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Vikentia [17]
3 years ago
15

1

Mathematics
1 answer:
LuckyWell [14K]3 years ago
6 0
A-true because you would add 130 and 50 = 180 which is the measure of a supplementary angle
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The mean throwing distance of a football for a Marco, a high school freshman quarterback, is 40 yards, with a standard deviation
Phoenix [80]

Answer:

a) One-tailed t-test about a mean.

b) The null hypothesis would be that there is no significant evidence to conclude that the adjusted grip leads to more distance on the thrown ball.

While the alternative hypothesis is that there is significant evidence to conclude that the adjusted grip leads to more distance on the thrown ball.

Mathematically,

The null hypothesis is represented as

H₀: μ ≤ 40 yards

The alternative hypothesis is given as

Hₐ: μ > 40 yards

c) p-value = 0.00621

d) The graph is presented in the attached image. The p-value obtained is less than the significance level at which the test was performed, hence, we accept the alternative hypothesis and say that there is significant evidence to conclude that the adjusted grip leads to more distance on the thrown ball.

Step-by-step explanation:

a) This test checks if the adjusted grip leads to more distance than before on the ball throws.

So, it is a one tailed test (testing only in one direction), a t-test about a mean.

b) For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

Since this question aims to test if adjusting the grip leads to more distance on the ball thrown.

The null hypothesis would be that there is no significant evidence to conclude that the adjusted grip leads to more distance on the thrown ball. That is, The adjusted grip leads to a distance lesser than or equal to the previous distance on the thrown ball.

While the alternative hypothesis is that there is significant evidence to conclude that the adjusted grip leads to more distance on the thrown ball.

Mathematically,

The null hypothesis is represented as

H₀: μ ≤ 40 yards

The alternative hypothesis is given as

Hₐ: μ > 40 yards

c) To do this test, we will use the z-distribution because there is information on the population standard deviation.

So, we compute the test statistic

z = (x - μ₀)/σ

x = 45 yards

μ₀ = 40 yards

σ = standard deviation = 2 yards

z = (45 - 40)/2 = 2.50

The p-value for a one-tailed test for z-test statistic of 2.50 is 0.00621

d) The sketch of the graph is presented in the attached image.

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.00621

0.00621 < 0.05

Hence,

p-value < significance level

This means that we reject the null hypothesis & accept the alternative hypothesis and say that there is enough evidence to conclude that the adjusted grip leads to more distance on the thrown ball.

Hope this Helps!!!

5 0
3 years ago
A city's population is 12,000 and grows at 2.6% rate. What will the population be after 25 years? A city's population is 230,000
Levart [38]

Answer:

The 12000 City would become 22,986 people, while the 230,000 city would become a population of 124,223.

Step-by-step explanation:

1st Part:

=12000⋅(0.026000000000000002⋅25)

=12000(2.718281828459045)(0.65)

=22986

2nd Part:

=230000⋅(−0.044000000000000004⋅14)

=230000(2.718281828459045)(−0.616)

=124223

3 0
2 years ago
Read 2 more answers
Write an addition problem that has the sum of 1- 3/5 and the two addends must have different signs
Galina-37 [17]
6 + (-4 2/5) = 1 3/5 <==
3 0
3 years ago
The volume of a spherical sculpture is 256 ft³. Rhianna wants to estimate the surface area of the sculpture. To do the estimate,
Brrunno [24]

Answer:

192 ft^2

Step-by-step explanation:

Given that

Volume of spherical sculpture = 256 ft³

\pi is used as 3.

To find:

Surface area of sculpture = ?

Solution:

First of all, let us learn about the formula for Volume and Surface Area of Sphere:

1. Volume =\frac{4}{3}\pi r^3

2. Surface\ Area = 4\pi r^2

Given volume is 256 ft³.

256 = \dfrac{4}{3}\pi r^3\\\Rightarrow 256 = \dfrac{4}{3}\times 3 r^3\\\Rightarrow 256 = 4 r^3\\\Rightarrow r^3=64\\\Rightarrow \bold{r = 4\ ft}

Now, let us put r = 4 in the formula of Surface Area to find the value of Surface Area:

Surface\ Area = 4\pi 4^2 = 4 \times 3 \times 16 = \bold{192\ ft^2}

So, approximate surface area of sculpture is 192 ft^2.

3 0
2 years ago
Apply the distributive property to create an equivalent expression. 12(2a - 6b+ 8) = 2 1 ​ (2a−6b+8)
liberstina [14]

Answer:

a+4=11b

Step-by-step explanation:

Distributive property in mathematics means to multiply the sum by a number of two or more add-ons will provide the same result that each add-on multiplies by a single number and then together add the products.

for example a( b+c) = ab+ac

Therefore, applying distributive property in asked eapression

12(2a - 6b+ 8) = 21(2a−6b+8)

24a+72b+96 = 42a-126b+168

198b=18a+72

9a +36=99b

3a+12=33b

a+4=11b

5 0
2 years ago
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