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aliya0001 [1]
3 years ago
15

the tens digit of a two digit number is twice the units digit. The sum of the digits is twelve. Find the original number.

Mathematics
1 answer:
KatRina [158]3 years ago
4 0
X - tens digit
y - units digit

x=2y\\
x+y=12\\\\
2y+y=12\\
3y=12\\
y=4\\\\
x=2\cdot4\\
x=8\\\\
10\cdot8+4=\boxed{84}

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Are AC and DF definitely parallel? How do you know?
SOVA2 [1]

Answer:

We know that,

Angle E = 123

Angle B = 57

We observe that,

Angle DEB and Angle E form a linear pair and are supplementary.

Angle DEB + Angle E = 180

Angle DEB = 180-123

=57

We know that if two lines are parallel, the corresponding angles are equal.

Conversely, if the corresponding angles are equal, then the two lines are parallel.

Here,

As Angle B and Angle DEB are corresponding angles are equal in measure (Angle B = Angle DEB = 57), we can say that Line AC and Line DF are parallel.

3 0
3 years ago
A classic rock radio station claims to play an average of 50 minutes of music every hour. However, it seems that every time you
tia_tia [17]

Answer:

a) 47.917-1.796\frac{2.811}{\sqrt{12}}=46.460    

47.917+1.796\frac{2.811}{\sqrt{12}}=49.374    

b) Null hypothesis: \mu =50

Alternative hypothesis: \mu \neq 50

And after analyze the interval obtained the upper limit not contains the value of 50, so then we can conclude that the claim is not satisfied for this case, and the population mean seems to be lower than 50 at 10% of significance.

Step-by-step explanation:

Previous concepts  

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

We have the following data: 44 49 45 51 49 53 49 44 47 50 46 48

And we can calculate the sample mean and deviation with the following formulas:

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

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

And replacing we got:

\bar X= 47.917, s= 2.811

\mu population mean (variable of interest)  

n=12 represent the sample size  

Part a: Calculate the confidence interval

The confidence interval for the mean is given by the following formula:  

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)  

The degrees of freedom are given:

df= n-1= 12-1=11

Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,11)".And we see that t_{\alpha/2}=1.796

Now we have everything in order to replace into formula (1):

47.917-1.796\frac{2.811}{\sqrt{12}}=46.460    

47.917+1.796\frac{2.811}{\sqrt{12}}=49.374    

Part b

For this case the system of hypothesis are:

Null hypothesis: \mu =50

Alternative hypothesis: \mu \neq 50

And after analyze the interval obtained the upper limit not contains the value of 50, so then we can conclude that the claim is not satisfied for this case, and the population mean seems to be lower than 50 at 10% of significance.

6 0
3 years ago
The ratio of the angles of a triangle is 3:8:4. What is the size of the largest angle?
Phantasy [73]

Answer: 96°

Step-by-step explanation:

Sum of angles of a triangle = 180°

3 + 8 + 4 = 15

The biggest angle is 8/15 * 180 = 96°

7 0
3 years ago
URGENT HELP ME PLEASE
Trava [24]

Answer:

(a)\log_3(\dfrac{81}{3})=3

(b)\log_5(\dfrac{625}{25})=2

(c)\log_2(\dfrac{64}{8})=3

(d)\log_4(\dfrac{64}{16})=1

(e)\log_6(36^4)=8

(f)\log(100^3)=6

Step-by-step explanation:

Let as consider the given equations are \log_3(\dfrac{81}{3})=?,\log_5(\dfrac{625}{25})=?,\log_2(\dfrac{64}{8})=?,\log_4(\dfrac{64}{16})=?,\log_6(36^4)=?,\log(100^3)=?.

(a)

\log_3(\dfrac{81}{3})=\log_3(27)

\log_3(\dfrac{81}{3})=\log_3(3^3)

\log_3(\dfrac{81}{3})=3        [\because \log_aa^x=x]

(b)

\log_5(\dfrac{625}{25})=\log_5(25)

\log_5(\dfrac{625}{25})=\log_5(5^2)

\log_5(\dfrac{625}{25})=2        [\because \log_aa^x=x]

(c)

\log_2(\dfrac{64}{8})=\log_2(8)

\log_2(\dfrac{64}{8})=\log_2(2^3)

\log_2(\dfrac{64}{8})=3        [\because \log_aa^x=x]

(d)

\log_4(\dfrac{64}{16})=\log_4(4)

\log_4(\dfrac{64}{16})=1        [\because \log_aa^x=x]

(e)

\log_6(36^4)=\log_6((6^2)^4)

\log_6(36^4)=\log_6(6^8)

\log_6(36^4)=8            [\because \log_aa^x=x]

(f)

\log(100^3)=\log((10^2)^3)

\log(100^3)=\log(10^6)

\log(100^3)=6            [\because \log10^x=x]

5 0
3 years ago
Number 12! Please show work
Allisa [31]
8 ounces because 1 quart equals 36 ounces. 36 Divided by her and her 3 friends equals 8 since 36 divided by four equals eight.
5 0
3 years ago
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