Which point is on the line y = 1/2 x + 2? A.(2, 4) B.(2, 2) C.(4, 4) D.(4, 5)

Solve the system of equations using the linear combination method. 4x−2y=7 3x+2y=0

Irina18 [472]

Answer:

x = 1

y = -3/2

Step-by-step explanation:

Step 1: Arrange the equations with like terms in column.

Step 2: You want 1 set of coefficients that are opposites. This problem already has opposites: -2y and +2y.

Step 3: Solve for x.

4x-2y=7

3x+2y=0

--------------

7x = 7

x = 1

Step 4: Substitute the value of x and solve for y.

4(1)-2y=7

4-2y=7

-2y=7-4

-2y=3

y=-3/2

7 0

4 years ago

A path 5m wide is to be built along the border and inside a square garden of side 90m. Find the cost of cementing the path at th

gizmo_the_mogwai [7]

Answer:

Total cost of cementing the path = Rs. 17,000.

Step-by-step explanation:

Let the square garden be ABCD

Let the region inside the garden (ABCD) be WXYZ.

Given the following data;

Length of sides of ABCD = 90m

Width of path = 5m

Cost = Rs. 10 per m²

Area of ABCD = 90 * 90

Area of ABCD = 8100m²

To find the area of WXYZ;

WX = WZ = 90 - (5 + 5)

WX = WZ = 90 - 10

WX = WZ = 80m

Area of WXYZ = WX * WZ

Substituting into the equation, we have;

Area of WXYZ = 80 * 80

Area of WXYZ = 6400 m²

Area of path = Area of ABCD - Area of WXYZ

Area of path = 8100 - 6400

Area of path = 1700 m²

Total cost of cementing the path = Area of path * cost

Total cost of cementing the path = 1700 * 10

Total cost of cementing the path = Rs. 17,000

6 0

3 years ago

Add. (2x + 5) + (3x - 7) A) x - 2 B) x + 2 C) 5x - 2 D) 5x + 2

MrRissso [65]

5x - 2. Just combine like terms, and distribute the + to the second term.

8 0

3 years ago

Read 2 more answers

7) please show the work thanks

Mrac [35]

Answer:

$it's upside-down$ Step-by-step explanation:

3 0

3 years ago

Based on an indication that mean daily car rental rates may be higher for Boston than for Dallas, a survey of eight car rental c

Elina [12.6K]

Answer:

$t=\frac{(47 -44)-(0)}{3\sqrt{\frac{1}{8}+\frac{1}{9}}}=2.058$

The degrees of freedom are:

$df=8+9-2=15$

And the p value would be:

$p_v =P(t_{15}>2.058) =0.0287$

Since we have a p value lower than the significance level given of 0.05 we can reject the null hypothesis and we can conclude that the true mean for car rental rates in Boston are signiﬁcantly higher than those in Dallas

Step-by-step explanation:

Data given

$n_1 =8$ represent the sample size for group Boston

$n_2 =9$ represent the sample size for group Dallas

$\bar X_1 =47$ represent the sample mean for the group Boston

$\bar X_2 =44$ represent the sample mean for the group Dallas

$s_1=3$ represent the sample standard deviation for group Boston

$s_2=3$ represent the sample standard deviation for group Dallas

We can assume that we have independent samples from two normal distributions with equal variances and that is:

$\sigma^2_1 =\sigma^2_2 =\sigma^2$

Let the subindex 1 for Boston and 2 for Dallas we want to check the following hypothesis:

Null hypothesis: $\mu_1 \leq \mu_2$

Alternative hypothesis: $\mu_1 > \mu_2$

The statistic is given by this formula:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$

Where t follows a t student distribution with $n_1+n_2 -2$ degrees of freedom and the pooled variance $S^2_p$ is given by this formula:

$\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}$

Replacing we got:

$\S^2_p =\frac{(8-1)(3)^2 +(9 -1)(3)^2}{8 +9 -2}=9$

And the deviation would be just the square root of the variance:

$S_p=3$

The statitsic would be:

$t=\frac{(47 -44)-(0)}{3\sqrt{\frac{1}{8}+\frac{1}{9}}}=2.058$

The degrees of freedom are:

$df=8+9-2=15$

And the p value would be:

$p_v =P(t_{15}>2.058) =0.0287$

Since we have a p value lower than the significance level given of 0.05 we can reject the null hypothesis and we can conclude that the true mean for car rental rates in Boston are signiﬁcantly higher than those in Dallas

5 0

4 years ago