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3 years ago

Solve: the sum of two numbers is 70. one number is 4 times the other. what are the two numbers?

1 answer:

8 0

Lets say two numbers are x and y

x+y=70-----------------------eq1

x=4y--------------------eq2

4y+y=70
5y=70
y=70/5
y=14

then x=4*14

x=56

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Special right triangles

Tasya [4]

Right angle is the answer I think ( not sure though )

8 0

2 years ago

-2(3x + 1) > - 6x + 7

svp [43]

Answer:

I am pretty sure this statement is false so it'd be: x= 0

Step-by-step explanation:

8 0

3 years ago

If A^2=A, which matrix is matrix A

Ronch [10]

Consider all options:

$\left[\begin{array}{cc}5&5\\-4&-4\end{array}\right] \cdot \left[\begin{array}{cc}5&5\\-4&-4\end{array}\right] =\left[\begin{array}{cc}5\cdot 5+5\cdot (-4)&5\cdot 5+5\cdot (-4)\\-4\cdot 5+(-4)\cdot (-4)&-4\cdot 5+(-4)\cdot (-4)\end{array}\right]=$

$=\left[\begin{array}{cc}5&5\\-4&-4\end{array}\right].$

This option is true.

$\left[\begin{array}{cc}6&5\\5&6\end{array}\right] \cdot \left[\begin{array}{cc}6&5\\5&6\end{array}\right] =\left[\begin{array}{cc}6\cdot 6+5\cdot 5&6\cdot 5+5\cdot 6\\5\cdot 6+6\cdot 5&5\cdot 5+6\cdot 6\end{array}\right]=$

$=\left[\begin{array}{cc}61&60\\60&61\end{array}\right].$

This option is false.

$\left[\begin{array}{cc}0.5&-0.5\\-0.5&0.5\end{array}\right] \cdot \left[\begin{array}{cc}0.5&-0.5\\-0.5&0.5\end{array}\right] =\left[\begin{array}{cc}0.5\cdot 0.5+(-0.5)\cdot (-0.5)&0.5\cdot (-0.5)+(-0.5)\cdot 0.5\\-0.5\cdot 0.5+0.5\cdot (-0.5)&-0.5\cdot (-0.5)+0.5\cdot 0.5\end{array}\right]=$

$=\left[\begin{array}{cc}0.5&-0.5\\-0.5&0.5\end{array}\right].$

This option is true.

$\left[\begin{array}{cc}0.5&0.5\\-0.5&0.5\end{array}\right] \cdot \left[\begin{array}{cc}0.5&0.5\\-0.5&0.5\end{array}\right] =\left[\begin{array}{cc}0.5\cdot 0.5+0.5\cdot (-0.5)&0.5\cdot 0.5+0.5\cdot 0.5\\-0.5\cdot 0.5+0.5\cdot (-0.5)&-0.5\cdot 0.5+0.5\cdot 0.5\end{array}\right]=$

$=\left[\begin{array}{cc}0&0.5\\-0.5&0\end{array}\right].$

This option is false.

$\left[\begin{array}{cc}-6&-6\\5&5\end{array}\right] \cdot \left[\begin{array}{cc}-6&-6\\5&5\end{array}\right] =\left[\begin{array}{cc}-6\cdot (-6)+(-6)\cdot 5&-6\cdot (-6)+(-6)\cdot 5\\5\cdot (-6)+5\cdot 5&5\cdot (-6)+5\cdot 5\end{array}\right]=$

$=\left[\begin{array}{cc}6&6\\-5&-5\end{array}\right].$

This option is false.

Answer: correct options are A and C.

8 0

3 years ago

Read 2 more answers

Torri had $20 to buy a birthday present for her dad.She decided to buy a DVD for $18.The sales tax is 7%.Does she have enough mo

Brut [27]

Yes, Torri does have enough.
How to find the answer:
Find the decimal of 7% which is 0.07
Multiply 0.07 times $18 which gives you 1.26
0.07 x 18 = 1.26
Add 1.26 to 18 which gives us 19.26
1.26 + 18 = 19.26
Our finale answer is 19.26
Torri has enough money to buy her dad the DVD.
Hope this helps! =)

6 0

3 years ago

Read 2 more answers

A scrap metal dealer claims that the mean of his sales is "no more than $80," but an Internal Revenue Service agent believes the

Artyom0805 [142]

Answer:

There is enough not evident to support dealer's claim that his sales is no more than $80.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = $80

Sample mean, $\bar{x}$ = $91

Sample size, n = 20

Alpha, α = 0.05

Sample standard deviation, s = $21

First, we design the null and the alternate hypothesis

$H_{0}: \mu \leq 80\text{ dollars}\\H_A: \mu > 80\text{ dollard}$

We use one-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{91 - 80}{\frac{21}{\sqrt{20}} } = 2.3425$

Now, $t_{critical} \text{ at 0.05 level of significance, 19 degree of freedom } = 1.729$

Since,

The calculated test statistic is greater than the critical value, we fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.

Conclusion:

There is enough not evident to support dealer's claim that his sales is no more than $80.

4 0

3 years ago