

Therefore,

radius of the cone = 7 units

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The area of the rectangle with a height of 222 and a width of 5x^2 - 2x + 35 is given by the expression 1110x^2 - 444x + 7770.

The rectangle has a height of 222 and a width of 5x^2 - 2x + 35.

To find the area of the rectangle, we multiply the height by the width. Let's substitute the given values:

Area = height * width

Area = 222 * (5x^2 - 2x + 35)

To simplify the expression, we can distribute the 222 to each term within the parentheses:

Area = 222 * 5x^2 - 222 * 2x + 222 * 35

Now, let's further simplify each term:

Area = 1110x^2 - 444x + 7770

Therefore, the area of the rectangle with a height of 222 and a width of 5x^2 - 2x + 35 is given by the expression 1110x^2 - 444x + 7770.

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Answer:

i cant see the picture

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Khan Academy

Answer:

(0.309,0.359)

Step-by-step explanation:

The probability model that either team Alpha or team Zeta will win is 1/2.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of teams in the quiz = 2

i.e

Team Alpha and team Zeta.

Now,

The probability that team Alpha will win.

= 1/2

The probability that team Zeta will win.

= 1/2

Thus,

The probability model that one team will win is 1/2.

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The most appropriate test statistic to use for an experiment on relaxation techniques is matched pairs test. So, option(a) is right one.

For determining the validity of an asserting claim, the appropriate test statistic is formulated based on the population parameter to be tested from the estimated test statistic. Determining a claim related to a single parameter (e.g., the population mean) an appropriate test statistic, i.e., t-statistic or z-statistic is chosen based on the sample size. Also, In the case of claim related to examining the relationship between two population parameters, the two-sample test for t- or z statistic is formulated, based on appropriate sample sizes. We have an experiment related to relaxation techniques. The subject's brain signals were noted before and after the relaxation exercises. Claim is that relaxation exercise slowed the brain waves. There is two data sets one before and other after the relaxation exercise. So, for check the claim is true or not we use the matched pairs. The matched-pair t-test (or paired t-test or dependent t-test) that is used when the data from the two groups can be presented in pairs.

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Answer:

1/8

Step-by-step explanation:

As you can see, I unit fraction is 1/8 or any fraction with a one mostly because unit means 1.. always remember that!

Answer:

The answer is Quadrant 1

Step-by-step explanation:

-4+5

=1

therefore the answer is A.

Answer:

D) x=4

Step-by-step explanation:

-x+5=1

-x=1-5

-x=-4

x=4

Answer:

To determine to measure of the unknown angle

Step-by-step explanation:

If two angles are given, add them together and then subtract from 180°. If two angles are the same and unknown, subtract the known angle from 180° and then divide by 2

"To determine to measure of the unknown angle, be sure to use the total sum of 180°. If two angles are given, add them together and then subtract from 180°. If two angles are the same and unknown, subtract the known angle from 180° and then divide by 2."

Answer:

Jennifer would save $0.25 per ounce.

Step-by-step explanation:

With the 32-ounce jar, the price per ounce is $0.25 per ounce. With the 8-ounce jar, the price is $0.50 per ounce. Jennifer would do better to buy the 32-ounce jar, as she would save $0.25 per ounce with that choice.

Answer:

C, at 0/25, 1/20, 2/15, 3/10,...

Answer:

C

Step-by-step explanation:

Answer:2

Step-by-step explanation:x is -1. -(-1) is 1. 1+1=2

The probability that an earthquake striking this region will exceed 5.0 on the richter scale is approximately 0.121 or 12.1%.

To find the probability that an earthquake striking this region will exceed 5.0 on the richter scale, we need to use the cumulative distribution function (CDF) of the exponential distribution.

The CDF of the exponential distribution is given by:

\(F(x) = 1 - e^{(-\lambda x)}\)

where λ is the rate parameter, which is equal to 1/mean for the exponential distribution.

So in this case, λ = 1/2.4 = 0.4167.

To find the probability that an earthquake will exceed 5.0 on the richter scale, we need to calculate:

P(X > 5) = 1 - P(X ≤ 5)

= 1 - F(5)

= \(1 - (1 - e^{(-0.4167*5))\)

=\(e^{(-2.0835)\)

= 0.121

Therefore, the probability that an earthquake striking this region will exceed 5.0 on the richter scale is approximately 0.121 or 12.1%.

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Answer:

Tony says that he does not have enough information to find the area of this parallelogram. Is he correct? Tony is correct, the base of the parallelogram is not given.