An isosceles right triangle has legs of equal length. If the hypotenuse is 30 centimeters​ long, find the length of each leg.


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Answer:

-8 (or) 5 and 5 (or) -8

Step-by-step explanation:

Let one of the numbers = x

Let other number = y

As the sum of two numbers = -3

x + y = -3

x = -3-y

As the the result of multiplication = -40

xy = -40

(-3-y)*y = -40

-3y-y² = -40

-y²-3y+40 = 0

-(y²+3y-40) = 0

-(y+8)(y-5) = 0

(-y-8)(y-5) = 0

-y-8 = 0 (or) y-5 = 0

-y = 8 (or) y = 5

y = -8 (or) y = 5

when y = -8

x = -3-y

x = -3-(-8)

x = -3+8

x = 5

when y = 5

x = -3-y

x = -3-5

x = -8

Answer:

It is not possible to determine Janet's gross income with the given information. The contribution to the unemployment insurance fund only provides information about a portion of her earnings.

The value of the digit 4 in 46,278 is 4000/400 = 10 times the value of the digit 4 in 24,350.

To calculate the value of a digit in a number, you need to determine its place value. In 46,278, the digit 4 is in the thousands place, which means its value is 4 x 1000 = 4000. In 24,350, the digit 4 is in the hundreds place, which means its value is 4 x 100 = 400.

To find how many times the value of the digit 4 in 24,350 is contained in the value of the digit 4 in 46,278, we simply divide 4000 by 400, which gives us 10. Therefore, the value of the digit 4 in 46,278 is 10 times the value of the digit 4 in 24,350.

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Answer:

(3 houses/acre)(100 acres)(.5) =

150 houses

The remaining land is 50 acres (100-50), and the builder plans to build three houses per acre. So, the number of houses that can be built on this property is (50 x 3) = 150 acres.

First, let's determine how much of the 100-acre plot is left for building houses after setting aside land for the school, playground, roads, drainage ditches, sidewalks, and the strip shopping area with parking and buffer.

1. School and playground: 20% of 100 acres = 0.20 * 100 = 20 acres
2. Roads, drainage ditches, and sidewalks: 15% of 100 acres = 0.15 * 100 = 15 acres
3. Strip shopping area with parking and buffer: 15% of 100 acres = 0.15 * 100 = 15 acres

Now, add up these reserved areas: 20 acres + 15 acres + 15 acres = 50 acres

The builder has set aside 20 acres for the school and playground, 15 acres for roads, drainage ditches, and sidewalks, and another 15 acres for the strip shopping area with parking and buffer. Therefore, the total area that has been allocated is 50 acres (20+15+15).

Subtract the total reserved area from the total plot area to find the area available for building houses: 100 acres - 50 acres = 50 acres

Since the builder plans to build three houses per acre, we can multiply the available area by the number of houses per acre: 50 acres * 3 houses/acre = 150 houses

The builder can build 150 homes on this property.

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The depth of water in tank A is modeled by a differentiable and increasing function h.

This means that the function h describes how the depth of water changes as time passes.

The fact that it is differentiable means that the function has a well-defined slope at every point, which indicates how quickly the depth is changing. This means that the function is continuous and smooth, with no sharp turns or corners.
Furthermore, the fact that the function is increasing means that the depth is always getting higher over time.

This makes sense since water is constantly being added to the tank.

Hence, the depth of water in tank A is described by a differentiable and increasing function h, which means that the function has a well-defined slope at every point and that the depth is always getting higher over time.

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An equation in slope-intercept form for the line is y = 2x - 2.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Based on the information provided about this equation, we have the following slope and y-intercept;

Slope, m = 2.

y-intercept, c = -5.

By substituting the given parameters, we have the following:

y = mx + c

y = 2x + (-2)

y = 2x - 2

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Complete Question:

Find an equation in slope-intercept form for the line: slope 2, y-intercept = -5

Answer: y=[tex]\frac{1}{2}[/tex]x - 2

Step-by-step explanation:

No graphs were shown to choose from but it would look like a line that has a positive slope, goes throuh y-axis at -2 and slope of 1/2

The percentage of students that like country are in grades 9-10 will be 61%. The Option D.

In order to get percentage of students that like country and are also in grades 9-10, we must look at the intersection of the "Country" row and the "Grades 9-10" column which has a frequency of 55.

After that, we will divide the frequency by the total number of students that like country which is (90).

The percentage of students that like country are in grades 9-10 will be:

= (55/90) x 100

= 0.61111111111 * 100

= 61%

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Area of the triangle is 6cm²

Area of the square = 4cm²

Area of the rectangle = 35cm²

Probability of landing in triangle = 13. 3%

Probability of landing in square = 8. 8%

Probability of landing in triangle or square = 22. 2%

Probability of not landing in triangle  = 86. 6%

The formula for calculating the area of a rectangle is expressed with the equation;

Area = lw

Such that;

Area of a triangle = 1/2 × base × height

Substitute the values

Area = 1/2 × 3 × 4

Multiply the values

Area = 6cm²

The area of the square = a²

Area = 2²

Find the square

Area = 4cm²

The area of the rectangle = 7(5)

Multiply the values

Area = 35cm²

Probability of landing in triangle = 6/45 = 0. 13× 100 = 13. 3%

Probability of landing in square = 4/45 = 8. 8%

Probability of landing in triangle or square = 13.3 + 8. 8 = 22. 2%

Probability of not landing in triangle = 39/45 = 86. 6%

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The percent decrease in population over the course of six years is -414%.

When the mortality rate surpasses the fertility rate, population size will diminish with time. This is because a greater number of rabbits dies than are born into the populace, resulting in an overall loss of individuals. With the newly supplied data, when the class of creatures reaches 600, the birth and death ratios will be transposed. Consequently, the fertility rate will outrival the mortality rate, leading to increased population figures.

It should be noted that to figure out the percentage fall in people size, we must measure the final population amount against the initial size. Taking an inaugural quantity of 100 bunnies as a base, it can be deduced that the mass will grow as follows:

Year 1: 200 rabbits (100 multiplied by 2)

Year 2: 400 rabbits (200 multiplied by 2)

Year 3: 600 rabbits (400 multiplied by 1.5)

Year 4: 570 rabbits (600 multiplied by 0.95)

Year 5: 541 rabbits (570 multiplied by 0.95)

Year 6: 514 rabbits (541 multiplied by 0.95)

Subsequently, the percent decrease in population over the course of six years is (100 minus 514) divided by 100 multiplied by 100% equals -414%.

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If an equation is expressed in vertex form, then the vertex can be found by simply reading off the values of the constants h and k. Specifically, the vertex is located at the point (h, k).

To find the axis of symmetry, you can use the equation of symmetry, which is x = h. This represents a vertical line that passes through the vertex and divides the parabola into two symmetric halves.

Answer:

Step-by-step explanation:

The formula is

y=a(x-h)+k

(h,k) is your vertex

h is inside with x, key is to take opposite sign

k is outside so take as is

EX 1.

y=2(x-4)+3

vertex (4, 3)

EX 2.

y=3(x+8)-2

vertex(-8,-2)

For, axis of symmetry, that's where you can fold it in half that happens at your vertex but to describe the line of axis of symmetry that comes from your x value in your vertex

so for

EX1.

x=4   is your axis of symmetry , just take your x value of vertex

EX2

x= -8 for axis of symmetry

2.8

Step-by-step explanation:

17-3=14

So 5x=14

14÷5=2.8

So x=2.8

Answer:

your answer is..15

Step-by-step explanation:

Requried, we can be 95% confident that the true mean time spent by someone in the shower is between 5.172 and 7.227 minutes.

Sample mean (X) = 6.2 minutes

Sample standard deviation (s) = 1.7 minutes

Sample size (n) = 13

Confidence level = 95%

Since the sample size is less than 30, we will use the t-distribution for calculating the confidence interval.

First, we need to find the t-value for a 95% confidence level with 12 degrees of freedom (n-1).

From the t-distribution table, we find the t-value to be 2.179.

Calculate the margin of error (E) using the formula:

E = t×value × (s/√n)

E = 2.179 × (1.7/√13)

E = 1.027

The confidence interval by adding and subtracting the margin of error from the sample mean:

CI = (X - E, X + E)

CI = (6.2 - 1.182, 6.2 + 1.182)

CI = (5.172, 7.227)

Thus, we can be 95% confident that the true mean time spent by someone in the shower is between 5.172 and 7.227 minutes.

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The probability that both marbles are red is 0.33

The probability formula defines the likelihood of the happening of an event. It is the ratio of favorable outcomes to the total favorable outcomes.

P(A) = Number of favorable outcomes/ total no. of possible outcomes

We have the information from the question:

Total marbles are there in bag is = 6

Red Marbles = 2

Green Marbles = 2

Yellow Marbles = 2

To find the probability that both marbles are red.

Now, According to the question:

The probabilities that are desirable for our cases are:

P(RR) = 2/6 = 1/3 = 0.33

Hence, The probability that both marbles are red is 0.33

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Answer:

1: Use the slope formula to find the slope of a line given the coordinates of two points on the line. The slope formula is m=(y2-y1)/(x2-x1), or the change in the y values over the change in the x values.

2: im not suree

Step-by-step explanation:

The graph of function f(x) is a curve that starts at the point (0,1) and grows exponentially as x increases.

We have,

The function f(x) = 2^x has several features:

- Exponential growth:

As x increases, the output of the function f(x) grows exponentially.

This means that the function grows very quickly, and the rate of growth increases as x gets larger.

- Increasing function:

The function f(x) is always increasing, which means that as x increases, so does the value of f(x).

- Continuous function:

The function f(x) is continuous, meaning that there are no breaks or jumps in the graph of the function.

- Domain and range:

The domain of f(x) is all real numbers, and the range of f(x) is all positive real numbers.

- Asymptote:

The function f(x) does not have a horizontal asymptote, meaning that the function grows without bound as x increases.

- Intercept:

The function f(x) has a y-intercept of 1, meaning that f(0) = 1.

Thus,

The graph of function f(x) is a curve that starts at the point (0,1) and grows exponentially as x increases.

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Answer:

The formula for the area of a regular heptagon is:

A = (7/2) * s * a

where:

s = length of one side

a = length of the apothem

Plugging in the given values, we get:

A = (7/2) * 7.0 cm * 7.3 cm

A ≈ 178.715 cm²

Therefore, the area of the given heptagon is approximately 178.715 cm².

By using the level of significance and p-value method with the TI-84 Plus calculator, we can determine if the mean number of dinners changed while the free dessert offer was in effect.

To perform the one-sample t-test on the TI-84 Plus calculator, we need to input the sample data and the null hypothesis. We will use the following steps:

Press STAT and then ENTER to access the list editor.

Enter the sample data into a list.

Press STAT again and then scroll right to TESTS.

Select t-Test and then highlight "Stats."

Enter the sample list name, the null hypothesis, and the level of significance.

Press ENTER and the calculator will output the t-statistic, degrees of freedom, and the p-value.

If the p-value is less than 0.05, we can reject the null hypothesis and conclude that the mean number of dinners changed while the free dessert offer was in effect.

If the p-value is greater than or equal to 0.05, we cannot reject the null hypothesis and conclude that there is insufficient evidence to suggest that the mean number of dinners changed.

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Answer: the answer is 8:1

Step-by-step explanation:

48:6/6

8:1

The main answer to the question is that the distance away from the billboard is approximately 69.5 feet.

To arrive at this answer, we need to use trigonometry. We can set up two right triangles, one for the bottom of the billboard and one for the top. In both triangles, the height of the billboard is the same (30 ft), and the angles of elevation are given (15 and 40 degrees). We can use the tangent function to find the length of the adjacent side (the distance from the billboard), and then use the Pythagorean theorem to find the hypotenuse (the total distance away).

For the bottom of the billboard, we have:

tan(15) = 30/x

x = 30/tan(15)

x ≈ 114.1 ft

For the top of the billboard, we have:

tan(40) = 30/x

x = 30/tan(40)

x ≈ 36.1 ft

To find the total distance away, we can subtract the two distances:

distance away = x - 30 cot(15) - 30 cot(40)

distance away ≈ 69.5 ft

Therefore, we can conclude that the distance away from the billboard is approximately 69.5 feet.

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The equation for the function is d = (1/10)t + 10.

We have,

Let's call the depth of the water in inches "d" and the time in minutes "t".

We know that the pool starts with a depth of 10 inches, and Ellie is adding water at a rate of 3 inches every 30 minutes.

This means that for every 30 minutes, the depth of the water increases by 3 inches.

To write an equation for this function, we can use the slope-intercept form of a linear equation, where "m" is the slope and "b" is the y-intercept:

d = mt + b

In this case, the slope is the rate of increase in depth per minute, which is 3/30 = 1/10 inches per minute.

The y-intercept is the initial depth of the pool, which is 10 inches.

So the equation for the function is:

d = (1/10)t + 10

This equation tells us that after "x" minutes, the depth of the water in the pool will be:

d = (1/10)x + 10 inches.

Thus,

The equation for the function is d = (1/10)t + 10.

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The number of years that coffee makers are covered by warranty is 3.128 years, under the condition that the Manufacturer wants to repair no more than 2. 5% of the coffee makers sold.

In order to solve this problem, we have to find the z-score that corresponds to a probability of 0.025 (2.5%). We need to utilize the standard normal distribution table

The formula derived for z-score is
z = (x - μ) / σ

here
x= value we want to find the probability
μ= mean
σ= standard deviation.
For the given  case, we have to find the value of x such that P(X > x) = 0.025,
Here X is the lifespan of a coffee maker.

Applying a standard normal distribution table  we evaluate that the z-score corresponding to a probability of 0.025 is -1.96.

Now we conduct the formula for z-score to find x:
-1.96 = (x - 4.5) / 0.7
x - 4.5 = -1.372
x = 3.128
The number of years that coffee makers are covered by warranty is 3.128 years.
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Answer: i think its 242

The value of the test statistic is t = -2.15.

To test whether the manufacturer's claim of 31.3 mpg is accurate, we can use a one-sample t-test. The null hypothesis is that the true mean mpg of the van is equal to the manufacturer's claim of 31.3 mpg, while the alternative hypothesis is that the true mean mpg is different from 31.3 mpg.

The test statistic for a one-sample t-test is calculated as

t = (x - μ) / (s / √(n))

where x is the sample mean, μ is the hypothesized population mean (31.3 mpg), s is the known standard deviation, and n is the sample size.

Plugging in the values given in the problem, we get:

t = (31.1 - 31.3) / (1.3 / √(140))

t = -0.2 / (1.1 / 11.83)

t = -0.2 × 10.75

t = -2.15

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The price of the apples and pears at the shop are £0.8 and £0.3, respectively

Given that

So, we have

4x + 3y = 4.10

5x + 8y = 6.40

Where

x = apple and y = pears

When solved graphically, we have

x = 0.8 and y = 0.3

Hence, the price of the apples and pears at the shop are £0.8 and £0.3, respectively

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50

Step-by-step solution:

    0.3x-42=0.1x-32

    -0.1x

    0.2x-42=-32

                   +42

      0.2x=10

               0.2                

        x=50

Answer:V=a3

Step-by-step explanation:

Answer: V=a3

Step-by-step explanation:

According to the binomial distribution concept,

a) The null hypothesis is 0.5

b) The alternative hypothesis is 0.5

c) The value of z - score is 2.131

d) The value of the variable p-value is 0.0326

e)  There is evidence to suggest that the proportion of respondents who believe we should replace passwords with biometric security is significantly different from 0.5.

The null hypothesis is that exactly half of the respondents believe we should replace passwords with biometric security. In other words, the proportion of respondents who believe this is 0.5.

The alternative hypothesis is that the proportion of respondents who believe we should replace passwords with biometric security is significantly different from 0.5.

The test statistic is the z-score, which measures how many standard deviations the sample proportion is from the null hypothesis proportion. In this case, we can calculate the z-score as follows:

z = (p - P) / √(P(1 - P)/n)

where:

p is the sample proportion (0.526)

P is the null hypothesis proportion (0.5)

n is the sample size (454)

Plugging in these values, we get:

z = (0.526 - 0.5) / sqrt(0.5(1 - 0.5)/454)

z = 2.131

To calculate the p-value, we can use a normal distribution table or a calculator. Using a calculator, we find that the area to the right of z = 2.131 is 0.0163. Since this is a two-tailed test, we need to double this value to get the p-value:

p-value = 2(0.0163) = 0.0326

Since the p-value (0.0326) is less than the significance level (0.10), we reject the null hypothesis. Specifically, since the sample proportion is greater than 0.5, we can conclude that more than half of the respondents believe we should replace passwords with biometric security.

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Answer: To solve the problem, we can use algebra. Let x be the number that is subtracted from 8. Then, we can write the equation:

(8 - x) / 5 = 1

To solve for x, we can first multiply both sides by 5:

8 - x = 5

Next, we can isolate x by subtracting 8 from both sides:

x = 3

Therefore, the number that is subtracted from 8 is 3.

Answer:

Darcy can choose 1 pair of earrings out of 16, 1 bracelet out of 11, and 1 ring out of 9. The number of possible combinations is the product of these choices:

16 * 11 * 9 = 1,584

Therefore, Darcy could buy 1,584 different combinations of 1 pair of earrings, 1 bracelet, and 1 ring.