I need help. Find the values of a b and c. Note diagram (attached) is not to scale.

In this quadrilateral x= A) 56. B) 67 C) 78 D) 89

Oxana [17]

the correct answer is c 78

Step-by-step explanation:

lit can't be a because to small and can't be b because also to small. and and 92 is uptus and this is an acute angle

6 0

3 years ago

Find the Area of the Shaded Region.

Mrac [35]

9514 1404 393

Answer:

610 m²

Step-by-step explanation:

If we extend the horizontal line across the right-hand portion of the figure, then the figure is divided into two rectangles:

bottom: 5 m × 50 m = 250 m²

top: 18 m × 20 m = 360 m²

The sum of these areas is the shaded area:

shaded area = 250 m² +360 m² = 610 m²

4 0

2 years ago

A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. Assume that the distr

Marianna [84]

Answer:

(a) Decision rule for 0.01 significance level is that we will reject our null hypothesis if the test statistics does not lie between t = -2.651 and t = 2.651.

(b) The value of t test statistics is 1.890.

(c) We conclude that there is no difference in the mean number of times men and women order take-out dinners in a month.

(d) P-value of the test statistics is 0.0662.

Step-by-step explanation:

We are given that a recent study focused on the number of times men and women who live alone buy take-out dinner in a month.

Also, following information is given below;

Statistic : Men Women

The sample mean : 24.51 22.69

Sample standard deviation : 4.48 3.86

Sample size : 35 40

Let $\mu_1$ = mean number of times men order take-out dinners in a month.

$\mu_2$ = mean number of times women order take-out dinners in a month

(a) So, Null Hypothesis, $H_0$ : $\mu_1-\mu_2$ = 0 {means that there is no difference in the mean number of times men and women order take-out dinners in a month}

Alternate Hypothesis, $H_A$ : $\mu_1-\mu_2\neq$ 0 {means that there is difference in the mean number of times men and women order take-out dinners in a month}

The test statistics that would be used here Two-sample t test statistics as we don't know about the population standard deviation;

T.S. = $\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }$ ~ $t__n_1_-_n_2_-_2$

where, $\bar X_1$ = sample mean for men = 24.51

$\bar X_2$ = sample mean for women = 22.69

$s_1$ = sample standard deviation for men = 4.48

$s_2$ = sample standard deviation for women = 3.86

$n_1$ = sample of men = 35

$n_2$ = sample of women = 40

Also, $s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2} }$ = $\sqrt{\frac{(35-1)\times 4.48^{2}+(40-1)\times 3.86^{2} }{35+40-2} }$ = 4.16

So, test statistics = $\frac{(24.51-22.69)-(0)}{4.16 \sqrt{\frac{1}{35}+\frac{1}{40} } }$ ~ $t_7_3$

= 1.890

(b) The value of t test statistics is 1.890.

(c) Now, at 0.01 significance level the t table gives critical values of -2.651 and 2.651 at 73 degree of freedom for two-tailed test.

Since our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that there is no difference in the mean number of times men and women order take-out dinners in a month.

(d) Now, the P-value of the test statistics is given by;

P-value = P( $t_7_3$ > 1.89) = 0.0331

So, P-value for two tailed test is = 2 $\times$ 0.0331 = 0.0662

4 0

3 years ago

What is the area of the parallelogram?

Marizza181 [45]

Answer:

0.6

Step-by-step explanation:

3 0

3 years ago

A bridge constructed over a bayou has a supporting arch in the shape of an inverted parabola. Find the equation of the parabolic

babymother [125]

Answer: f(x) = -0.016x² + 1.6x

Step-by-step explanation:

If the lenght of the road over the arch is 100m, we can consider a coordinate plane and say that the road starts at point (0,0) and finishes at (100,0). The vertice of the parabola is at point (50,40), because the maximum height is 40 and it is always in the middle point of the roots.

So, we have

(0,0) (50,40) (100,0)

A quadratic function is always on the form: f(x) = ax² + bx + c

0 = a0² + b0 + c

40 = a50² + b50 + c

0 = a100² + b100 + c

0 = a0² + b0 + c → c = 0 ∴

40 = a50² + b50

0 = a100² + b100

_________________________

2500a + 50b = 40 (*2)

10000a + 100b = 0

_________________________

5000a + 100b = 80

10000a + 100b = 0 (-)

__________________________

-5000a = 80

-a=80/5000

a=-0.016

∴

2500a + 50b = 40

2500.(-0.016) + 50b = 40

-40 + 50b = 40

50b = 80

b = 80/50

b = 1.6

This way f(x) = -0.016x² + 1.6x

6 0

3 years ago