An 18-foot board is leaning against a wall. It is set 6 feet from the base of the wall. How far up the wall does the board reach? Round your answer to the nearest tenth of a foot.

Answer:

48

Step-by-step explanation:

Answer:

Average of 3mph

Step-by-step explanation:

If Sarah goes uphill at 2mph and downhill at 4mph.

Then to find the average you can:

Add 2 plus 4

which equals 6

Then divide the sum of 6 by the number of values given, there are two values (2 and 4)

6 divided by 2 equals 3

So the average is 3mph

Answer:

840

Step-by-step explanation:

2% of 700 is 14. Multiply 14 by 10 years, and then add that result (140) to the original amount

Answer:

6

Step-by-step explanation:

Answer:

-486

Step-by-step explanation:

Answer:

143 is for the 715 miles and 55 is for the 275 miles no I don't think they have the same rate.

Step-by-step explanation:

275/5= 55

715/5= 143

Therefore, the 90% confidence interval for the mean height of the population of female runners is (64.77, 66.83) inches.

A confidence interval is a range of values that provides an estimate of the unknown population parameter with a certain level of confidence. The confidence level represents the percentage of times that the true population parameter will be contained within the interval, based on repeated sampling.

a) Using a t-distribution with 11 degrees of freedom (n-1), and a 90% confidence level, the t-value is 1.796.

The left boundary of the confidence interval is:

65.80 - (1.796 * (1.95 / √(12))) = 64.77 inches (rounded to two decimal places)

b) The right boundary of the confidence interval is:

65.80 + (1.796 * (1.95 / √(12))) = 66.83 inches (rounded to two decimal places)

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Answer:

6.3x+8.1 simplify

Step-by-step explanation:

Answer:

8 + 4

Step-by-step explanation:

It is a fact family.

Answer:

12= 4+8

Step-by-step explanation:

Answer:

\(2x+1\)

Step-by-step explanation:

Use the rise over run method.

\(\frac{rise}{run}\) = \(\frac{2}{1}\)

To find the y-intercept, look where the line crosses on the y-axis. In this case, the line crosses on 1.

Now plug in the numbers:

\(y=mx+b\)

m = slope

b = y-intercept

\(y=2x+1\)

\(2x+1\)

Hence the equation of the line is, \(2x+1\).

The sampling error is usually smaller with larger samples and decreases as the sample size increases.

When we talk about sampling error, we refer to the discrepancy or difference between the sample statistic (e.g., mean, proportion) and the population parameter it is intended to estimate. The sampling error arises due to the inherent variability in the data and the fact that we are working with a sample rather than the entire population.

By increasing the sample size, we are capturing a more extensive representation of the population, reducing the impact of random variation. As a result, the estimate tends to be more accurate and closer to the true population parameter.

Therefore, larger samples tend to have smaller sampling errors.

It's important to note that although increasing the sample size generally reduces sampling error, there may be other factors to consider, such as the sampling design, representativeness of the sample, and the quality of data collection, which can also influence the accuracy of the estimate.

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The equation for the transformed logarithm that passes through the points (3,0) and (0,2) can be written as f(x) = -b * log(base a)(x - h) + k, where a, b, h, and k are constants to be determined.

To find the equation for the transformed logarithm, we need to use the given points (3,0) and (0,2) to determine the values of a, b, h, and k. Let's start with the point (3,0). Plugging the x-coordinate (3) into the equation, we have:

0 = -b * log(base a)(3 - h) + k

Next, we'll use the point (0,2) to obtain another equation. Plugging the x-coordinate (0) into the equation, we get:

2 = -b * log(base a)(0 - h) + k

Simplifying these equations, we have a system of equations to solve for a, b, h, and k. However, since the equation involves a logarithm, we need more information to determine the specific values of a, b, h, and k.The transformed logarithm function includes transformations such as vertical stretches/compressions (b), horizontal shifts (h), and vertical shifts (k). Without more specific information about these transformations or the base of the logarithm, it is not possible to determine the equation uniquely.

In general, the equation for a transformed logarithm can be written as f(x) = -b * log(base a)(x - h) + k, where a, b, h, and k are constants determined by the specific transformations applied to the logarithm function. It's important to have additional information or instructions to determine the values of a, b, h, and k and provide an equation that accurately represents the given transformed logarithm.

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C and D are parallel line because ∠1 and ∠5 are congruent.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, vertically opposite angles, linear angles, same side interior angles etc

Therefore, the measure of ∠1, ∠4, and ∠5 are 120 degrees.  The measure of ∠7 is ∠60 degrees.

Therefore, let's find if the line c and d are parallel.

Yes c and d are parallel because ∠1 and ∠5 are congruent.

∠1 and ∠5 are corresponding angles.

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The return value of the function call round(3.14159, 3) is c. 3.14. The round function rounds the first argument (3.14159) to the number of decimal places specified in the second argument (3). In this case, it rounds to 3.14.

The function call in your question is round(3.14159, 3). The "round" function takes two arguments: the number to be rounded and the number of decimal places to round to. In this case, the number to be rounded is 3.14159 and the desired decimal places are 3.

The return value is the result of the rounding operation. In this case, rounding 3.14159 to 3 decimal places gives us 3.142.

So, the correct answer is:

b. 3.142

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0.0188 is the probability of obtaining a sample of 1012 adults in which 67% or fewer say they drink the cereal milk.

The value reduced by the mean, divided by the standard deviation, is the z-score:

Z = x - μ / σ

= \(\frac{0.67 - 0.70}{0.0144}\)

≈ - 2.08

Using table A, calculate the corresponding probability:

P(X ≤ 67 % )

= P (Z < -2.08)

=0.0188

As a result, we highlight that this is an uncommon conclusion given the extremely low chance.

The likelihood that something will happen is what is commonly referred to as probability. We can talk about the chance or likelihood of various outcomes when we don't know how such an event will turn out. Events that match a probability distribution are the subject of statistics. Potential is described by probability. This branch of mathematics examines the probability of a random event. The value's range is 0 to 1.

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Answer:

9 feet

Step-by-step explanation:

3X3=9 feet therefore 3 yards is equal to 9 feet

the height of the building is approximately 732.7 feet.

The tangent function is a trigonometric function that relates the ratio of the lengths of the opposite and adjacent sides of a right triangle to the angle between them. Specifically, for an acute angle theta in a right triangle, the tangent of theta is defined as:

tan(theta) = opposite/adjacent

We can use the tangent function to find the height of the building.

Let h be the height of the building. Then, we have:

tan(8 degrees) = h/1 mile

We can solve for h by multiplying both sides by 1 mile:

h = 1 mile * tan(8 degrees)

Using a calculator, we get:

h ≈ 0.139 miles

To convert this to feet, we can multiply by the conversion factor 5280 feet/mile:

h ≈ 0.139 * 5280 feet

h ≈ 732.72 feet

Therefore, the height of the building is approximately 732.7 feet.

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Answer:

The displacement of the dog which is the shortest distance between the two points is 5 meters 53.13° North of East

Step-by-step explanation:

The given parameters are;

The dog's displacement due East = 3 meters

The dog's displacement due North = 4 meters

The displacement, D motion of the dog can be written in vector form as follows;

D = 3i + 4j

The magnitude of the displacement is given as follows;

\(\left | D\right | = \sqrt{(3 \ meters)^2 + (4 \ meters)^2} = \sqrt{25 \ meters^2} =5 \ meters\)

The displacement is the shortest distance between two points

The direction is given tan⁻¹(4/3) = 53.13° North of East

The displacement of the dog which is the shortest distance between the two points = 5 meters 53.13° North of East.

With a mass of 210.0 g and a density of 10.5 g/ml, the volume is calculated to be 20 ml.

To calculate the volume of the silver nugget, we can use the formula:

Volume = Mass / Density

Given that the mass of the silver nugget is 210.0 g and the density of silver is 10.5 g/ml, we can substitute these values into the formula to find the volume.

Volume = 210.0 g / 10.5 g/ml

Volume = 20 ml

Therefore, the volume of the silver nugget is 20 ml.

In summary, the volume of the silver nugget is found by dividing its mass by its density. In this case, with a mass of 210.0 g and a density of 10.5 g/ml, the volume is calculated to be 20 ml.
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The coordinate of the centroid of the given triangle will be at (-2.33,5).

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The given triangle with vertices has been drawn.

The midpoint of H( – 6, 3) and F(1, 5) will be as,

x = (-6 + 1)/2 = -2.5

y = (3 + 5)/2 = 4 so D(-2.5,4)

The coordinate of the centroid will intersect 2:1 of the median from the vertex side.

Thus by intercept formula,

x = (2 × -2.5 + 1 × -2)/(2 + 1) and y = (2 × 4 + 1 × 7)/(2 + 1)

x = -2.33 and y = 5

So the coordinate of vertices will be (-2.33,5).

Hence "The specified triangle's centroid's coordinate will be at (-2.33,5)".

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Answer: the three given points are the vertices of a triangle. solve the triangle, rounding lengths tot he nearest tenth and angle measures to the nearest degree A(0,0) B(-3,5) C(3,-2)

***

Plot given points to form a triangle with angle A at (0,0), B at (-3,5) and C at (3,-2).

Using distance formula:

AB=√(0+3)^2+(0-5)^2)=√(9+25)=√34

AC=√(0-3)^2+(0+2)^2)=√(9+4)=√13

BC=√(-3-3)^2+(5+2)^2)=√(36+49)=√85

..

Law of cosine: c^2=a^2+b^2-2abcosA

(BC)^2=(AB)^2+(AC)^2-2*AB*ACcosA

√85^2=34+13-2*√34*√13cosA

85=47-2√442cosA

38=-42cosA

cosx=-38/42

A=154.8˚

..

using law of sin:

BC/sin(154.8˚)=AC/sinB

sinB=AC*sin(154.8˚)/BC=0.1665

B=9.6˚

..

BC/sin(154.8˚)=AB/sinC

sinC=AB*sin(154.8˚)/BC=0.2693

C=15.6˚

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

because if you add 18, 4 times or 18 x 4 it will give your 72

hope this helps

Jonathan and Oscar will have the same amount of money saved after  2 weeks.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

An equation in math is an equality relationship between two expressions written on both sides of the equal to sign.

For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7. There are different types of equations like linear, quadratic, cubic, etc.

If they have same amount of money then,

f(x) = g(x)

18x+5 = 8x+25

10x = 20

x = 2 weeks

Therefore, Jonathan and Oscar will have the same amount of money saved after  2 weeks.

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The 95% confidence interval for the proportion of voters planning to vote for the incumbent candidate is approximately 0.536 to 0.664.

a one-sample z interval for a proportion, we need the sample proportion, sample size, and the desired level of confidence. Let's use the given information to calculate the confidence interval.

Sample proportion (p(cap)) = 60% = 0.60 Sample size (n) = 150

Let's assume a desired level of confidence of 95%. This means we want to construct a 95% confidence interval.

To construct the interval, we follow these steps:

The standard error (SE) of the sample proportion: SE = √(p(cap) × (1 - p(cap)) / n)

SE = √(0.60 × 0.40 / 150)

The critical value (z) corresponding to the desired level of confidence. For a 95% confidence interval, the z value is approximately 1.96. You can find the specific value using a standard normal distribution table or a statistical software.

The margin of error (ME)

ME = z × SE

ME = 1.96 × SE

The lower and upper bounds of the confidence interval:

Lower bound = p(cap) - ME

Upper bound = p(cap) + ME

Lower bound = 0.60 - ME

Upper bound = 0.60 + ME

Now, substitute the calculated values into the formulas

SE = √(0.60 × 0.40 / 150)

ME = 1.96 × SE

Lower bound = 0.60 - ME

Upper bound = 0.60 + ME

Calculate the values to find the confidence interval

SE ≈ 0.0326

ME ≈ 0.064

Lower bound ≈ 0.60 - 0.064 ≈ 0.536

Upper bound ≈ 0.60 + 0.064 ≈ 0.664

Therefore, the 95% confidence interval for the proportion of voters planning to vote for the incumbent candidate is approximately 0.536 to 0.664.

The sample size is 150, and 60% of the selected voters (0.6 × 150 = 90 voters) plan to vote for the incumbent candidate. Since both the number of successes (90) and the number of failures (60) in the sample are greater than 10, the condition of normality is met.

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The number of students  that are studying abroad in 2001 is 150.38 thousand

The number of students that are studying abroad in 2018 is 467.53 thousand

The given equation that represents the growth in the number of students that are studying abroad is known as an exponential equation. An exponential equation is a non-linear equation.

The given exponential equation is 123.1(1.069)^x

Where:

Number of students studying abroad in 2001 = 123.1(1.069)^3= 150.38 thousand

Where x = 2001 - 1998 - 3

Number of students studying abroad in 2018 = 123.1(1.069)^20 = 467.53 thousand

Where x = 2018 - 1998 = 20.

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Answer:

The answer will be

= -11, -1, √5, 3, 13

Please mark me as the brainliest.

The measures of the angles are ∠1 = 127°, ∠2 = 53°, ∠3 = 127°, ∠4 = 37°, ∠5 = 53°, ∠6 = 90°, ∠7 = 37°, ∠8 = 143°, ∠9 = 37° and ∠10 = 143°

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

The transversal lines and the other lines

So, we have

∠1 = 180 - 53

Evaluate

∠1 = 127°

Also, we have

∠5 = 53°

By vertical angles, we have

∠2 = 53°

∠3 = 127°

Next, we have

∠4 = 127 - 90°

∠4 = 37°

Solving further, we have

∠6 = 90°

By corresponding angles, we have

∠7 = 37°

∠9 = 180 - 90 - 53°

∠9 = 37°

∠10 = 90 + 53°

∠10 = 143°

∠8 = 143°

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Answer:

These two triangles are congruent.

Step-by-step explanation:

You know this bc the markings on the drawing show that Angle B and Angle D are congruent. Also that AB is parallel to CD. This means that Angle BAC and Angle DCA are congruent by ALTERNATE INTERIOR ANGLES. Also, AC is congruent to itself. That makes the two triangles congruent by ANGLE-SIDE-ANGLE.

Now, you need to know that "congruent" triangles (and shapes in general) are the same size and shape. "Similar" triangles (shapes) are the same shape but not necessarily the same size.

We choose option B: The P-value gives strong evidence against H_0. The P-value indicates that the null hypothesis is not plausible.

a. To find the test statistic z, we use the formula:

z = (p - P) / sqrt [P(1-P) / n]

where p is the sample proportion, P is the hypothesized proportion under the null hypothesis, and n is the sample size.

Plugging in the values given, we get:

z = (0.43 - 0.5) / sqrt [0.5(1-0.5) / 100] = -1.96

b. To find the P-value for H_a: p < 0.50, we look up the probability of getting a z-score less than -1.96 in a standard normal distribution table. The P-value is the area under the standard normal curve to the left of -1.96.

The P-value is approximately 0.025.

c. Since the P-value is less than the significance level of 0.05, we can reject the null hypothesis at the 5% level of significance. The P-value gives strong evidence against H_0. Therefore, we choose option B: The P-value gives strong evidence against H_0. The P-value indicates that the null hypothesis is not plausible.

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In standard form, this third-order polynomial - call it p(x) - has real coefficients a, b, c, d so that it is written as

p(x) = a x ³ + b x ² + c x + d

We're told the leading coefficient is a = 1, so

p(x) = x ³ + b x ² + c x + d

Since the coefficients are all real, any complex roots with non-zero imaginary part occurs alongside its complex conjugate, so the fact that -2 + i is a root means that its conjugate, -2 - i is also a root.

Then by the factor theorem, we can write p(x) as the product of linear terms involving its roots:

p(x) = (x - (-2 + i )) (x - (-2 - i )) (x - 7)

Now just expand this to get

p(x) = x ³ - 3 x ² - 23 x - 35