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2 years ago

If x = 8 units, y = 3 units, and h = 2 units, then what is the area

Mathematics

1 answer:

solniwko [45]2 years ago

7 0

Answer:

8 sq.units

Step-by-step explanation:

x= base of triangle= 8units

h= height of triangle= 2 units

area of triangle= 1/2*b*h

=1/2* 8* 2

=8 sq.units

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4 friends evenly divided up a n- slice pizza. One of the friends , Harris, ate 1 fewer slice than he received. How many slices o

LenKa [72]

4 friends evenly dividing up a n - slice pizza

So each one get $\frac{n}{4}$ slices of pizza.

For example, if n = 12 slice then each friend gets 12/4 = 3 pieces. If Harris ate one slice less then he ate $\frac{12}{4}-1$ =3 -1 = 2 pieces.

So the general expression for slices of pizza did Harris eat is

$\frac{n}{4}-1$

6 0

3 years ago

Read 2 more answers

The quadratic function f (x) = - 45x2 + 350x + 1,590 models the population of a city where x represents the number of years sinc

kramer

Answer: 2,215,000

Step-by-step explanation:

Given: The quadratic function $f (x) = - 45x^2 + 350x + 1,590$ models the population of a city where x represents the number of years since 2005.

To Find: population of the city in 2010

We need to put x= 2010-2005 = 5

$f (5) = - 45(5)^2 + 350(5) + 1,590\\\\=-1125+1750+1590 =2215$

Hence, the estimated population of the city in 201 = 2215 thousands or 2,215,000 .

3 0

2 years ago

Find gradient xe^y + 4 ln y = x² at (1, 1)

cricket20 [7]

$xe^y+4\ln y=x^2$

Differentiate both sides with respect to x, assuming y = y(x).

$\dfrac{\mathrm d(xe^y+4\ln y)}{\mathrm dx}=\dfrac{\mathrm d(x^2)}{\mathrm dx}$

$\dfrac{\mathrm d(xe^y)}{\mathrm dx}+\dfrac{\mathrm d(4\ln y)}{\mathrm dx}=2x$

$\dfrac{\mathrm d(x)}{\mathrm dx}e^y+x\dfrac{\mathrm d(e^y)}{\mathrm dx}+\dfrac4y\dfrac{\mathrm dy}{\mathrm dx}=2x$

$e^y+xe^y\dfrac{\mathrm dy}{\mathrm dx}+\dfrac4y\dfrac{\mathrm dy}{\mathrm dx}=2x$

Solve for dy/dx :

$e^y+\left(xe^y+\dfrac4y\right)\dfrac{\mathrm dy}{\mathrm dx}=2x$

$\left(xe^y+\dfrac4y\right)\dfrac{\mathrm dy}{\mathrm dx}=2x-e^y$

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x-e^y}{xe^y+\frac4y}$

If y ≠ 0, we can write

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2xy-ye^y}{xye^y+4}$

At the point (1, 1), the derivative is

$\dfrac{\mathrm dy}{\mathrm dx}\bigg|_{x=1,y=1}=\boxed{\dfrac{2-e}{e+4}}$

4 0

3 years ago

Order from least to greatest 3.06, 3.601, 3.0059

Semenov [28]

Answer:3.0059 , 3.601 , 3.06

Step-by-step explanation:

the number with less digits behind the decimal has less value

7 0

3 years ago

Read 2 more answers

A null hypothesis is that the mean nose lengths of men and women are the same. The alternative hypothesis is that men have a lon

algol [13]

Answer:

b. There is not enough evidence to say that the populations of men and women have different mean nose lengths.

See explanation below.

Step-by-step explanation:

Develop the null and alternative hypotheses for this study?

We need to conduct a hypothesis in order to check if the means for the two groups are different (men have longer mean nose length than women), the system of hypothesis would be:

Null hypothesis: $\mu_{men} \leq \mu_{women}$

Alternative hypothesis: $\mu_{men} > \mu_{women}$

Assuming that we know the population deviations for each group, for this case is better apply a z test to compare means, and the statistic is given by:

$z=\frac{\bar X_{men}-\bar X_{women}}{\sqrt{\frac{\sigma^2_{men}}{n_{men}}+\frac{\sigma^2_{women}}{n_{women}}}}$ (1)

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Let's assume that the calculated statistic is $z_{calc}$

Since is a right tailed test test the p value would be:

$p_v =P(Z>z_{calc})=0.225$

And we know that the p value is 0.225. If we select a significance level for example 0.05 or 0.1 we see that $p_v >\alpha$

And on this case we have enough evidence to FAIl to reject the null hypothesis that the means are equal. So then the best conclusion would be:

b. There is not enough evidence to say that the populations of men and women have different mean nose lengths.

8 0

2 years ago