MATHEMATICS COLLEGE

To paint his apartment, Alex but 6 gallons of paint to cover 1440 ft.². What is the ratio of square feet to gallons of paint?

Answers

Answer 1

Answer:

Answer & Step-by-step explanation:

The ratio of square feet to gallons of paint:

$1440:6$

This can also be written as:

$(1440)/(6)$

This fraction can be simplified by dividing the numerator and denominator by 6:

$(1440)/(6)=(240)/(1)$

So, the ratio of square feet to gallons of paint is:

1 gallon for every 240 ft².

:Done

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A random sample of size 13 is selected from men with hypertension. For each person, systolic blood pressure was measured right before and one hour after taking the medicine. The mean reduction of the blood pressures was 10.1 and the standard deviation of the difference was 11.2. Test if there is sufficient evidence to conclude that the hypertension medicine lowered blood pressure. What is the value of the test statistic (round off to second decimal place)

Answers

Answer:

Yes, hypertension drugs lowers blood pressure.

Step-by-step explanation:

Claim: The hypertension medicine lowered blood pressure.

The null and alternative hypothesis is

H0:\mu_{d}\geq 0

H1:\mu_{d}< 0

Level of significance = 0.05

Sample size = n = 13

Sample mean of difference = \bar{d} = 10.1

Sample standard deviation of difference = s_{d} = 11.2

Test statistic is

t=\frac{\bar{d}}{s_{d}/\sqrt{n}}

t = ((10.1) / (11.2 /squre root of 13)) = 3.251

Degrees of freedom = n - 1 = 13 - 1 = 12

Critical value =2.179( Using t table)

Test statistic | t | > critical value we reject null hypothesis.

In Conclusion: The hypertension medicine lowered blood pressure

Factor completely 56 s to the second power + 23 SW - 63 W to the second power

Answers

(8s-7w)(7s+9w) is the complete factored form.

A regular octagon dividesinto how many triangles
(drawn from a point in the
center of the octagon)?

Answers

Answer:

Step-by-step explanation:

a triangle for each side

Estimate the quotient by rounding the expression to relate to a one-digit fact. Explain your thinking in the space below. a. 432 ÷ 73 ___________ b. 1,275 ÷ 588 ___________

Answers

Estimations are used to get the approximated value of an expression.

The estimate of 432 ÷ 73 is 5.714
The estimate of 1,275 ÷ 588 is 1.667

$\mathbf{(a)\ 432 / 73}$

Round up to 1 digit

$\mathbf{432 / 73 \approx 400 / 70}$

Divide

$\mathbf{432 / 73 \approx 5.714}$

Hence, the estimate of 432 ÷ 73 is 5.714

$\mathbf{(b)\ 1275 / 588}$

Round up to 1 digit

$\mathbf{ 1275 / 588 \approx 1000 / 600}$

Divide

$\mathbf{ 1275 / 588 \approx 1.667}$

Hence, the estimate of 1,275 ÷ 588 is 1.667

Answers

the tree that casts a 48 foot shadow is 24 feet

Point A is located at (-2, 2), and point M is located at (1,0). If point M is the midpoint of AB, find the location of point B.O(-0.5, 1)

O (4,-2)

O(-5,4)

O(-1,1)

Answers

Answer:

B. $B = (4,-2)$

Step-by-step explanation:

GIven that $A = (-2, 2)$ and $M = (1, 0)$ , and that point M is the midpoint of AB, the midpoint can be determined as a vectorial sum of A and B. That is:

$M = (1)/(2)\cdot A + (1)/(2)\cdot B$

The location of B is now determined after algebraic handling:

$(1)/(2)\cdot B = M - (1)/(2)\cdot A$

$B = 2\cdot M -A$

Then:

$B = 2\cdot (1,0)-(-2,2)$

$B = (2\cdot 1, 2\cdot 0)-(-2,2)$

$B = (2,0) -(-2,2)$

$B = (4,-2)$

Which corresponds to option B.

The coordinate of point B will be (4, -2). Then the correct option is B.

What is coordinate geometry?

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

Point A is located at (-2, 2), and point M is located at (1,0).

If point M is the midpoint of AB.

Then the location of point B will be

We know that the mid section formula

$\rm (x, y) = \left ( (x_1+x_2)/(2), (y_1+y_2)/(2) \right)$