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10 days ago

Which equation could be used to find the length of the hypotenuse ?

Mathematics

2 answers:

PIT_PIT [12.4K]10 days ago

4 0

The equation is: 2² + 5² = c²
Step-by-step explanation:
To ascertain the hypotenuse length of a right triangle, the Pythagorean theorem can be expressed as: a² + b² = c², where c symbolizes the hypotenuse's length, and a and b denote the lengths of the other two triangle sides.
In this scenario, a = 2, b = 5, and c = c, thus according to the Pythagorean theorem:
2² + 5² = c².

Inessa [12.5K]10 days ago

3 0

The Pythagorean theorem is a foundational principle. Given that 2 and 5 represent the lengths of the legs while c denotes the hypotenuse, the relevant equation would be stated as such, corresponding to the first option.

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Which graph represents a reflection of f(x) = 6(0.5)x across the x-axis?

Inessa [12570]

The blue line depicted in the attached image illustrates the reflection of f(x) across the x-axis. To elucidate, the function f(x) is an exponential function displaying the characteristics: the y-intercept calculates as f(0) = 6(0.5)⁰ = 6; the multiplicative rate of change is 0.5, signifying a decay function (decreasing); and the horizontal asymptote exists at y = 0, defining the limit of f(x) as x approaches positive infinity. The reflection across the x-axis for f(x) results in a function denoted as g(x) = -f(x), leading to g(x) reflecting the features discussed including growth into the third quadrant while never intersecting the x-axis. Therefore, using these insights, it is feasible to sketch the corresponding graph across the x-axis.

5 0

9 days ago

Read 2 more answers

An experiment was conducted to record the jumping distances of paper frogs made from construction paper. Based on the sample, th

tester [12383]

Answer:

$9.9676 - 2.326*0.5904 =8.594$

$9.9676 + 2.326*0.5904 =11.341$

Step-by-step explanation:

Notation

$\bar X$ is the sample mean

$\mu$ indicates the population mean (the variable of interest)

s signifies the sample standard deviation

n denotes the sample size

Solution to the problem

The mean's confidence interval is derived from the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In this instance, the 9% confidence interval corresponds to:

$8.8104 \leq \mu \leq 11.1248$

We can determine the mean using the following:

$\bar X = \frac{8.8104 +11.1248}{2}= 9.9676$

Additionally, the margin of error can be calculated as:

$ME= \frac{11.1248- 8.8104}{2}= 1.1572$

The margin of error for this situation is expressed as:

$ME = t_{\alpha/2}\frac{s}{\sqrt{n}} = t_{\alpha/2} SE$

Next, we find the standard error:

$SE = \frac{ME}{t_{\alpha/2}}$

The critical value for a 95% confidence interval using a normal standard distribution is roughly 1.96, and substituting gives us:

$SE = \frac{1.1572}{1.96}= 0.5904$

For the 98% confidence interval, the significance corresponds to $\alpha=1-0.98= 0.02$ and $\alpha/2 = 0.01$ with a critical value of 2.326, yielding a confidence interval of:

$9.9676 - 2.326*0.5904 =8.594$

$9.9676 + 2.326*0.5904 =11.341$

8 0

1 month ago

If rs 500 amounts to Rs 725 at 9% simple interest in sometime ,what will Rs 600amount to at 11% in same time?

AnnZ [12381]

Answer:

$Rs\ 930$

Step-by-step explanation:

The formula for calculating simple interest is

$A=P(1+rt)$

Here,

A refers to the Total Amount of Investment

P denotes the Initial Investment

r indicates the interest rate

t represents the duration in time periods

step 1

Determine the duration t

For this scenario, we have

$t=?\ years\\ P=Rs\ 500\\ A=Rs\ 725\\r=0.09$

Plugging into the formula above and solving for t

$725=500(1+0.09t)$

$t=[(725/500)-1]/0.09$

$t=5\ years$

step 2

What will Rs 600 grow to at 11% over the same duration?

We have

$t=5\ years\\ P=Rs\ 600\\ A=?\\r=0.11$

Insert into the formula

$A=600(1+0.11*5)$

$A=600(1.55)$

$A=Rs\ 930$

6 0

1 month ago

data was collected at a tennis court. it showed that being older implies that a player will stay for a shorter length of time. w

AnnZ [12381]

Answer:

A relationship exists between age and duration of stay; however, causation has not yet been established. Additional research would be necessary to clarify this matter.

Step-by-step explanation:

The answer was checked

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27 days ago

A rectangular prism with integer side lengths has a height of $3$. If the surface area of the prism is equal to $52$, then what

lawyer [12517]

The given details include: Height of the rectangular prism, h = 3 units, Surface area of the prism, A = 52 sq units. We need to determine the volume of the prism. The volume of a rectangular prism can be calculated using the formula: l = length and b = breadth. Given that the surface area of the prism, A = lb, we have it equal to 52 sq units. Consequently, the volume is 156 cubic units.

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1 month ago