line in the Cartesian plane passes through the points (1, 3) and (5, 4). What is the slope of the line?

Answers

Answer 1

Answer: $\bf \begin{array}{ccccccccc}&&x_1&&y_1&&x_2&&y_2\n% (a,b)&&(~ 1 &,& 3~) % (c,d)&&(~ 5 &,& 4~)\end{array}\n\n\n% slope = mslope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-3}{5-1}\implies \cfrac{1}{4}$

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The perimeter of a rectangle is 80 cm. The width is 10 cm more than twice the length. Whatis the length and width of this rectangle? P=2W+2L

Answers

Answer:

L=10cm , W=30cm

Step-by-step explanation:

First use the given that W=10+2*L

Use P=2W+2L=80, substitute W in the perimeter formula

2(10+2L)+2L=80 and solve for L,

20+4L+2L=80 isolate variable L and combine like terms,

6L=80-20,

L=10, so W=10+2*10=10+20=30

What value of x makes the equation 4(5-7x)=6-12x

Answers

Do distributive property
20 - 28x = 6 - 12x
Add 28x to both sides
20 = 6 + 16x
Subtract 6
14 = 16x, x = 14/16 = 7/8
Solution: x = 7/8

4> Solve by using Laplace transform: y'+5y'+4y=0; y(0)=3 y'(o)=o

Answers

Answer:

$y=3e^(-4t)$

Step-by-step explanation:

$y''+5y'+4y=0$

Applying the Laplace transform:

$\mathcal{L}[y'']+5\mathcal{L}[y']+4\mathcal{L}[y']=0$

With the formulas:

$\mathcal{L}[y'']=s^2\mathcal{L}[y]-y(0)s-y'(0)$

$\mathcal{L}[y']=s\mathcal{L}[y]-y(0)$

$\mathcal{L}[x]=L$

$s^2L-3s+5sL-3+4L=0$

Solving for $L$

$L(s^2+5s+4)=3s+3$

$L=(3s+3)/(s^2+5s+4)$

$L=(3(s+1))/((s+1)(s+4))$

$L=\frac3{s+4}$

Apply the inverse Laplace transform with this formula:

$\mathcal{L}^(-1)[\frac1{s-a}]=e^(at)$

$y=3\mathcal{L}^(-1)[\frac1{s+4}]=3e^(-4t)$

A hot air balloon rose from a height of 100 m to 400 m in 3 minutes. What was the balloon’s rate of change?

Answers

Answer:

1.666666667 meter per sec^2

Step-by-step explanation:

I feel like this is physic

using acceleration formla Vf-Vi/t

so 400-100/180sec

300/180

1.666666667 meter per sec^2

Hey im still learning tell me if you feel like im wrong OwO

The following figures are similar, find the value of x

Answers

Answer:

x=143

Step-by-step explanation:

scale factor (if that is the correct term) is 13. you find that by matching sides to side. this means that 91/7=13, therefore you know that 4*13 is 52 and 11*13 is 143

The answer is x =143 I’m pretty sure

lled a 12:3:112:3:1 ratio. Such a model can provide the basis for the null hypothesis in a significance test. A cross of white and green summer squash plants gives the number of squash in the second generation F2:131F2:131 white squash, 3434 yellow squash, and 1010 green squash. Are these data consistent with a 12:3:112:3:1 dominant epistatic model of genetic inheritance( white being dominant)? The null hypothesis for the chi‑square goodness‑of‑fit test is

Answers

Here is the full question:

When a species has several variants of a phenotype passed on from generation to generation, we can form a hypothesis about the genetics of the trait based on Mendelian theories of genetic inheritance. For example, in a two-gene dominant epistatic model, the first gene masks the effect of the second gene, leading to the expression of three phenotype variants. Crossing the dominant and recessive homozygote lines would result in a second generation represented by a mix of dominant, intermediate, and recessive phenotype variants in the expected proportions: and respectively, also called a 12:3: 1 ratio.

Such a model can provide the basis for the null hypothesis in a significance test. A cross of white and green summer squash plants gives the number of squash in the second generation F2: 131 white squash, 34 yellow squash, and 10 green squash. Are these data consistent with a 12: 3: 1 dominant epistatic model of genetic inheritance( white being dominant)?

The null hypothesis for the chi-square goodness-of-fit test is

Answer:

The null hypothesis for the chi-square goodness-of-fit test is :

$\mathbf{H_o:p_(white) = (12)/(16), p_(yellow) = (3)/(16); p_(green) = (1)/(16) }$

Step-by-step explanation:

The objective of this question is to state the null hypothesis for the chi-square goodness-of-fit test.

Given that:

There are three colors associated with this model . i,e White , yellow and green and they are in the ratio of 12:3:1

The total number of these color traits associated with this model = 12 + 3 + 1 = 16

Thus ;

The null hypothesis for the chi-square goodness-of-fit test is :

$\mathbf{H_o:p_(white) = (12)/(16), p_(yellow) = (3)/(16); p_(green) = (1)/(16) }$

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