A 15-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 14 feet from the base of the building. How high up the wall does the ladder reach?
The ladder reaches feet up the wall. (Round to the nearest hundredth.)
HELPP!!

To find the common roots between two functions, we need to find the roots (or solutions) of each function individually and then identify the shared solutions.

For the function f(x) = x^2 + x - 6, we can find the roots by setting the function equal to zero and solving for x:

x^2 + x - 6 = 0

To factorize this quadratic equation, we need to find two numbers that multiply to -6 and add up to 1 (the coefficient of x). The numbers that satisfy these conditions are 3 and -2:

(x + 3)(x - 2) = 0

Setting each factor equal to zero:

x + 3 = 0 or x - 2 = 0

Solving for x in each equation:

x = -3 or x = 2

Therefore, the function f(x) = x^2 + x - 6 has two roots: x = -3 and x = 2.

To find the common roots between this function and another function, we would need to know the second function. If you provide the second function, I can help determine if there are any shared roots.

The confidence interval is 0.559 < p < 0.641 and expected value is 0.600

To construct a confidence interval for the true population proportion, we can use the formula:

p ± Z * √((p × (1 - p)) / n)

Where:

p = sample proportion (336/560)

Z = critical value for the desired confidence level

95% confidence = Z-value of approximately 1.96

n = 560

Let's calculate the confidence interval:

p = 336/560 ≈ 0.600

Z ≈ 1.96 (for a 95% confidence level)

n = 560

Plugging these values into the formula:

p ± Z × √((p × (1 - p)) / n)

0.600 ± 1.96 × √((0.600 × (1 - 0.600)) / 560)

0.600 ± 1.96 × √((0.240) / 560)

0.600 ± 1.96 × √(0.0004285714)

0.600 ± 1.96 × 0.020709611

0.600 ± 0.040564459

The confidence interval is:

0.559 < p < 0.641

Therefore, the 95% confidence interval for the true population proportion of adults with children is 0.559 < p < 0.641.

For proportions, the expected value is simply the sample proportion, which is approximately 0.600.

Learn more on confidence interval: https://brainly.com/question/15712887

#SPJ1

The best description of the car's motion as shown in the graph is: A. It travels for 1 hour, then stops for 1 hour, and finally travels again for 3 hours.

In a distance-time graph, an horizontal line implies no distance was covered within that time frame, meaning there was a stop.

Thus, in the graph given, the stop occurred 1 and 2, which is equivalent to an hour. From 2 to 5 on the x-axis means there was movement for up to 3 hours.

Therefore, the best description is: A. It travels for 1 hour, then stops for 1 hour, and finally travels again for 3 hours.

Learn more about distance-time graph on:

https://brainly.com/question/16990017

#SPJ1

Answer:

4ssssssssssssssssssssssssssss

Answer:

G=(T²+N²)/4

Step-by-step explanation:

(√4G-N²)²=T²

4G-N²=T²

4G=T²+N²

G=(T²+N²)/4

if anything is unclear, ask freely.

Answer: choice A

Step-by-step explanation:

the transposed matrix would be

5 3

2 -1

so

5*5+2*2=29

3*5+2*-1=13

5*3-2*-1=13

3*3+-1*-1=10

which gives us the answer

29 13

13 10

Answer

k = 0.25399 ohms.in²/ft

R = 18996.48 ohms

Explanation

The resistance, of a wire varies directly as its length and inversely as the square of its diameter implies

Where R is the resistance of the wire, l is the length, d is the diameter, and k is a constant of proportionality.

Putting R = 17072 ohms, l = 4900 ft, and d = 0.27 inches, we have:

To find the R, put l = 2700 ft, and d = 0.19 inches:

A. The distributions of the periods is that using the five number summary is that

B. The box and whisker plot of the periods is attached

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

7th Period

66, 72, 77, 78, 78, 80, 82, 84, 84, 87, 88, 88, 89, 89, 90 92, 92, 93, 94, 94 96, 96

3rd Period

52, 60, 62, 64, 64, 65, 68, 71, 72, 74, 75, 76, 78, 79, 83, 84, 85, 88, 89, 93, 94, 97

The distributions of the periods will be compared using the five-number summaries

Using a graphing tool, the five-number summaries are:

7th Period

3rd Period

The box and whisker plot of the periods is added as an attachment

From the box and whisker plot attached, we can see the five-number summaries of the periods

Read more about box plot at

https://brainly.com/question/3473797

#SPJ1

Answer:

ME = 3.64

Step-by-step explanation:

Given:

Sample size, n = 21

Sample mean, X' = 95

Standard deviation \( \sigma \) = 8.

Confidence interval = 95%

Significance level \( \alpha\) = 0.05

Required:

Find margin of error

To find the margin of error, use the formula below:

\( M.E = \frac{\sigma}{\sqrt{n}} * t_\alpha_/_2; _d_f \)

Where,

\( t_\alpha_/_2 = 0.05/2 = 0.025\)

degree of freedom, df = n - 1 = 21 - 1 = 20

Therefore,

\( M.E = \frac{8}{\sqrt{21}} * t_0_._0_2_5; _2_0 \)

Using the table at 95% Confidence interval, we have:

\( = \frac{8}{\sqrt{21}} * 2.086 \)

\( = 3.6416 \)

Rounding to 2 decimal places,

ME = 3.64

Answer:

f[g(x)]= 7x + 27

Step-by-step explanation:

g(x) = x + 2,

f(x) = 7x + 13,

f[g(x)] means you substitute the value of g(x) into the variable of f(x);

Which is 7( x+2) + 13 = 7x +14 +13

= 7x + 27

Answer:

2(x-3)

Step-by-step explanation: 2 is being multiplied by the difference (subtraction) of x-3.

Answer:

1/12

Step-by-step explanation:

1/2 x 1/6=

denominator(1) x denominator(1)=1

numerater (2)x numerator(6)=12

Step-by-step explanation:

3 is cross multiplication

2 is proportion

and 1 is equal

Vocabulary word related to the statement 1 is equal, vocabulary word related to the statement 2 is proportion and vocabulary word related to the statement 3 is cross multiplication.

Proportions are said to be the mathematical statements where two or more ratios are made to be equivalent to each other.

For any numbers or quantities if,

p : q = r : s, then p/q = r/s.

First statement says that a comparison of two quantities or numbers as a quotient.

Every two quantities or numbers as a quotient are connected with an equal sign.

Second statement says that two ratios are equal.

When two ratios are stated as equal, then they are directly proportional. That is, as one set of numbers increases or decreases, the other set also increases or decreases.

Two set of numbers are said to be inversely proportional, id one quantity increases, other decreases and vice versa.

Take a set of proportion,  \(\frac{x}{y}\) and \(\frac{a}{b}\).

When  \(\frac{x}{y}\)  = \(\frac{a}{b}\) , this implies that bx = ay.

Multiplying diagonally across the equal sign in proportion is called cross multiplication.

Hence the vocabulary term related to statement 1, 2 and 3 are equal, proportion and cross multiplication respectively.

To learn more on Proportions, click:

https://brainly.com/question/21584688

#SPJ2

Answer:

Angle ABC,

Step-by-step explanation:

Please give more detail to your question, this doesn't help at all...

Answer:

It's in the attached file below :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

To check whether the given credit card number is valid or not, we need to apply the Luhn algorithm or the mod-10 algorithm. The Luhn algorithm works by adding up all the digits in the credit card number and checking if the sum is divisible by 10 or not. If it is, then the credit card number is considered valid, otherwise, it is invalid.

Let's apply the Luhn algorithm to the given credit card number:

Step 1: Starting from the rightmost digit, double every second digit

| 5 | 4 | 2 | 4 | 9 | 8 | 1 | 3 | 2 | 7 | 2 | 0 | 0 | 0 | 8 | 5 |

|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

| | 8 | | 8 | | 16| | 6 | | 14| | 0 | | 0 | | 10|

Step 2: If the doubled value is greater than 9, add the digits of the result

| 5 | 4 | 2 | 4 | 9 | 8 | 1 | 3 | 2 | 7 | 2 | 0 | 0 | 0 | 8 | 5 |

|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

| | 8 | | 8 | | 7 | | 6 | | 5 | | 0 | | 0 | | 1 |

Step 3: Add up all the digits in the credit card number, including the check digit

5 + 4 + 2 + 4 + 9 + 8 + 1 + 3 + 2 + 7 + 2 + 0 + 0 + 0 + 8 + 5 + 1 = 61

Step 4: If the sum is divisible by 10, then the credit card number is valid, otherwise, it is invalid.

61 is not divisible by 10, therefore the given credit card number is invalid.

Hence, it can be concluded that 5424 9813 2720 0085 is an invalid MASTERCARD credit card number.

The per capita GDP can be calculated by dividing the total GDP by the population.

$1.65 trillion (GDP) / 36,732,000 (population) = $45,073.58 (per capita GDP)

This means that, on average, each person in Canada has a GDP of $45,073.58. However, it's important to note that this number doesn't necessarily reflect the distribution of wealth within the country. It's just a way of measuring the overall economic output of a country on a per person basis.

Additionally, it's worth noting that this number only takes into account the GDP and population at the time of the calculation. The inflation rate of 2.5% would increase the GDP but not the population so it's not considered in this calculation

Learn more about economic output here:

brainly.com/question/13718196

#SPJ4

Answer: No

Step-by-step explanation:

Answer:

I believe it should be rounded to 11, if not decimal would be 10.88

Step-by-step explanation:

49 divided by 9 equals 5.44 which is the amount times the 49cm^2 triangle is compared to the 9cm^2. So then the side is 2cm, multiply by the amount times bigger the other triangle is which would be 10.88. Hopefully I'm not wrong:)

Answer:

The answer is 4 and 2/3 cm²

Step-by-step explanation:

Take the square root of 49 and 9 and you'll get 7 and 3 since the scale factor is the large area over the small area.

The large area would be √49 cm²

The small area would be √9 cm²

  7          x cm

------ =  ----------, cross multiply

  3         2 cm

7 × 2 = 3 × x

14 = 3x

x = 14/3, x = 4 and 2/3

Answer:

K5.60.

Step-by-step explanation:

Answer: She has walked 9/20 miles in total

Step-by-step explanation:

1/5*4=4/20

1/4*5=5/20

4/20+5/20=9/20 miles

Answer:

s=2

Step-by-step explanation:

-4s-5=-13

+5. +5

-4s = -8 ÷ -4

The options that are valid conclusions about the data include:

More than half of the students are not enrolled in French or Spanish. This conclusion is valid, as 25 out of 120 students are not enrolled in either French or Spanish, and 25 is more than half of 120.

Of the students that are enrolled in French, fewer than half of them are also enrolled in Spanish. This conclusion is valid, as only 30 out of 50 students enrolled in French are also enrolled in Spanish, which is less than half.

Therefore, the valid conclusions are B and E.

Learn more about data on

https://brainly.com/question/26711803

#SPJ1

Answer:

8 + 11i

Step-by-step explanation:

hope it is well understood

Answer:

31 15/22 acres

Step-by-step explanation:

2/11=4/22

1/2=11/22

=15/22

37-6=31

31+15/22=31 15/22