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2 years ago

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Greg only has enough plywood to make at most 8 chairs or tables total. Let x represent the number of chairs and y represent the

number of tables that Greg can make. Which of the following graphs best represents the relationship between x and y

1 answer:

Dimas [21]2 years ago

3 0

Answer:

C

Step-by-step explanation: ǝuo sᴉɥʇ uo ǝɯ ʇsnɹʇ (;

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A ride at an amusement park moves the riders in a circle at a rate of 6.0 m/s. The radius of the ride is 9.0 meters. Which of th

lana [24]

Answer with explanation:

It is given that , ride at an amusement park moves the riders in a circle at a rate of 6.0 m/s.

$a=\frac{dv}{dt}=6 m/s$

Radius of Circle = 9.0 meters

Acceleration is rate of change of velocity,which will be perpendicular to radius vector.

Also, in terms of mathematics, line from center that is radius , to point of contact that is tangent line ,which is on the circle are perpendicular to each another.

→r(radius vector) ⊥ a(Acceleration vector).

So, In option A, Radius vector is Perpendicular to acceleration of riders.

4 0

2 years ago

Two samples each of size 20 are taken from independent populations assumed to be normally distributed with equal variances. The

Harlamova29_29 [7]

Answer:

$t=\frac{(43.5 -40.1)-(0)}{3.678\sqrt{\frac{1}{20}+\frac{1}{20}}}=2.923$

The degrees of freedom are

$df=20+20-2=38$

And the p value is given by:

$p_v =2*P(t_{38}>2.923) =0.0058$

Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different

Step-by-step explanation:

When we have two independent samples from two normal distributions with equal variances we are assuming that

$\sigma^2_1 =\sigma^2_2 =\sigma^2$

And the statistic is given by this formula:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$

Where t follows a t distribution with $n_1+n_2 -2$ degrees of freedom and the pooled variance $S^2_p$ is given by this formula:

$S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}$

The system of hypothesis on this case are:

Null hypothesis: $\mu_1 = \mu_2$

Alternative hypothesis: $\mu_1 \neq \mu_2$

We have the following data given:

$n_1 =20$ represent the sample size for group 1

$n_2 =20$ represent the sample size for group 2

$\bar X_1 =43.5$ represent the sample mean for the group 1

$\bar X_2 =40.1$ represent the sample mean for the group 2

$s_1=4.1$ represent the sample standard deviation for group 1

$s_2=3.2$ represent the sample standard deviation for group 2

First we can begin finding the pooled variance:

$\S^2_p =\frac{(20-1)(4.1)^2 +(20 -1)(3.2)^2}{20 +20 -2}=13.525$

And the deviation would be just the square root of the variance:

$S_p=3.678$

The statistic is givne by:

$t=\frac{(43.5 -40.1)-(0)}{3.678\sqrt{\frac{1}{20}+\frac{1}{20}}}=2.923$

The degrees of freedom are

$df=20+20-2=38$

And the p value is given by:

$p_v =2*P(t_{38}>2.923) =0.0058$

Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different

6 0

2 years ago

What are the solutions of the equation 9x4 – 2x2 – 7 = 0? Use u substitution to solve. tions of the equation 9

skelet666 [1.2K]

Answer:

Step-by-step explanation:

Let $u^2=x^4\\u = x^2$

Subbing in:

$9u^2-2u-7=0$

a = 9, b = -2, c = -7

The product of a and c is the aboslute value of -63, so a*c = 63. We need 2 factors of 63 that will add to give us -2. The factors of 63 are {1, 63}, (3, 21}, {7, 9}. It looks like the combination of -9 and +7 will work because -9 + 7 = -2. Plug in accordingly:

$9u^2-9u+7u-7=0$

Group together in groups of 2:

$(9u^2-9u)+(7u-7)=0$

Now factor out what's common within each set of parenthesis:

$9u(u-1)+7(u-1)=0$

We know this combination "works" because the terms inside the parenthesis are identical. We can now factor those out and what's left goes together in another set of parenthesis:

$(u-1)(9u+7)=0$

Remember that $u=x^2$

so we sub back in and continue to factor. This was originally a fourth degree polynomial; that means we have 4 solutions.

$(x^2-1)(9x^2+7)=0$

The first two solutions are found withing the first set of parenthesis and the second two are found in other set of parenthesis. Factoring $(x^2-1)$ gives us that x = 1 and -1. The other set is a bit more tricky. If

$9x^2+7=0$ then

$9x^2=-7$ and

$x^2=-\frac{7}{9}$

You cannot take the square root of a negative number without allowing for the imaginary component, i, so we do that:

$x=$ ± $\sqrt{-\frac{7}{9} }$

which will simplify down to

$x=$ ± $\frac{\sqrt{7} }{3}i$

Those are the 4 solutions to the quartic equation.

5 0

2 years ago

Jazmin is completing an art project. She has two pieces of construction paper. The first piece is 444444 inches wide and the sec

Neko [114]

Answer:

11

Step-by-step explanation:

Khan academy

3 0

2 years ago

The value of which of these expressions is closest to e?

jeka57 [31]

Answer:

b

Step-by-step explanation:

8 0

2 years ago