Greg builds a new pond which has a volume of 7.35m3, it is 4.2m long and 50cm deep, what is the width of the pond

Yesenia swims laps at a pool. For every 10 laps she swims the backstroke, she swims 15 laps of freestyle.

Svet_ta [12734]

Response:

A 2:3

Detailed Explanation:

10:15

which is equivalent to 10/15

which simplifies to 2/3

I hope this assists you

<3

Red

4 0

26 days ago

Read 2 more answers

(a) For what values of k does the function y = cos(kt) satisfy the differential equation 81y'' = −4y? (Enter your answers as a c

tester [12383]

Answer:

$k = \frac{2}{9}, k=\frac{-2}{9}$

Step-by-step explanation:

The initial scenario is a specific case of the subsequent one, so we will address the second case first.

Consider $y = A\sin(kt) + B\cos(kt)$ . Through the utilization of derivatives and trigonometric function properties, it is determined that

$y' = A\cdot k \cos(kt)- B \cdot k \sin(kt) = k (A\cos(kt)-B\sin(kt))$

$y'' = k(-A\cdot k \sin(kt)-B\cdot k \cos(kt)) = -k^2(y)$

The equation is represented as $81y''=-4y$ . It's important to note that since $y'' = -k^2y$ it leads to the equation

$-k^2 81y=-4y$ ,

which signifies that $k^2 = \frac{4}{81}$ . Consequently, $k=\pm\frac{2}{9}$

It's notable that in this instance, the value of k is independent of A and B. Thus, it applies universally to any values of A and B. The first scenario is included since it corresponds to A=0 and B=1.

5 0

1 month ago

From past experience, a company has found that in carton of transistors: 92% contain no defective transistors 3% contain one def

zzz [12365]

To determine the variance, we need to first calculate the second moment as follows: The variance can be determined using this equation: The standard deviation is simply the square root of the variance, which gives us the result.

8 0

1 month ago

The graphs below have the same shape. What is the equation of the blue graph?

AnnZ [12381]

Answer: OPTION B

Step-by-step explanation:

The red graph depicts the fundamental form of a quadratic function (the most basic version), with its vertex located at the origin.

The function g(x) results from moving the parent function 2 units to the right and 1 unit upwards.

As a consequence, considering this, the transformation takes the following structure:

$g(x)=(x-h)^2+k$

The horizontal displacement is dictated by the value of h, while the vertical shift is determined by k.

<pThus, the resulting function is:

$g(x)=(x-2)^2+1$

5 0

1 month ago

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Student researchers Haley, Jeff, and Nathan saw an article on the Internet claiming that the average vertical jump for teens was

tester [12383]

Answer:

At the α = 0.10 level, there is no substantial evidence indicating that the average vertical jump for students at this school differs from 15 inches.

Step-by-step explanation:

A hypothesis test is necessary to verify the assertion that the average vertical jump of students diverges from 15 inches.

The null and alternative hypotheses are:

$H_0: \mu=15\\\\H_a: \mu\neq15$

The significance level is set at 0.10.

The sample mean recorded is 17, and the sample standard deviation is 5.37.

The degrees of freedom are calculated as df=(20-1)=19.

The t-statistic is:

$t_{19}=\frac{M-\mu}{s_M/\sqrt{n}} =\frac{17-15}{5.37/\sqrt{20}}=\frac{2}{5.37/4.47} =2/1.20=1.67$

The two-tailed P-value corresponding to t=1.67 is P=0.11132.

<pSince this P-value exceeds the significance level, the result is not significant. Therefore, the null hypothesis remains unchallenged.

At the α = 0.10 level, there is no compelling evidence that the average vertical jump of students at this school deviates from 15 inches.

7 0

1 month ago