Given the measure of an acute angle in a right triangle, we can tell the ratios of the lengths of the triangle's sides relative to that acute angle.

Here are the approximate ratios for angle measures

55

°

55°55, degree,

65

°

65°65, degree, and

75

°

75°75, degree.

Angle

55

°

55°55, degree

65

°

65°65, degree

75

°

75°75, degree

adjacent leg length

hypotenuse length

hypotenuse length

adjacent leg length

​

start fraction, start text, a, d, j, a, c, e, n, t, space, l, e, g, space, l, e, n, g, t, h, end text, divided by, start text, h, y, p, o, t, e, n, u, s, e, space, l, e, n, g, t, h, end text, end fraction

0.57

0.570, point, 57

0.42

0.420, point, 42

0.26

0.260, point, 26

opposite leg length

hypotenuse length

hypotenuse length

opposite leg length

​

start fraction, start text, o, p, p, o, s, i, t, e, space, l, e, g, space, l, e, n, g, t, h, end text, divided by, start text, h, y, p, o, t, e, n, u, s, e, space, l, e, n, g, t, h, end text, end fraction

0.82

0.820, point, 82

0.91

0.910, point, 91

0.97

0.970, point, 97

opposite leg length

adjacent leg length

adjacent leg length

opposite leg length

​

start fraction, start text, o, p, p, o, s, i, t, e, space, l, e, g, space, l, e, n, g, t, h, end text, divided by, start text, a, d, j, a, c, e, n, t, space, l, e, g, space, l, e, n, g, t, h, end text, end fraction

1.43

1.431, point, 43

2.14

2.142, point, 14

3.73

3.733, point, 73

Use the table to approximate

m

∠

L

m∠Lm, angle, L in the triangle below.


3.2

3.2

11.9

11.9

L

L

K

K

J

J

Choose 1 answer:

Solving for Y

3x+y=2

y=2-3x

y=2-3x,x R

Solving for X

3x+y=2

3x=2-y

x= 2/3-1/3y

x=2/3-1/3y

Find the x-intercept

3x+y=2

3x+0=2

3x=2

x=2/3

Find the y-intercept

3x+y=2

3 times 0+y=2

y=2

Answer:

of Example 6

5 and 14

Step-by-step explanation:

IN EXAMPLE 6

Opposite angles are equal so you equate the first one like this

3x + 20 = 10x - 15

15 + 20 = 7x

35/7 = x

x = 5

In next question b

It is a straight line thus it's 180°

so 4n + 22 +8n -10 = 180

12n + 12 = 180

12n = 180 - 12

n =168÷ 12

n = 14

Answer:

464m^2

Step-by-step explanation:

Given data

Dimension of the regular playground

Length= 28m

Width= 15 m

We want to extend both sides by 1 m

Length= 28+1= 29m

Width= 15+1= 16m

Hence the area

Area=Length*Width

Area= 29*16

Area= 464m^2

The Area is 464m^2

The to your question is that we can use the normal distribution to estimate the probability that the product will last between 16.536 and 8.054 years.


In this case, we want to calculate the probability for x = 16.536 and x = 8.054. The mean (μ) is 14.242 years, and the standard deviation (σ) is 3.978 years.

Using the formula, we can calculate the z-scores for both values:
For x = 16.536: z = (16.536 - 14.242) / 3.978
For x = 8.054: z = (8.054 - 14.242) / 3.978

Once we have the z-scores, we can look up the corresponding probabilities in the standard normal distribution table or use a calculator. Subtracting the probability for the lower z-score from the probability for the higher z-score will give us the probability that the product will last between 16.536 and 8.054 years.

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The length of AC in triangle ABC, rounded to three significant figures, is 16.3.

To find the length of AC in the triangle ABC, we can use trigonometric ratios.

Given that CAB is a right angle (90°) and ABC is 57°, we can deduce that AC is the hypotenuse of the right triangle. AB, which is given as 8.8, is one of the legs of the right triangle.

To find the length of the hypotenuse AC, we can use the trigonometric function cosine (cos). Cosine is defined as the ratio of the adjacent side to the hypotenuse in a right triangle.

In this case, the adjacent side is AB and the hypotenuse is AC. So, we can write the equation:

cos(ABC) = AB / AC

Rearranging the equation to solve for AC:

AC = AB / cos(ABC)

Substituting the given values:

AC = 8.8 / cos(57°)

Using a calculator to evaluate the cosine of 57° (cos(57°) ≈ 0.5403):

AC ≈ 8.8 / 0.5403

AC ≈ 16.2648

Rounding to three significant figures, the length of AC is approximately 16.3.

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Answer:

A. 1/6

B. 1

Step-by-step explanation:

A. 9/j x j/54= 9/54 = 1/6

B. 6k/8m : 3k/4m = 6k/8m : 4m / 3k = 2/2 =1

Answer:

a. 3/2

b. 1

Step-by-step explanation:

A. To simplify the expression, we can cancel out the common factor of j:

9/j * j/54 = (9/1 * 1/6) = 3/2

Therefore, 9/j * j/54 simplifies to 3/2.

B. To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction. That is,

(a/b) ÷ (c/d) = (a/b) x (d/c)

Using this rule, we can simplify the given expression as follows:

6k/8m ÷ 3k/4m = (6k/8m) x (4m/3k)

             = (6/8) x (4/3)  

             = 2/2

             = 1

Answer:

c

Step-by-step explanation:

Answer:

76

Step-by-step explanation:

180-(56+48)

put in calculator

76

The absolute maximum and minimum values of the function f(x, y) = x^2 + y^2 - 2y on the set R = {(x, y): x^2 + y^2 ≤ 9} can be found by analyzing the critical points and the boundary of the region R.

To find the critical points, we take the partial derivatives of f(x, y) with respect to x and y, and set them equal to zero. Solving these equations, we find that the critical point occurs at (0, 1).

Next, we evaluate the function f(x, y) at the boundary of the region R, which is the circle with radius 3 centered at the origin. This means that we need to find the maximum and minimum values of f(x, y) when x^2 + y^2 = 9. By substituting y = 9 - x^2 into the function, we obtain f(x) = x^2 + (9 - x^2) - 2(9 - x^2) = 18 - 3x^2.

Now, we can find the maximum and minimum values of f(x) by considering the critical points, which occur at x = -√2 and x = √2. Evaluating f(x) at these points, we get f(-√2) = 18 - 3(-√2)^2 = 18 - 6 = 12 and f(√2) = 18 - 3(√2)^2 = 18 - 6 = 12.

Therefore, the absolute maximum value of f(x, y) is 12, which occurs at (0, 1), and the absolute minimum value is also 12, which occurs at the points (-√2, 2) and (√2, 2).

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Answer:

∠ 2 = 34°

Step-by-step explanation:

∠ 1 + ∠ 2 = ∠ WXY , that is

37° + ∠ 2 = 71° ( subtract 37° from both sides )

∠ 2 = 34°

Answer:

mark each line about 1 in. apart

Plzzzzz give me Brainliest!!!!!  

Answer:

Step-by-step explanation:

(-3, 2)

Horizontal is y = 2

Vertical is x = -3

In the same way (1, 4) is

y = 4

x = 1.

Answer:

(a)Range = 96

(b)Variance=1059.36

(c)Standard Deviation =32.55

Step-by-step explanation:

(a)Range

Range = Highest Value - Lowest Value

=97-1

=96

(b)Variance

The variance of a sample for ungrouped data is defined by the formula:

\(Variance, s^2 = \dfrac{\sum(x-\overline{x})^2}{n-1}\)

First, we determine the mean of the sample data.

\(Mean = \dfrac{40 +39+ 8+ 82+ 25+ 53+ 97+ 1+ 28+ 41+ 94}{11} \\=\dfrac{508}{11}\\\\ \overline{x}=46.2\)

\(\sum(x-\overline{x})^2=(40-46.2)^2 +(39-46.2)^2+ (8-46.2)^2+ (82-46.2)^2+ (25-46.2)^2+ (53-46.2)^2+ (97-46.2)^2+ (1-46.2)^2+ (28-46.2)^2+ (41-46.2)^2+ (94-46.2)^2\\\\=38.44+51.84+1459.24+1281.64+449.44+46.24+2580.64+2043.04+331.24+27.04+2284.84\)

=10593.64

Therefore:

Variance, Variance,

\(Variance, s^2 = \dfrac{10593.64}{11-1}\\\\=1059.36\)

(c)Standard Deviation

\(s=\sqrt{Variance}\\ =\sqrt{1059.36}\\s=32.55\)

The results tell us that there is great variability in the number of jerseys of the player as evidenced by the high standard deviation and range.

Answer:

80m

Step-by-step explanation:

Pythageoreum Theorum since it is a right triangle.

a^2 + b^2 = c^2

60^2 + b^2 = 100^2

3600 + b^2 = 10,000

-3600              -3,600

b^2 = 6,400

Square root both sides of the equation

b = \(\sqrt{6400}\)

\(\sqrt{6400}\) = 80

The length of side a is 80 m

Answer: -15 divided by 0.3 is the same as -15/3/10 but to solve we can do -15 times 10/3 witch is -150/3=-50

Step-by-step explanation:

Answer:

5 seconds

Step-by-step explanation:

The same person also took a midterm in their marketing course and the class mean for this exam was 77 with a standard deviation of 4.7. The z-score for the score on this exam is 1.9. Calculate the actual score this person received for the marketing exam (to 2 decimal places).

Here is how we can calculate the actual score this person received for the marketing exam. First, we know that the Z score is given by the formula:

Z = (X - μ)/ σ

where X = actual score, μ = Mean, σ = Standard Deviation

Given that the Z score is 1.9, i.e., Z = 1.9

Hence,X = μ + Zσ

On substituting the given values, we get: X = 77 + 1.9 * 4.7X = 86.13 (approx.)

Therefore, the actual score that this person received for the marketing exam is 86.13 (to 2 decimal places).Note that the score is rounded to 2 decimal places as required by the question.

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It will take approximately 8 minutes to fill the water truck, and the weight of the water load will be approximately 30,296 pounds.

First, we need to convert the dimensions of the tank from inches to feet:

68 inches diameter = 68/12 feet = 5.67 feet diameter

24 feet long = 24 feet long

Next, we can calculate the volume of the tank in cubic feet:

Since 1 cubic foot of water weighs 62.4 pounds, we can calculate the weight of the water in the tank in pounds:

To find out how long it will take to fill the tank, we can use the flow rate of the fire hydrant:

Finally, we can divide the volume of the tank by the flow rate to find out how long it will take to fill the tank:

Therefore, it will take approximately 8 minutes to fill the water truck, and the weight of the water load will be approximately 30,296 pounds.

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Answer:

\(P(A\ n\ B) = 6\%\)

Step-by-step explanation:

Given

\(P(A) = 0.2\)

\(P(B) = 0.3\)

Required

Determine \(P(A\ n\ B)\)

Since both events are independent;

\(P(A\ n\ B) = P(A) * P(B)\)

\(P(A\ n\ B) = 0.2 * 0.3\)

\(P(A\ n\ B) = 0.06\)

Convert to %

\(P(A\ n\ B) = 0.06 * 100\%\)

\(P(A\ n\ B) = 6\%\)

The system of inequalities that represents the scenario is:

x^2 - 2y ≥ 6,000

2x + 5y ≤ 2,000


To represent the company's goal of maintaining a stock value of at least $6,000, we use the inequality x^2 - 2y ≥ 6,000. This means that the value of x^2 - 2y must be greater than or equal to $6,000 in order for the company to meet their goal.

To represent the company's goal of keeping purchases below $2,000, we use the inequality 2x + 5y ≤ 2,000. This means that the value of 2x + 5y must be less than or equal to $2,000 in order for the company to meet their goal.

Therefore, the system of inequalities that represents the scenario is:

x^2 - 2y ≥ 6,000

2x + 5y ≤ 2,000

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To find the result of multiplying vector a by vector b, we use the dot product or scalar product. The dot product of two vectors is calculated by multiplying the corresponding components and summing them up.

Given:

a = [1, 3, 5]

b = [1, 3, 5]

To find a · b, we multiply the corresponding components and sum them:

\(a . b = (1 * 1) + (3 * 3) + (5 * 5)\\ = 1 + 9 + 25\\ = 35\)

So, a · b equals 35.

Now, let's plot the coordinate (35) on a graph paper. Since the coordinate consists of only one value, we'll plot it on a one-dimensional number line.

On the number line, we mark the point corresponding to the coordinate (35). The x-axis represents the values of the coordinates.

First, we need to determine the appropriate scale for the number line. Since the coordinate is 35, we can select a scale that allows us to represent values around that range. For example, we can set a scale of 5 units per mark.

Starting from zero, we mark the point at 35 on the number line. This represents the coordinate (35).

The graph paper would show a single point labeled 35 on the number line.

Note that since the coordinate consists of only one value, it can be represented on a one-dimensional graph, such as a number line.

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9514 1404 393

Answer:

  see below

Step-by-step explanation:

The term y/2 tells you that any integer solution must include an even value of y. That is, y=3 cannot be part of an integer solution.

When we use the ordered pair (x, y) = (2, -4) in the equation, we get ...

  6(2) -(-4)/2 = 12 +2 = 14 . . . . . satisfies the equation

Of the two points offered, only (2, -4) is a solution.

$9.10 in all nickels is how many nickels

9.10 / 0.05

how many 5 cent pieces add up to that

182 nickels

a penny is one cent

just move the decimal place over twice

9.10

910.0

910 pennies

Hope this helps

- Jeron :- )

All parts of the problem given have been explained and provided below.

Variables in any particular dataset are defined as any characteristics, numbers, or quantity that can be measured or counted to give information about any object, on which the dataset is based.

So, the variables in this given dataset are;

Overall score

Recommended

owner satisfaction

Overall miles per gallon

Acceleration (0-60) sec

Categorical or qualitative variables are those which can't be quantified or measured. Their values are defined by an order relation between the different categories.

the categorical variables in this dataset are,

Recommended

Owner satisfaction

Quantitative variables are those which can be measured in an order to provide information about an object.

the quantitative variables in this dataset are,

Overall score

Overall miles per gallon

Acceleration (0-60) sec

In the given dataset, 7 vehicles are recommended,

So their percentage would be,

7/15 × 100 = 46.67%

The average overall miles per gallon of these 15 vehicles is 25.4.

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The specific null and alternative hypotheses for a hypothesis test will depend on the research question being investigated and the type of data being analyzed.

We have,

Equivalent expressions can be stated as the expressions which perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

For a two-tailed hypothesis test, we know that, an appropriate null hypothesis indicating that the population correlation is equal to zero would be:

H₀: ρ = 0

where ρ represents the population correlation coefficient.

This null hypothesis states that there is no significant correlation between the two variables being analyzed.

In a two-tailed hypothesis test, the alternative hypothesis would be that there is a significant correlation, either positive or negative, between the two variables:

Hₐ: ρ ≠ 0

This alternative hypothesis states that there is a significant correlation between the two variables, but does not specify the direction of the correlation.

It's important to note that the specific null and alternative hypotheses for a hypothesis test will depend on the research question being investigated and the type of data being analyzed.

Additionally, the choice of null and alternative hypotheses will affect the statistical power of the test, which is the probability of correctly rejecting the null hypothesis when it is false.

Hence, the specific null and alternative hypotheses for a hypothesis test will depend on the research question being investigated and the type of data being analyzed.

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Complete Question:

For a two-tailed hypothesis test, which of the following would be an appropriate null hypothesis indicating that the population correlation is equal to o?

A. H₀: 1 = 2, B. H₀ : M₁ = M₂ C. H₀: O = 0  

D. None of the options above are correct.

Based on the information given, if Ozzie uses his coupon and pays 7% sales tax, the amount tax that he will pay for two dozen cookies is $10.18 (Option C).

Given:

The sale price is 85% of the original price, and the coupon

This means that Ozzie will pay 95% of that.

The added tax causes the resulting price to be multiplied by 107%, so for 2 dozen cookies.

Hence, Ozzie to compute how much tax Ozzie will pay, we say:

 2(5.89)(0.85)(0.95)(1.07)

= $10.18

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Answer:

The cost of 4 dozen eggs is 4 * $1.25 = $5.

The cost of half a gallon of milk is $2.97.

The total cost of the eggs and milk is $5 + $2.97 = $7.97.

Since Chase has only $10, the minimum price for a dozen eggs is $10 - $7.97 = $2.03.

So the answer is 2.03

Step-by-step explanation:

Answer:

40%

Step-by-step explanation:

10 minutes late would mean 18 minutes late on the graph. The graph goes from 10-30 which creates a difference of 20. 8 divided by 20 equals 40 percent.

40 percent of the time does Oliver arrives within 10 minutes of John's arrival time.

Given that,

Oliver is typically 10–30 minutes late for his shift at work.

The distribution for the minutes he is late forms a consistent pattern, which can be graphed as the given uniform density curve.

John and Oliver are working a shift that starts at the same time. John always arrives 8 minutes late.

We have to determine,

What percentage of the time does Oliver arrive within 10 minutes of John's arrival time?

According to the question,

Oliver is typically 10–30 minutes late for his shift at work.

John and Oliver are working a shift that starts at the same time.

John always arrives 8 minutes late.

From the complete information, the probability distribution will be:

\(= \dfrac{1}{b-a}\\\\= \dfrac{1}{30-10}\\\\= \dfrac{1}{20}\)

Here, John always arrives 8 minutes late.

Therefore,

The percentage of the time that Oliver arrives within 10 minutes of John's arrival time is,

\(\rm = 8 \times \dfrac{1}{20}\\\\= \dfrac{2}{5}\\\\= 0.4 \times 100 \\\\= 40 \ Percent\)

Hence, 40 percent of the time does Oliver arrives within 10 minutes of John's arrival time.

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The slope of the tangent line is the limit of the slopes of the secant lines as the change in x approaches zero.

To find the slope of the secant line PQ for different values of z, we need to determine the coordinates of point Q. The y-coordinate of Q is given by x^2+z+7, where x is the x-coordinate of P. Therefore, the coordinates of Q are (z, x^2+z+7).

Using the formula for the slope of a line, which is (change in y) / (change in x), we can calculate the slope of the secant line PQ for each value of z.

For x=2.1, the coordinates of Q are (z, 2.1^2+z+7). We can calculate the slope of PQ using the coordinates of P and Q.

Similarly, for x=2.01, the coordinates of Q are (z, 2.01^2+z+7), and we can calculate the slope of PQ.

Likewise, for x=1.9 and x=1.99, we can calculate the slopes of PQ using the respective coordinates of Q.

By observing the calculated slopes of PQ for different values of z, we can make an estimation of the slope of the tangent line at point P(2,13). The slope of the tangent line is the limit of the slopes of the secant lines as the change in x approaches zero.

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