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lara [203]
3 years ago
6

These are statements about factors and prime and composite numbers. Which statements are true? Check all that apply. The numbers

4, 9, 25, and 49 are composite numbers. The number 1 is a prime number. The first prime number is 2. A composite number can be written as the product of prime numbers.
Mathematics
2 answers:
4vir4ik [10]3 years ago
8 0
<h2>Answer: <u><em>A,C,D!!! These are correct!!!</em></u></h2>

Savatey [412]3 years ago
5 0

Answer:

The numbers 4, 9, 25, and 49 are composite numbers.

The number 1 is a prime number.

Step-by-step explanation:

A prime number can be defined as a number that is divisible by 1 and itself only. Examples are: 1, 3, 5, 7, 11 e.t.c

A composite number can be defined as a positive number that can be formed by multiplying two smaller positive numbers together. These two positive integers may or may not be prime number.

It is a positive integer that has at least one divisor other than 1 and itself.

Examples are: 4, 6, 8, 9, 12, 25, 49, e.t.c

Therefore, the true statements in the questions above =

The numbers 4, 9, 25, and 49 are composite numbers.

The number 1 is a prime number.

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The following data comparing wait times at two rides at Disney are listed below: Position Pirates Splash Mountain Sample Size 32
myrzilka [38]

Answer:

a) (14.68 -18.77) - 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =-12.968

(14.68 -18.77) + 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =4.788

b) t=\frac{14.68-18.77}{\sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}}}}=-1.10  

Step-by-step explanation:

Data given and notation

\bar X_{A}=14.68 represent the mean for Pirates

\bar X_{B}=18.77 represent the mean for Splash Mountain

s_{A}=11.87 represent the sample standard deviation for the sample Pirates

s_{B}=16.79 represent the sample standard deviation for the sample Slpash Mountain

n_{A}=32 sample size selected for Pirates

n_{B}=30 sample size selected for Splash Mountain

\alpha=0.02 represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

p_v represent the p value for the test (variable of interest)

Part a

The confidence interval would be given by:

(\bar X_A -\bar X_B) \pm t_{\alpha/2} \sqrt{\frac{s^2_{A}}{n_{A}}+\frac{s^2_{B}}{n_{B}}}

The degrees of freedom are given by:

df = n_A +n_B -2 = 32+30-2 = 60

Since we want 98% of confidence the significance level is \alpha =1-0.98 =0.02 and \alpha/2 =0.01, we can find in the t distribution with df =60 a critical value that accumulates 0.01 of the area on each tail and we got:

t_{\alpha/2}= 2.39

And replacing we got for the confidence interval:

(14.68 -18.77) - 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =-12.968

(14.68 -18.77) + 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =4.788

Part b

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the means are equal, the system of hypothesis would be:

Null hypothesis:\mu_{A} = \mu_{B}

Alternative hypothesis:\mu_{A} \neq \mu_{B}

the statistic is given by:

t=\frac{\bar X_{A}-\bar X_{B}}{\sqrt{\frac{s^2_{A}}{n_{A}}+\frac{s^2_{B}}{n_{B}}}} (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Calculate the statistic

We can replace in formula (1) the info given like this:

t=\frac{14.68-18.77}{\sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}}}}=-1.10  

6 0
3 years ago
Find the value of x. Round your answer to the nearest tenth. tan 12 degrees= ten over (x)
Lorico [155]
Tan(12)=-0.6358599287. That means -0.6358599287 = 10/x so you can swap the x to the other side to make x = 10/-0.6358599287 Which equals -15.7 rounded to the nearest tenth.
5 0
3 years ago
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13. After Valentine's Day, boxes of chocolates go on sale and are marked down 10%. The
Anna007 [38]

Answer:

$27.00

Step-by-step explanation:

First, 10% of 30 = 3.

Second, 30 - 3 = 27

Hope this helps!

5 0
3 years ago
Prove the identity (sina-cosatanb)/(cosa+sinatanb) = tan (a+b)
OLga [1]
Sina - (cosa)(tanb)/cosa + (sina)(tanb)
sina ≡ (tana)(cosa)

(tana)(cosa) - (cosa)(tanb)/cosa + (tana)(cosa)(tanb)
= cosa(tana - tanb)/cosa(1 + tanatanb)
(cosas cancel out)
= (tana - tanb)/(1 + tanatanb) ≡ tan(a-b)
7 0
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Simplify 3(2 - c) - C​
kondor19780726 [428]

Answer:

6-3c-C

Step-by-step explanation:

3(2-c)-C

3(2)-3(c)-C

6-3c-C

7 0
3 years ago
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