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3 years ago

What value of d makes the equation true 2/9=d/27

Mathematics

2 answers:

lys-0071 [83]3 years ago

5 0

2/9 = d / 27
cross multiply
(9)(d) = (27)(2)
9d = 54
d = 54/9
d = 6 <==

liubo4ka [24]3 years ago

3 0

To do this, you will have to cross multiply the proportion.
2/9=d/27 (Original)
2*27=9*d (Cross multiply)
54=9d (Simplify)
d=6 (Divide by 9)
The answer is d=6.

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fredd [130]

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4 0

3 years ago

The rectangle below has an area of 81-x^2 square meters and a width of 9-x meters. What expression represents the length of the

oksian1 [2.3K]

For this case we have that by definition, the area of a rectangle is given by:

$A = w * l$

Where:

w: Is the width of the rectangle

l: is the length of the rectangle

According to the data of the statement we have:

$A = 81-x ^ 2\\w = 9-x$

So, the length is given by:

$l = \frac {A} {w}\\l = \frac {81-x ^ 2} {9-x}$

We factor the numerator:

$l = \frac {(9 + x) (9-x)} {9-x}$

We simplify:

$l = 9 + x$

So, the length is $9 + x$

Answer:

$9 + x$

3 0

3 years ago

The Nellie Mae organization conducts an extensive annual study of credit card usage by college students. For their 2004 study, t

Masja [62]

Answer:

1. Null Hypothesis, $H_0$ : $p_1-p_2=0$ or $p_1=p_2$

Alternate Hypothesis, $H_A$ : $p_1-p_2\neq 0$ or $p_1\neq p_2$

2. Test statistics = 4.63

P-value = 0.00001

3. We conclude that the proportion of undergraduate students who held a credit card differed between these two years.

Step-by-step explanation:

We are given that the Nellie Mae organization conducts an extensive annual study of credit card usage by college students.

For their 2004 study, they analyzed credit bureau data for a random sample of 1,413 undergraduate students between the ages of 18 and 24. They found that 76% of the students sampled held a credit card. Three years earlier they had found that 83% of undergraduates sampled held a credit card.

Let $p_1$ = population proportion of undergraduate students who held a credit card in year 2001

$p_2$ = population proportion of undergraduate students who held a credit card in year 2004

1. Null Hypothesis, $H_0$ : $p_1-p_2=0$ or $p_1=p_2$ {means that the proportion of undergraduate students who held a credit card does not differed between these two years}

Alternate Hypothesis, $H_A$ : $p_1-p_2\neq 0$ or $p_1\neq p_2$ {means that the proportion of undergraduate students who held a credit card differed between these two years}

The test statistics that will be used here is Two-sample z proportion statistics;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1} +\frac{\hat p_2(1-\hat p_2)}{n_2}} }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of undergraduate students who held a credit card in 2001 = 83%

$\hat p_2$ = sample proportion of undergraduate students who held a credit card in 2004 = 76%

$n_1$ = sample of students surveyed in 2001 = 1,413

$n_2$ = sample of students surveyed in 2004 = 1,413

So, test statistics = $\frac{(0.83-0.76)-(0)}{\sqrt{\frac{0.83(1-0.83)}{1,413} +\frac{0.76(1-0.76)}{1,413}} }$

= 4.63

2. Hence, the value of test statistics is 4.63.

Also, P-value is given by the following formula;

P-value = P(Z > 4.63) = 1 - P(Z $\leq$ 4.63)

= 1 - 0.99999 = 0.00001

3. Since in the question we are not given the level of significance so we assume it to be 5%. Now at 5% significance level, the z table gives critical values between -1.96 and 1.96 for two-tailed test. Since our test statistics is does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the proportion of undergraduate students who held a credit card differed between these two years.

6 0

3 years ago

the angle between the length of a rectangle and its diagonal is 30degrees. if the length of the rectangle is 6cm, find the lengt

adell [148]

Answer:

view the picture

Step-by-step explanation:

It is self explanatory

4 0

3 years ago

What is the area of triangle EDF?

Ann [662]

Answer:

4.5

Step-by-step explanation:

∠BAC ~ ∠EDF means that the triangles are similar. So the legs of the triangle share the same proportions, even if the sizes are different.

Since they share the same proportions, the same operations can be performed on each base to find the area.

The answer can be found with the knowledge that the area of a triangle is half of the height * width. You know the width of ∠BAC is 4, and the area is 8, so 16 (the area doubled) / 4 is the height. The width and height of ∠BAC are the same, and since the proportions are also the same, the width and height of ∠EDF are both 3. So the area is the width (3) times the height (3) divided by 2.

3*3 = 9

9/2 = 4.5

So the area is 4.5

6 0

3 years ago