a shoreline is changing -3 centimeters each year due to erosion. what is the change in shoreline over 6 years?

Two-thirds of a number, decreased by thirty-six, is at most twenty-two. Find the number.

Nataliya [291]

Answer:

87 is the number

Step-by-step explanation:

6 0

2 years ago

Evangeline is making snack bags for her class. If she can fill 5/8 of her snack bags with 1 2/3 cups of pretzels, how many cups

brilliants [131]

Answer:

2 2/3

Step-by-step explanation:

For each of her snack bag, she can fill it with a 1/3 cup of pretzels

1/3 x 8 = 2 2/3 cups

4 0

2 years ago

Which statement correctly describes the end behavior of the function f ( x ) = − x 2 + 3 x + 12

Yuri [45]

X—>-infinity f(x)—>-infinity
X—>infinity f(x)—> 12

8 0

3 years ago

Line p has a slope of -3. Line t is perpendicular to line p and passes through the point (9,2). What is the equation for line t?

olganol [36]

Answer:

y = (1/3)x - 1

Step-by-step explanation:

The product of the slopes of perpendicular lines is -1. That makes the slopes of perpendicular lines negative reciprocals. Since line p has slope -3, the slope of line t is 1/3. Also, line t passes through point (9, 2).

y = mx + b

m = slope

y = (1/3)x + b

Now we replace x and y with the x- and y-coordinates of the given point, respectively, and we solve for b.

2 = (1/3)(9) + b

2 = 3 + b

b = -1

Now we replace b with -1.

y = (1/3)x - 1

8 0

3 years ago

A national grocery store chain wants to test the difference in the average weight of turkeys sold in Detroit and the average wei

Arte-miy333 [17]

Answer:

Calculated value t = 1.3622 < 2.081 at 0.05 level of significance with 42 degrees of freedom

The null hypothesis is accepted .

Assume the population variances are approximately the same

Step-by-step explanation:

Explanation:-

Given data a random sample of 20 turkeys sold at the chain's stores in Detroit yielded a sample mean of 17.53 pounds, with a sample standard deviation of 3.2 pounds

The first sample size 'n₁'= 20

mean of the first sample 'x₁⁻'= 17.53 pounds

standard deviation of first sample S₁ = 3.2 pounds

Given data a random sample of 24 turkeys sold at the chain's stores in Charlotte yielded a sample mean of 14.89 pounds, with a sample standard deviation of 2.7 pounds

The second sample size n₂ = 24

mean of the second sample "x₂⁻"= 14.89 pounds

standard deviation of second sample S₂ = 2.7 pounds

Null hypothesis:-H₀: The Population Variance are approximately same

Alternatively hypothesis: H₁:The Population Variance are approximately same

Level of significance ∝ =0.05

Degrees of freedom ν = n₁ +n₂ -2 =20+24-2 = 42

Test statistic :-

$t = \frac{x^{-} _{1} - x_{2} }{\sqrt{S^2(\frac{1}{n_{1} } }+\frac{1}{n_{2} } }$

where $S^{2} = \frac{n_{1} S_{1} ^{2}+n_{2}S_{2} ^{2} }{n_{1} +n_{2} -2}$

$S^{2} = \frac{20X(3.2)^2+24X(2.7)^2}{20+24-2}$

substitute values and we get S² = 40.988

$t= \frac{17.53-14.89 }{\sqrt{40.988(\frac{1}{20} }+\frac{1}{24} )}$

t = 1.3622

Calculated value t = 1.3622

Tabulated value 't' = 2.081

Calculated value t = 1.3622 < 2.081 at 0.05 level of significance with 42 degrees of freedom

Conclusion:-

The null hypothesis is accepted

Assume the population variances are approximately the same.

6 0

3 years ago