Factor the common factor out of

The points (0,2) and (1,5) are on a line which of these points is on the same line

katrin [286]

Answer:

y = 3x + 2

Step-by-step explanation:

The equation for two points on a line is generated from the straight line equation y = mx + b ---------------- eqn (i)

where m, the slope = (y2 - y1) / (x2 - x1)

therefore for (0,2) and (1,5) m = (5 - 2)/(1 - 0) = 3

This implies that eqn (i) can be rewritten as:

y = 3x + b ------------------- eqn (ii)

pickintg the point (0,2) and substituting into eqn (ii)

2 = 3(0) + b

this implies that b = 2

for confirmation with (1,5)

5 = 3(1) + b

b = 5 - 3 = 2

hence m = 3, b = 2

the equation is y = 3x + 2

6 0

3 years ago

Peter spent $450 on groceries in 3 months.What is the amount he spent every month on groceries, if he spent the same amount ever

WITCHER [35]

The amount he spends per week is 450/3=$150.

6 0

3 years ago

Sarah claims that the thickness of the spearmint gum she produces is 7.5 one-hundredths of an inch. A quality control specialist

satela [25.4K]

Answer:

$t=\frac{7.55-7.5}{\frac{0.103}{\sqrt{10}}}=1.539$

$p_v =2*P(t_{(9)}>1.539)=0.158$

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis.

Step-by-step explanation:

Data given and notation

Data: 7.65, 7.60, 7.65, 7.7, 7.55, 7.55, 7.4, 7.4, 7.5, 7.5

We can begin calculating the sample mean given by:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And the sample deviation given by:

$s=\sart{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And we got:

$\bar X=7.55$ represent the sample mean

$s=0.103$ represent the sample standard deviation

$n=10$ sample size

$\mu_o =7.5$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is equal to 7.5 or no, the system of hypothesis would be:

Null hypothesis: $\mu = 7.5$

Alternative hypothesis: $\mu \neq 7.5$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{7.55-7.5}{\frac{0.103}{\sqrt{10}}}=1.539$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=10-1=9$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(9)}>1.539)=0.158$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis.

3 0

4 years ago

Can I get help with this please

drek231 [11]

Answer:

3) 1 5/6 mi

4) a. 4 cm, 6 ft

b. 6.4 cm, 9.6 ft

c. same as part a

Step-by-step explanation:

3) Each of the given distances appears twice in the sum of side measures that is the perimeter. Hence by walking the perimeter twice, Kyle walks each of the given distances 4 times. His total walk is ...

4×1/3 + 4×1/8 = 4/3 + 4/8

= 1 1/3 + 1/2 = 1 2/6 + 3/6

= 1 5/6 . . . . . miles

___

4) Since the figure is rectilinear (all angles are right angles, and all sides are straight lines), the sum of partial dimensions in one direction is equal to the whole dimension in that direction.

a. 8 cm = 4 cm + x

8 cm - 4 cm = x = 4 cm

The distance in the room is ...

(4 cm)×(1.5 ft/cm) = 6 ft

b. 10.3 cm = 3.9 cm + y

10.3 cm - 3.9 cm = y = 6.4 cm

The distance in the room is ...

(6.4 cm)×(1.5 ft/cm) = 9.6 ft

c. The answer to part b was obtained in the same way as the answer to part a. The unknown dimension is the difference of given dimensions. The actual length in the room is the model length multiplied by the inverse of the scale factor.

3 0

3 years ago

Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 10

WINSTONCH [101]

Answer:

The function for the outside temperature is represented by $T(t) = 85\º + 15\º \cdot \sin \left[\frac{t-6\,h}{24\,h} \right]$ , where t is measured in hours.

Step-by-step explanation:

Since outside temperature can be modelled as a sinusoidal function, the period is of 24 hours and amplitude of temperature and average temperature are, respectively:

Amplitude

$A = \frac{100\º-70\º}{2}$