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4 years ago

What is the product of -3 1/4 × -1 1/2

Mathematics

2 answers:

Dmitry [639]4 years ago

4 0

For this case we must find the product of the following expression:

$-3 \frac {1} {4} * - 1 \frac {1} {2} =$

So, we have:

$(\frac {4 * (3) +1} {4}) * (\frac {2 * (1) +1} {2}) =\\\frac {12 + 1} {4} * \frac {2 + 1} {2} =\\(- \frac {13} {4}) * (- \frac {3} {2}) =$

By law of signs of multiplication is fulfilled:

$- * - = +\\\frac {13 * 3} {4 * 2} =\\\frac {39} {8}$

ANswer:

$\frac {39} {8}$

OLga [1]4 years ago

4 0

Answer:

$4\frac{7}{8}$

Step-by-step explanation:

$-3\frac{1}{4} \times -1\frac{1}{2} = -\frac{13}{4} \times -\frac{3}{2} = \frac{39}{8} = 4\frac{7}{8}$

I am joyous to assist you anytime.

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AB is parallel to ED.

ivolga24 [154]

Answer:

BE = 22.4 cm

Step-by-step explanation:

Δ CAB and Δ CDE are similar , then ratios of corresponding sides are equal, that is

$\frac{CB}{CE}$ = $\frac{AB}{DE}$ , substitute values

$\frac{6.4}{CE}$ = $\frac{8}{20}$ ( cross- multiply )

8 CE = 128 ( divide both sides by 8 )

CE = 16 cm

Then

BE = BC + CE = 6.4 + 16 = 22.4 cm

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3 years ago

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Irina18 [472]

I believe 4(x - 3)=32 could help I haven’t done an equation from the unit in months so hopefully that looks familiar to you.

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3 years ago

3(x 2) 11 is greater than 20

Allushta [10]

3(x+2)+11>20
minus 11 both sides
3(x+2)>9
divide both sides by 3
x+2>3
minus 2 both sides
x>1

4 0

3 years ago

An educator claims that the average salary of substitute teachers in school districts is less than $60 per day. A random sample

valentina_108 [34]

Answer:

$t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626$

The degrees of freedom are given by:

$df=n-1=8-1=7$

The p value would be given by:

$p_v =P(t_{(7)}$

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

Step-by-step explanation:

Information given

60, 56, 60, 55, 70, 55, 60, and 55.

We can calculate the mean and deviation with these formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

Replacing we got:

$\bar X=58.875$ represent the mean

$s=5.083$ represent the sample standard deviation for the sample

$n=8$ sample size

$\mu_o =60$ represent the value that we want to test

$\alpha=0.1$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to test if the true mean is less than 60, the system of hypothesis would be:

Null hypothesis: $\mu \geq 60$

Alternative hypothesis: $\mu < 60$

The statistic would be given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing the info we got:

$t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626$

The degrees of freedom are given by:

$df=n-1=8-1=7$

The p value would be given by:

$p_v =P(t_{(7)}$

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

3 0

3 years ago

Find an equation for the perpendicular bisector of the line segment whose endpoints

TEA [102]

Answer:

y= -2x -8

Step-by-step explanation:

I will be writing the equation of the perpendicular bisector in the slope-intercept form which is y=mx +c, where m is the gradient and c is the y-intercept.

A perpendicular bisector is a line that cuts through the other line perpendicularly (at 90°) and into 2 equal parts (and thus passes through the midpoint of the line).

Let's find the gradient of the given line.

$\boxed{gradient = \frac{y1 -y 2}{x1 - x2} }$

Gradient of given line

$= \frac{1 - ( - 5)}{3 - ( - 9)}$

$= \frac{1 + 5}{3 + 9}$

$= \frac{6}{12}$

$= \frac{1}{2}$

The product of the gradients of 2 perpendicular lines is -1.

(½)(gradient of perpendicular bisector)= -1

Gradient of perpendicular bisector

= -1 ÷(½)

= -1(2)

= -2

Substitute m= -2 into the equation:

y= -2x +c

To find the value of c, we need to substitute a pair of coordinates that the line passes through into the equation. Since the perpendicular bisector passes through the midpoint of the given line, let's find the coordinates of the midpoint.

$\boxed{midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2}) }$