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andriy [413]
3 years ago
6

A high school soccer goalie blocked the ball from going into the goal 4 out of 5 times. If the ball kicked toward the goal 25 ti

mes,how many blocks did the goalie make ?
Mathematics
2 answers:
malfutka [58]3 years ago
8 0
Hello!

You have to find \frac{4}{5} of 25

\frac{4}{5} =  \frac{x}{25}

Cross multiply

25 × 4 = 100

100 ÷ 5 = 20

The goalie made <u>20 blocks</u>
miskamm [114]3 years ago
4 0
We can use a ratio expression to find the answer to this problem.

Set up the ratio.
4/5 = x/25
Multiply both sides by 25.
100/5 = x
Divide by 5.
20 = x
This means out of 25 times the ball is kicked toward the goal, the goalie will block it 20 times.
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sammy [17]

Answer: it’s 1/5

Step-by-step explanation:

6 0
3 years ago
The mean points obtained in an aptitude examination is 159 points with a standard deviation of 13 points. What is the probabilit
Korolek [52]

Answer:

0.4514 = 45.14% probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 159, \sigma = 13, n = 60, s = \frac{13}{\sqrt{60}} = 1.68

What is the probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled?

This is the pvalue of Z when X = 159+1 = 160 subtracted by the pvalue of Z when X = 159-1 = 158. So

X = 160

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{160 - 159}{1.68}

Z = 0.6

Z = 0.6 has a pvalue of 0.7257

X = 150

Z = \frac{X - \mu}{s}

Z = \frac{158 - 159}{1.68}

Z = -0.6

Z = -0.6 has a pvalue of 0.2743

0.7257 - 0.2743 = 0.4514

0.4514 = 45.14% probability that the mean of the sample would differ from the population mean by less than 1 point if 60 exams are sampled

7 0
3 years ago
9x-22=23+4x I don't understand how to do this
anygoal [31]
9x-22=23+4x Now you subtract 4x from both sides to get the variable on one side.. 5x-22=23 Now solve as you would solve a 2 step equation. 5x=45 Divide both sides by 5 to get the variable by itself. x=9
4 0
3 years ago
Are either of these linear?
sesenic [268]
The 2nd one is linear
7 0
3 years ago
Point F is at (0, -10) and point H is at (-6, 5). Find the coordinates of point G on line segment FH such that the ratio of FG t
Tanya [424]

Answer:

G(x,y)=(-4,0)

Step-by-step explanation:

We use the section formula:

(x,y)=\left(\dfrac{mx_2+nx_1}{m+n}, \dfrac{my_2+ny_1}{m+n}\right)

Given:

F(x_1,y_1)=(0, -10)\\H(x_2,y_2)=(-6, 5)\\FG:GH=m:n=2:1

We substitute the values to get:

G(x,y)=\left(\dfrac{2*-6+1*0}{2+1}, \dfrac{2*5+1*-10}{2+1}\right)\\=\left(\dfrac{-12}{3}, \dfrac{10-10}{3}\right)\\=\left(\dfrac{-12}{3}, \dfrac{0}{3}\right)\\\\G(x,y)=(-4,0)

5 0
3 years ago
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