a 12 foot ladder is resting against the side of a building. The bottom of the ladder is 3 ft from the building find the measure of the angle the ladder makes with the ground. Rodger answers to the nearest tenth of a degree

Answer:

(3,0)

Step-by-step explanation:

Answer:

Its B

Step-by-step explanation:

Answer:

Here is the solution solution-

(-15x+6y)-(-10x+7y)

= -15x+6y+10x-7y

= (-15x+10x)+(6y-7y)

= -5x-y

Answer:

=10

Step-by-step explanation:

because 20÷10=2

70÷10=7

50÷10=5

Answer and Step-by-step explanation:

(i) The solution for equation: 2(3x-3) - 5 = 2(x-3) + 15 is:

2(3x-3) - 5 = 2(x-3) + 15

6x - 6 - 5 = 2x - 6 +15

6x - 2x = - 6 + 15 + 6 + 5

4x = 20

x = 5

The solution x is a real number and equals 5.

(ii) Since the order of hot sauce that goes into the gumbo doesn't matter, use combination:

\(C^{10}_{3}\) = \(\frac{10!}{3! (10-3)!}\)

\(C^{10}_{3}\) =  \(\frac{10.9.8.7!}{3.2.1.7!}\)

\(C^{10}_{3}\) = 120

There are 120 ways of picking 3 sauces out of 10.

(iii) Interest is calculated as:

interest = principal*rate*time

Principal is the value of the loan;

Rate is how much it will increase;

Time is for how long the loan will be taken. In this case, time is 9/12 since it was for months;

Interest = 3000 * \(\frac{11.75}{100}*\frac{9}{12}\)

Interest = 264.37

The interest the student will pay will be: $264.37.

Future Value = principal + interest

future value = 3000 + 264.37

future value = 3264.37

The future value for the student is $3264.37.

(iv) As shown in the image in the attachment, the sum of the equations equals 90:

2x + 30 + 2x + 40 = 90

4x = 20

x = 5

The angles are 40° and 50°

Using the definition of expected value, it is found that Ayo can be expected to make a profit of £55.8.

The expected value is given by the sum of each outcome multiplied by it's respective probability.

In this problem:

Hence, his expected profit for a single game is:

\(E(X) = -6\frac{1}{72} - 3\frac{17}{72} + 1.4\frac{54}{72} = \frac{-6 - 3(17) + 54(1.4)}{72} = 0.2583\)

For 216 games, the expected value is:

\(E = 216(0.2583) = 55.8\)

Ayo can be expected to make a profit of £55.8.

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The calculated value of the degree measure of angle c is 16°

From the question, we have the following parameters that can be used in our computation:

The figure (see attachment)

The sum of angles in a triangle is 180 degrees

This means that

x + 20 + 62 = 180

Evaluate the like terms

This gives

x + 82 = 180

So, we have

x = 98

The measure of angle c is then calculated as

c + 2 * (180 - 98) = 180

Collect the like terms

c = 180 - 2 * (180 - 98)

Evaluate

c = 16

Hence, the degree measure of angle c is 16°

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Answer:

y  =  x  +  3 z

Step-by-step explanation:

The given statement can be formulated as follows: A batch of 150 iPads is inspected by choosing a sample of four iPads. Eight of the 150 iPads do not conform to specifications.

How many samples of four contain exactly one non-conforming iPad?

Let's solve the given problem step by step.

Step 1: We have 8 non-conforming iPads and 142 conforming iPads in the batch of 150 iPads. We need to find the number of ways to choose 4 iPads that include exactly one non-conforming iPad.

Step 2: We choose one non-conforming iPad in 8 ways and choose 3 conforming iPads in 142C3 ways, where nCk is the number of ways to choose k objects from n distinct objects without regard to order.

Thus the total number of ways to choose 4 iPads with exactly one non-conforming iPad is given by:

=8 × 142C3

\(8 \times \frac{142 \times 141 \times 140}{3 \times 2 \times 1}\)

= 2,107,280

Therefore, there are 2,107,280 samples of four that contain exactly one non-conforming iPad.

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The relative frequency of heads is reasonably close to 40%.Mr. Clark's claim about the theoretical probability is likely to be false. This means that the theoretical probability of tails is most likely 0.60.

The relative frequency is the ratio of the number of times an event occurred to the total number of trials. In this case, the relative frequency of heads is 0.38 and tails is 0.62.The theoretical probability of an event is the number of favorable outcomes divided by the total number of possible outcomes.

Here, Mr. Clark claims that the coin is weighted so that the probability of heads is 40%. Therefore, the theoretical probability of heads is 0.40.However, the relative frequency of heads after 200 trials is only 0.38, which is reasonably close to 0.40. Hence, the relative frequency of heads is reasonably close to 40%.

Mr. Clark's claim about the theoretical probability of heads is likely to be false because the relative frequency of heads is less than the theoretical probability of heads (0.38 < 0.40).Therefore, the theoretical probability of tails is 1 - 0.40 = 0.60 because the coin is fair, so the probabilities of heads and tails should add up to 1. Thus, the theoretical probability of tails is most likely 0.60.

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Answer:

C. The answer is molecular motion.

Step-by-step explanation:

When a molecule moves it would heat up. Therefore, by moving it would heat up.

Answer:

1- Product of powers rule.

2- Quotient of powers rule.

3- Power of a power rule.

4- Power of a product rule.

5- Power of a quotient rule.

6- Zero power rule.

7- Negative exponent rule.

Step-by-step explanation:

Hope I helped! ^v^

The constant rate of change and initial value for the given graph are 40 and 20 respectively. the initial value might represent the fixed cost of the soil.

The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference. The negative slope indicates the rate of decrease while the positive shows the rate of increase.

The given problem can be solved as follows,

(a) The graph given is a straight line that passes through (0, 40) and (10, 240).

The constant rate of change is equivalent to the the slope of the line given as,

⇒ (240 - 40)/(10 - 0) = 20

(b) The initial value of the graph is given as the y-intercept of the line.

Which is given as 40.

It might represent the fixed cost.

Hence, the constant rate of change is given as 40 and the initial value is 20 which might represent the fixed cost.

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The missing graph is attached here.

Answer:

Rational numbers include positive and negative numbers and when multiplying those, there are two rules that you should follow: The Same Sign Multiplication Rule: The product of two positive or two negative numbers is positive. If the signs are the same then the result is positive.

Step-by-step explanation:

Therefore, the equation in point-slope form of the line that passes through the point (-2, 10) and has a slope of -4 is y - 10 = -4(x + 2).

The equation in point-slope form of a line is given by y - y1 = m(x - x1), where (x1, y1) represents a point on the line and m represents the slope of the line.

In this case, the point (-2, 10) lies on the line, and the slope is -4.

Substituting the values into the point-slope form equation, we have:

y - 10 = -4(x - (-2))

Simplifying further:

y - 10 = -4(x + 2)

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The given probability density function (pdf) is a valid pdf. The cumulative distribution function (cdf) can be calculated based on the pdf.

The probabilities of the random variable lying within specific intervals can be determined using the cdf. The value of the pdf at a specific point can also be calculated. Lastly, the 80th percentile of the distribution can be found using the cdf.

a. To show that the given function is a pdf, we need to ensure that it is non-negative over its domain and integrates to 1 over its entire range, which can be verified in this case.

b. The cdf, denoted as F(x), can be obtained by integrating the pdf from negative infinity up to x. In this case, since the pdf is constant between 1 and 6, the cdf will be a step function with a value of 0 up to x = 1, and a value of 0.2 from x = 1 to x = 6.

c. To find P(2 < X < 5), we calculate F(5) - F(2) using the cdf. Substituting the respective values, we get (0.2 * 5) - 0 = 1.

d. To find P(4 > X), we calculate 1 - F(4) using the cdf. Substituting the value, we get 1 - 0.2 = 0.8.

e. To find f(3), we simply substitute x = 3 into the given pdf, which gives a value of 0.2.

f. The 80th percentile corresponds to the value x for which F(x) = 0.8. From the cdf, we can see that F(x) = 0.2 for x ≤ 1, and F(x) = 0.2 for 1 < x ≤ 6. Therefore, the 80th percentile lies within the range 1 < x ≤ 6, specifically at x = 6.

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Answer:

x = ±\(\sqrt{7}\) - 5

Step-by-step explanation:

x^2 - 10x = -18

x^2 - 10x + 18 = 0

(x + 5)^2 - 5^2 + 18 = 0

(x + 5)^2 - 7 = 0

(x + 5)^2  = 7

\(\sqrt{(x + 5)^2}\) \(=\) ±\(\sqrt{7}\)

x = ±\(\sqrt{7}\) - 5

Answer:

\(\boxed {24p - 35}\)

Step-by-step explanation:

Solve the following expression:

\(1 + 4 (6p - 9)\)

-Use Distributive Property:

\(1 + 4(6p - 9)\)

\(1 + 24p - 36\)

-Combine like terms:

\(1 + 24p - 36\)

\(\boxed {24p - 35}\)

Therefore, the answer is \(24p - 35\).

Answer:

24p-35

Step-by-step explanation:

The distance between the man and the starting point will be 13.08 km.

Trigonometry is the branch of mathematics which set up a relationship between the sides and angles of right-angle triangles.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.

Given that a man walks due west for 4km. He then changes direction and walks on a bearing of 197°.

The distance will be calculated as,

tanΘ = P/B

tan(73) = y / 4

y = 4tan73

y = 13.08 km

Therefore, the distance between the man and the starting point will be 13.08 km.

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If t-shirts be t

The expression is

\(\\ \rm\rightarrowtail 12t>100\)

\(\\ \rm\rightarrowtail 12t-100>0\)

To determine the number of unique ways to order a frozen yogurt with one flavor and one topping, we need to multiply the number of options for each category.

Starting with the yogurt flavor, there are three choices: vanilla, chocolate, and strawberry.

Next, for the toppings, there are four choices: fudge, caramel, fruit, or plain.

To find the total number of unique combinations, we can multiply the number of options for each category.

3 (yogurt flavors) x 4 (topping choices) = 12 unique ways to order a frozen yogurt.

So, there are 12 different ways you can order a frozen yogurt if you can only select one flavor of yogurt and one topping. This means that you can enjoy different combinations of frozen yogurt and toppings each time you order and never get bored.

However, it's always good to remember to keep a balanced and healthy diet even when enjoying sweet treats like frozen yogurt.

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Answer:

find by using formula that 1/2×base×height

Hello!

Answer:

\(\huge\boxed{V = 60 m^{3}}\)

Formula for the volume of a triangular pyramid:

V = 1/3(bh)

The base is a triangle, so b = 1/2(b · h)

Solve for the base:

b = 1/2(8 · 5)

b = 1/2(40)

b = 20 m²

Solve for the volume:

V = 1/3(20 · 9)

V = 1/3(180)

V = 60 m³.

Hope this helped you!

Answer:

60 cubic meters

Step-by-step explanation:

I used the formula V = 1/3 AH to figure it out

The line plot is used to show the lengths of the string colors using  check marks above the line

From the complete question, we have the following frequency table

String color      Length

Black string        \(3\frac 12 \ in\)

Blue string          4 in

White string         \(3\frac 12 \ in\)

Brown string         \(3\frac 14 \ in\)

Green string         \(4\frac 34 \ in\)

Express as improper fraction

String color      Length

Black string        \(\frac {14}4 \ in\)

Blue string          \(\frac{16}4\ in\)

White string        \(\frac {14}4 \ in\)

Brown string       \(\frac {13}4 \ in\)

Green string        \(\frac {19}4 \ in\)

Since the lengths are fractions and the string color is a text, then

We plot the lengths on the x-axis and the string color on the y-axis

See attachment for the line plot

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Answer:

7>0x

0x<7

Step-by-step explanation:

4x-6>6x-20

-6>2x-20

14>2x

7>x

To form a triangle, the set of line segments must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we need to check if the given line segments 8 cm, 4 cm, and 3 cm meet this requirement.

We can start by checking if the sum of the two smaller sides (3 cm and 4 cm) is greater than the largest side (8 cm). 3 cm + 4 cm = 7 cm, which is less than 8 cm. Therefore, these three line segments cannot form a triangle.

In general, for a set of line segments to form a triangle, the largest side must be smaller than the sum of the other two sides. In this case, the line segment of 8 cm is too long compared to the other two sides, which makes it impossible to form a triangle.

In conclusion, there are no line segments that meet the requirements to form a triangle with lengths of 8 cm, 4 cm, and 3 cm.

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The answer is b.) -2

Answer:

slope would be -2

Step-by-step explanation:

slope formula

\( \frac{ {y}^{2} - {y}^{1} }{ {x}^{2} - {x}^{1} } \)

We know: (1, 9) and (4, 3)

plug in the numbers

\( \frac{9 - 3}{1 - 4} \)

subtract

\( \frac{6}{ - 3} \)

divide

\( - 2\)

Tadaaaa

Answer:

For 3x + 5y = -13 the answer is x= -13/3 + 5y/3

and for 2x + 15y=3 the answer x= 1.5 + (-15y/2)

Step-by-step:

For 3x+5y=-13 you have to add 5y on both sides. Then you have to divide by 3 on both sides and cancel out the common factor of 3. Then you would get x= 13/3 + 5y/3.

For 2x + 15y=3 you have to subtract 15y on both sides of the equation. You should have 2x=3 + (-15y). Then divide by 2 on both sides. 3 divided by 2 is 1.5 and -15y divided by 2 is -15y/2 since 2 doesn't have the same variable. so the answer should be x= 1.5 + (-15y/2).