What mathematical term describes both 5.3 and 8.2 in the expression 5.3x-8.2y+11.1?

The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a

AlekseyPX

Answer:

The time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.

Step-by-step explanation:

We are given that the time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds.

The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition.

Let X = time for this event for boys in secondary school

SO, X ~ Normal( $\mu=460,\sigma^{2} =40^{2}$ )

The z-score probability distribution for normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean time = 460 seconds

$\sigma$ = standard deviation = 40 seconds

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, it is given that the fitness association wants to recognize the fastest 10% of the boys with certificates of recognition, which means;

P(X > x) = 0.10 {where x is the required time which boy need to beat}

P( $\frac{X-\mu}{\sigma}$ > $\frac{x-460}{40}$ ) = 0.10

P(Z > $\frac{x-460}{40}$ ) = 0.10

So, the critical value of x in the z table which represents the top 10% of the area is given as 1.2816, that is;

$\frac{x-460}{40} =1.2816$

${x-460}{} =1.2816\times 40$

$x$ = 460 + 51.264 = 511.264 seconds

Hence, the time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.

8 0

3 years ago

Please Help!!!

algol [13]

$f\left(\dfrac\beta2\right)=\sin\dfrac\beta2$

Recall the half-angle identity:

$\sin^2\dfrac\beta2=\dfrac{1-\cos\beta}2\implies\sin\dfrac\beta2=\pm\sqrt{\dfrac{1-\cos\beta}2}$

So in order to find $f\left(\dfrac\beta2\right)$ , we only need to know the value of $\cos\beta$ . But there are two possible values. To decide which to take, we use the given information: we know that $\beta$ lies in quadrant III, which means $\pi$ , so $\dfrac\pi2$ , which places $\dfrac\beta2$ in quadrant II. In this quadrant, the sine of angle is positive, and so

$\sin\dfrac\beta2=\sqrt{\dfrac{1-\cos\beta}2}$

$\beta$ is an angle of a ray whose terminal point, $\left(-\dfrac13,y\right)$ lies on the circle $x^2+y^2=1$ . The $x$ -coordinate is all we need to know in order to find that $\cos\beta=-\dfrac13$ . So,

$\sin\dfrac\beta2=\sqrt{\dfrac{1-\left(-\frac13\right)}2}=\sqrt{\dfrac46}=\dfrac{\sqrt2}{\sqrt3}=\dfrac{\sqrt6}3$

6 0

3 years ago

if cot theta = -24/7 and cos theta < 0, name the quad in which theta lies, then find the exact value of csc theta

NemiM [27]

Cot θ = -24/7 and cos θ < 0

"cos θ < 0" means cosine is negative

Remember osmething like "ALL students Take Calculus"?

all is positive in quadrant 1
sine/cosecant is positive only in quadrant 2
tangent/cotangent is positive only in quadrant 3
cosine/secant is positive only in quadrant 4

since cot(angent) is the reciprocal of tangent, tangent must also be negative.

tangent is negative in quadrants II and IV
cosine is negative in quadrants II and III

therefore, θ must lie in quadrant II.

remember the tan θ = y / x. it is the y-coordinate divided by the x-coodinate. the y-coordinate would be the height of this 90 degree triangle that forms. the x-coordinate would be the bottom leg of the 90 degree triangle

then cot θ = x / y. therefore, cot θ = -24 / 7 means x = -24 and y = 7. we draw a triangle with these dimensions.

csc θ = r / y = hypotenuse over opposite (when you view the reference angle labeled as the one to base the hypotenuse/oppoiste on) because it is the reciprocal of sine

the hypotenuse can be found w/ pythagorean theorem

hypotenuse = √[(-24)² + 7²] = 25

therefore,
cot θ = 25/7

4 0

3 years ago

PLZ helPZ me Wendell plans to paint the doghouse after it’s built. He wants to know what the surface area of the outside of the

Basile [38]

Answer: sometimes, there are a lot of rectangles that are composite shapes so that could work. also, most composite shapes have two dimensions.

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Use the discriminant to describe the roots of each equation. Then select the best description.

Paha777 [63]

The quadratic equation 3 · x² + 7 · x - 2 = 0 has a positive discriminant. Thus, the expression has two distinct real roots (real and irrational roots).

<h3>How to determine the characteristics of the roots of a quadratic equation by discriminant</h3>

Herein we have a quadratic equation of the form a · x² + b · x + c = 0, whose discriminant is:

d = b² - 4 · a · c (1)

There are three possibilities:

d < 0 - conjugated complex roots.
d = 0 - equal real roots (real and rational root).
d > 0 - different real roots (real and irrational root).

If we know that a = 3, b = 7 and c = - 2, then the discriminant is:

d = 7² - 4 · (3) · (- 2)

d = 49 + 24

d = 73

The quadratic equation 3 · x² + 7 · x - 2 = 0 has a positive discriminant. Thus, the expression has two distinct real roots (real and irrational roots).

To learn more on quadratic equations: brainly.com/question/2263981

#SPJ1

7 0

3 years ago