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3 years ago

The width of the rectangle is 75% of its length. The length is 8 cm. What is the width of the rectangle?

Mathematics

1 answer:

hjlf3 years ago

6 0

Given :

The length of the rectangle, l = 8 cm/

The width of the rectangle, w = 75% of 8 cm

$= \frac{75}{100} \times 8$

$=\frac{15}{20} \times 8$

= 0.75 x 8

= 6

Therefore, the width of the rectangle is 6 cm.

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In 2004, a magazine's circulation was about 1,000,000 readers. In 2014, the magazine had about 2,000,000 readers. Write a linear

Sever21 [200]

Answer:

$m= \frac{r_2 -r_1}{t_2 -t_1}= \frac{2000000-1000000}{14-4}=100000$

And then we can use for example the first point $(t_1, r_1) = (4, 1000000)$ to find the intercept:

$1000000= 100000*4 + b$

$b=600000$

So then the linear model for this case should be:

$r = 100000 t + 600000$

Step-by-step explanation:

For this case we want to find a linear model given by:

$r =mt+b$

Where r = represent the number of readers , t= years after 2000

m = the slope for the model and b the intercept

For this case we can define the following points from the data given:

$(t_1, r_1) = (4, 1000000)$ 4 years after 2000

$(t_2, r_2) = (14, 2000000)$ 14 years after 2000

We can find the slope with the following formula:

$m= \frac{r_2 -r_1}{t_2 -t_1}= \frac{2000000-1000000}{14-4}=100000$

And then we can use for example the first point $(t_1, r_1) = (4, 1000000)$ to find the intercept:

$1000000= 100000*4 + b$

$b=600000$

So then the linear model for this case should be:

$r = 100000 t + 600000$

8 0

4 years ago

An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating. An independent testing firm has been contra

d1i1m1o1n [39]

Answer:

The calculated value z = 1.3145 < 2.326 at 0.02 level of significance

The null hypothesis is accepted

Hence An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.

Step-by-step explanation:

Step(i):-

An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.

The mean of the Population 'μ' = 28.0miles/gallon

Given data after testing 270 cars, they found a mean MPG of 27.8. Assume the variance is known to be 6.25.

The sample size 'n' = 270

Mean of the sample 'x⁻' = 27.8

Given Population variance 'σ² = 6.25

The standard deviation of Population 'σ' = √6.25 = 2.5

Step(ii):-

Null hypothesis :H₀: 'μ' = 28.

Alternative hypothesis :H₁: 'μ' ≠28.

The test statistic

$Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }$

$Z = \frac{27.8-28 }{\frac{2.5}{\sqrt{270} } } = \frac{-0.2}{0.15214}$

Z = -1.3145

|Z| = |-1.3145|= 1.3145

Step(iii):-

The tabulated value of z-score at 0.02 level of significance = 2.326

The calculated value z = 1.3145 < 2.326 at a t 0.02 level of significance

The null hypothesis is accepted

Hence An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.

8 0

4 years ago

Worth 10 points please help me ASAP

Nitella [24]

(2,-2) would be the answer I think

8 0

3 years ago

In clinical trials of a newly developed cold medicine, it was found that 45 out of 200 individuals that took the new medicine (G

ddd [48]

Answer:

Step-by-step explanation:

Group 1 Information:

sample size : n₁ = 200

individuals with stomach as a side effect x₁ = 45

p₁ = 45 / 200 p₁ = 0,225 then q₁ = 1 - p₁ q₁ = 0,775

Group 2 Information:

sample size : n₂ = 150

individuals with stomach as a side effect x₂ = 33

p₂ = 33/150 p₂ = 0,22 q₂ = 0,78

Hypothesis Test:

Null Hypothesis: H₀ p₁ = p₂

Alternative Hypothesis Hₐ p₁ > p₂

The alternative hypothesis indicates that the test is a one-tail test to the right

Significance level is α = 0,01 ( confidence interval 99%)

From z-table we get z(c) for that α z(c) = 2,32

To calculate z(s)

z(s) = ( p₁ - p₂ ) / EED

EED = √ ( p₁*q₁)/n₁ + ( p₂*q₂)/n₂

EED = √ ( 0,225*0,775)/200 + (0,22*0,78)/150

EED = √ 0,0008718 + 0,001144

EED = 0,045

z(s) = ( 0,225 - 0,22 ) / 0,045

z(s) = 0,005 / 0,045

z(s) = 0,11

Comparing z(s) and z(c)

z(s) < z(c) 0.11 < 2.32

Then z(s) is in the acceptance region. We accept H₀ . We don´t have evidence to support differences between the two groups.

6 0

3 years ago

Please help me

morpeh [17]

Answer:

No, because the cone has a smaller volume than the ice cream

Step-by-step explanation:

V=4

3πr3=4

3·π·33≈113.09734

Volume of scoop: 113.1 cm^2

V=πr2h

3=π·2.52·10

3≈65.44985

Volume of cone: 65.45 cm^2

65.45 < 113.1

6 0

3 years ago