Utility workers need to reach the roof of a 32 foot building by using an
extended ladder. The ladder can extend to 40 feet. What angle of elevation
do the workers need place the ladder so that the top reaches the building's
roof line?

Answer:

8000

Step-by-step explanation:

80 i think............

Given the inequalities

(-4 -x)(x+7)(x-3) >0

Step 1: Find the zeros of the polynomials

For (-4 -x)

For (x+7)

For (x-3)

Step 2: Draw the range of values on a number line

Step 3: Construct a table to test the range

The table tests the ranges that were obtained from the number line

column 1 shows the range

The values are then tested for each range.

Column 6 shows the product of all the values gotten

The solution to the polynomial is that which was accepted

Since the inequality sign is that of a greater sign, we will accept those that are positive

Hence the solution is

Answer:

0.41666666666

Step-by-step explanation:

Answer:

The value is 5/12

Answer:

20 people

Step-by-step explanation:

if 6 ppl 30%

then the 100% equals to

6 × 100% ÷ 30% = 20 ppl

Answer:

20 ppl

Step-by-step explanation:

Answer:

y = 2

Step-by-step explanation:

Hi there!

\(2y=7(y-2)+4\)

\(2y=7y-14+4\\2y=7y-10\\0=5y-10\\5y=10\\y=2\)

I hope this helps!

Step-by-step explanation:

2y = 7(y-2) + 4

→ 2y = 7y - 14 + 4

→ 2y = 7y - 10

→ 2y - 7y = -10

→ - 5y = -10

Therefore, y = 10:5 = 10/5 = 2 Ans.

Answer:

Clare failed to flip the inequality when dividing by a negative number

Step-by-step explanation:

-4x+3 < 23

Subtract 3 from each side

-4x+3-3 < 23-3

-4x < 20

Divide each side by -4, remembering to flip the inequality

-4x/-4 > 20/-4

x > -5

Clare failed to flip the inequality when dividing by a negative number

The number of sets is 128 by using the multiplication principle.

The multiplication principle states that if there are k events, and if the first event can happen in n_1 ways, the second event can happen in n_2 ways, and so on, then the k events can happen in n_1 × n_2 × ... × n_k ways.

To find the number of sets of four marbles include one of each color other than lavender, A bag contains two red marbles, four green ones, one lavender one, four yellows, and four orange marbles.

There are two red marbles.

There are four green ones.

There are four yellows.

There are four orange marbles.

So, total of 2 + 4 + 1 + 4 + 4 = 15 marbles in the bag.

To find the total number of sets of four marbles including one of each color other than lavender, use the multiplication principle.

In this question, there are 5 events (choosing one of each color).

The first event can happen in 2 ways.

The second event can happen in 4 ways.

The third event can happen in 4 ways.

The fourth event can happen in 4 ways.

Therefore, by the multiplication principle, the total number of sets of four marbles includes one of each color other than lavender

= 2 × 4 × 4 × 4 ⇒ 128 sets.

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Answer:

Average rate of change = 5

Step-by-step explanation:

Using the triangle inequality theorem, the largest possible whole-number length for the third side is 4.

The third side of a triangle must be shorter than the sum of the other two sides and longer than the difference between the other two sides.

So, for a triangle with sides of length 1, 4, and x (where x is the length of the third side), we have:

1 + 4 > x

4 + x > 1

1 + x > 4

Simplifying these inequalities, we get:

5 > x

x > 3

x > -3 (this inequality is always true)

The largest possible whole-number length for the third side is 4, since it is the largest integer that satisfies the above inequalities.

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Therefore , the solution of the given problem of inequality comes out to be the inequality x -5 is option B.

Regardless of the equal symbol, a connection or group of numbers variables can be an inequality in mathematics. Equilibrium is always followed by equity. Inequality happens when ideals are still incompatible. Differences exist between inequality expression and fairness. We chose to utilize the most prevalent symbol because elements aren't always similar or comparable (). No mater how few or many variations there are, they can all be used to evaluate values.

Here,

Option B) B is the proper response.

We must isolate x on one side of the inequality in order to answer the inequality x + 2 -3. By taking 2 away from both edges, we arrive at:

=> x < -5

According to this inequality, x is any integer that is less than -5. Since x cannot equal -5,

we must create an open circle at this point on the number line and shade to the left of it to represent all the different values of x that could be used.

Looking at the available choices, we can see that the only graph that accurately depicts the inequality x -5 is option B) B.

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Based on the information, we can conclude that we have a 5% chance (probability) of getting 1 in this test of throwing the dice 50 times.

Taking into account the results of the graph, we can establish the probability of getting the number 1 in the 50 throws made. To do this, we must perform the following procedure:

In accordance with the above and based on the results of the test we can establish that we have a 5% probability of getting 1. This could be expressed as a 0.05 probability, in which 0 is not at all likely and 1 is very likely.

Note: This question is incomplete because there is some information missing. Here is the complete information:

Image attached

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If two triangles, A and B, are proportional, this means that exists some number k such that:

We know that:

Triangle A:

BaseA = 10cm

HeightA = 8cm

Triangle B:

BaseB = 15cm

HeightB = x

Then, we can find k by:

And solve:

Now that we know the value of k, we can find the unknown height:

Thus, the answer is:

The height of the second triangle is 12cm

The equation model of the given statement in question is 6 + 7× x.

The model of equation is defined as the model of the given situation in the form of an equation using constants and variables.

In math, it deals with numbers of operations given according to the statements. The four major arithmetic operators are, addition, subtraction, multiplication, and division.

Given that;

6 is added to product of a number and 7

Now,

Let, the number multiplied by 7 be x,

=7*x

6 is added to the product;

= 6 + 7 × x

Therefore, the equation of model will be given as 6 + 7 × x;

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To determine whether the series ∑(n=1 to ∞) 1/(n+2) is convergent or divergent, we can use the Integral Test. By evaluating the integral ∫(1/(x+2)) dx from 1 to ∞, we find that the integral converges. Therefore, the given series is also convergent.

The Integral Test states that if f(x) is a continuous, positive, and decreasing function on the interval [1, ∞) and if the series ∑(n=1 to ∞) f(n) is represented by the integral ∫(f(x)) dx from 1 to ∞, then the series and integral either both converge or both diverge.

In this case, the series is ∑(n=1 to ∞) 1/(n+2). To apply the Integral Test, we evaluate the integral ∫(1/(x+2)) dx from 1 to ∞. The integral is given by:

∫(1/(x+2)) dx = ln|x+2| + C

To find the value of the integral from 1 to ∞, we evaluate ln|x+2| at the limits of integration:

ln|∞+2| - ln|1+2| = ln(∞) - ln(3)

Since ln(∞) is infinity and ln(3) is a finite value, the integral evaluates to infinity.

Since the integral diverges, by the Integral Test, the series ∑(n=1 to ∞) 1/(n+2) also diverges.

Therefore, the given series is divergent.

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To show that (A^-1) = A for A = [[3, 7], [-a, -1]], we can find the inverse of matrix A and then compare it to matrix A itself.

The formula for finding the inverse of a 2x2 matrix A = [[a, b], [c, d]], where D = ad - bc ≠ 0, is: A^-1 = (1/D) * [[d, -b], [-c, a]], where D is the determinant of matrix A.
For the given matrix A = [[3, 7], [-a, -1]], we can compute the determinant: D = (3 * -1) - (7 * -a) = -3 + 7a. Since D ≠ 0 (assuming a ≠ 0), we can proceed to find the inverse: A^-1 = (1/D) * [[-1, -7], [a, 3]].

Comparing A^-1 to A, we see that they are not equal. Therefore, the statement (A^-1) = A is not true for the given matrix A. A step-by-step approach to determine whether the given matrix A is equal to its inverse (A^-1). It begins by stating the formula for finding the inverse of a 2x2 matrix and then applies it to the given matrix A. By computing the determinant and finding the inverse, it is demonstrated that the inverse of A is not equal to A, indicating that the statement (A^-1) = A is false.

The explanation highlights the key calculations and concepts involved in determining the validity of the statement.

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We have a basket and a hat.

The basket has the numbers 1, 2, 3, 4 and 5.

The hat contains the letters A, B, C and D.

We have to calculate the probabiltiy of drawing a number that is greater than 3 from the basket and drawing the letter C from the hat.

We have two events:

- Drawing a number greater than 3 from the basket

- Drawing a C from the hat

They are independent as the probability of each on does not depend on the outcome of the other event.

Then, we can calculate the probability of the two events happening together as the product of its probabilities:

The probability of drawing a number greater than 3 can be described as 2/5, as we have 2 numbers greater than 3 (4 and 5) out of 5 numbers in the basket.

The probability of drawing a letter C can be described as 1/4, as we have one letter C out of 4 letters available.

Then, we can calculate the probability as:

Answer: the probability is 1/10 or 0.1.

Answer:

b x 3 +6  =4

Step-by-step explanation:

To evaluate the definite integral of f(g(4)) - f(g(2)), we need to consider the composition of functions and the Fundamental Theorem of Calculus.

Let's break down the steps to find the definite integral: Evaluate g(4) and g(2) using the function g. Substitute the values of g(4) and g(2) into the function f. Find the antiderivative of f(g(x)) with respect to x, denoted as F(g(x)). Apply the Fundamental Theorem of Calculus, which states that the definite integral of F'(x) from a to b is equal to F(b) - F(a), where F'(x) is the derivative of F(x).

Evaluate F(g(4)) - F(g(2)) using the antiderivative F(g(x)). Note that the expression F(g(4)) - F(g(2)) represents the change in the antiderivative F(g(x)) over the interval from g(2) to g(4). Therefore, the definite integral for f(g(4)) - f(g(2)) is F(g(4)) - F(g(2)).

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Answer:

y=13

Step-by-step explanation:

Answer:

Step-by-step explanation:

those are vertical angles so are congruent

9y +7 = 2y +98; subtract 2y and 7 from both sides

9y- 2y = 98 -7; combine like terms

7y = 91 ; divides both sides by 7

y= 13

Abby did not make a square corner because the rectangle is about 0.888 feet longer on one diagonal than the other diagonal

To determine whether Abby made a square corner, lets use the Pythagorean theorem, which states that for a right triangle with legs of length a and b and hypotenuse of length c, we have:

c^2 = a^2 + b^2

Lets use the theorem to check if the diagonal (c) is the hypotenuse of a right triangle with sides of length 4 feet and 5 feet.

Lets convert the length of the diagonal from inches to feet:

76 inches = 76/12 feet = 6.333... feet (rounded to the nearest thousandth)

Now, we can use the Pythagorean theorem to check if the sides of the rectangle form a right triangle:

c^2 = a^2 + b^2

(6.333... feet)^2 = (4 feet)^2 + (5 feet)^2

40.111... feet^2 = 16 feet^2 + 25 feet^2

40.111... feet^2 = 41 feet^2 (rounded to the nearest thousandth)

Since the equation is not true, Abby did not make a square corner.

This means that the rectangle is about 0.888 feet longer on one diagonal than the other diagonal

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a) The null hypothesis (H0) in this case would be that the median household income in Atlanta did not change between 1999 and 2003. The alternative hypothesis (Ha) would be that the median household income in Atlanta increased over the same period.

b) To test this, we can use a box model. The box represents the distribution of incomes in 1999, and the alternative hypothesis suggests that the median income in 2003 shifted to the right. We can calculate the z-score for the sample proportion (56%) using the formula z = (p - P0) / sqrt(P0(1-P0)/n), where p is the sample proportion, P0 is the hypothesized population proportion (52%), and n is the sample size. This will give us the test statistic.

To calculate the p-value, we can use the standard normal distribution table or a calculator to find the area under the curve beyond the test statistic. The p-value represents the probability of observing a sample proportion as extreme as the one we found, assuming that the null hypothesis is true.

c) If the p-value is smaller than a pre-determined significance level (e.g., 0.05), we would reject the null hypothesis. This would suggest that there is sufficient evidence to conclude that the median household income in Atlanta did increase between 1999 and 2003. If the p-value is larger than the significance level, we would fail to reject the null hypothesis and would not have enough evidence to conclude that the median household income increased.

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B. ordered pair (-4,1); y-intercept -5

Step-by-step explanation:

To find the y-intercept, you see which “Y” number has a 0 as their “x” value.

We can see (0,5) on top red dot.

The ordered pair would be that other red dot, the x value is -4 and the y value is 1.

By the way, x = the horizontal numbers, y = vertical numbers.

The expected weekly bonus for the workers is $20.

Given that each worker gets a bonus every Friday with an amount of probabilities $10-0.75, $50-0.25. We are to determine the expected weekly bonus.

Expected value is the weighted average of all possible values. The formula to find the expected value is as follows:

Expected Value = ∑ (value × probability)

Thus, the expected value of the weekly bonus can be calculated as follows:

Expected weekly bonus = (10×0.75) + (50×0.25) = 7.5 + 12.5 = $20

Therefore, the expected weekly bonus for the workers is $20.

Note: Expected value helps to determine the average value of a random variable. It is a theoretical value that represents the average amount one can expect to win or lose on an average on a given bet if it were repeated many times.

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When the bananas cost 3 IBS for $1.10, the cost for six Bananas is $2.20.

From the information, bananas cost 3 IBS for $1.10, In this his case, the first thing to do is to calculate the price for each. This will be:

= $1.10 / 3

= $0.367

Therefore the cost for six bananas will be:

= Cost for each banana × Number of banana

= $0.367 × 6

= $2.20

The cost is $2.20.

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The difference between the lowest price in store 1 and the lowest price in store 2 is the result of the key used to identify the store. The difference between the highest prices in store 1 and store 2 is the result of the key used to identify the store, with both stores having the same price.

The difference between the two terms is that "difference" refers to the way in which two or more things are not the same, whereas "difference" is more of a comparison between two or more things.

The difference between the lowest price in store 1 and the lowest price in store 2 is the difference between the first digit of each store's key. In the case of store 1, the key is 110 and the first digit is 1. In the case of store 2, the key is 210 and the first digit is 2. The difference between the two digits is 1.

The difference between the highest prices in store 1 and store 2 is the difference between the last digit of each store's key. In the case of store 1, the key is 110 and the last digit is 0. In the case of store 2, the key is 210 and the last digit is 0. The difference between the two digits is 0.

The difference between the lowest price in store 1 and the lowest price in store 2 is the result of the key used to identify the store. In the case of store 1, the key is 110 and the first digit is 1. In the case of store 2, the key is 210 and the first digit is 2. The difference between the two digits is 1. This difference is reflected in the lowest prices of each store, with store 1 having a lower price than store 2.

The difference between the highest prices in store 1 and store 2 is the result of the key used to identify the store. In the case of store 1, the key is 110 and the last digit is 0. In the case of store 2, the key is 210 and the last digit is 0. The difference between the two digits is 0. This difference is reflected in the highest prices of each store, with both stores having the same price.

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The mass of a single washer can be calculated by dividing the total mass of the box (1.2314 kg) by the number of washers (1000). The mass of a single washer is expressed in milligrams.

To calculate the mass of a single washer, we divide the total mass of the box (1.2314 kg) by the number of washers (1000).

1.2314 kg divided by 1000 washers equals 0.0012314 kg per washer.

To convert the mass from kilograms to milligrams, we need to multiply by the appropriate conversion factor.

1 kg is equal to 1,000,000 milligrams (mg).

So, multiplying 0.0012314 kg by 1,000,000 gives us 1231.4 mg.

Therefore, the mass of a single washer is 1231.4 milligrams (mg).

Note: In scientific notation, this would be written as 1.2314 x 10^3 mg, where the exponent of 3 represents the milli prefix.

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Answer:

955

Step-by-step explanation:

8 squared = 64

x 3 X 5 = 960

-5

= 955