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Westkost [7]
3 years ago
13

2 numbers are such that if 7 is added to the first number, a number twice the second number is obtained. If 20 is added to the s

econd number, the number obtained is four times the first number. Find the two numbers​
Mathematics
1 answer:
Eduardwww [97]3 years ago
5 0

Answer:

1st= 47/7 or 6.71

2nd= 48/7 or 6.857

Step-by-step explanation:

1st number =X and 2nd number = Y

According to question, X+7=2Y

20+Y=4X

X=2Y-7 (from 1st condition)

putting in it second

20+Y=4(2Y-7)

20+Y=8Y-28

20+28=8Y-Y

48=7Y

Y=48/7

so X=2(48/7)-7

=96-49/7

47/7

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Irene knows there are 2 cups in 1 pint. She writes the equation c=2p to find the number of cups, c, in any number of pints, p. U
Natasha2012 [34]

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as there are no options to select from.

However, a general explanation is as follows.

Given

2\ cups = 1\ pint

Required

Is c = 2p a correct expression?

Let

c = cups

p = pint

So:

2\ cups = 1\ pint

becomes

2 * c = 1 * p

2c = p

Divide both sides by 2

c =\frac{1}{2}p

Hence:

c = 2p is incorrect

4 0
2 years ago
Consider the following hypothesis test: H0: LaTeX: \mu_1-\mu_2=0μ 1 − μ 2 = 0 Ha: LaTeX: \mu_1-\mu_2\ne0μ 1 − μ 2 ≠ 0 The follow
Pavel [41]

Answer:

z=\frac{104-\bar 106}{\sqrt{\frac{8.4^2}{80}+\frac{7.6^2}{70}}}}=-1.53

Step-by-step explanation:

Data given and notation

\bar X_{1}=104 represent the mean for the sample 1

\bar X_{2}=106 represent the mean for the sample 2

\sigma_{1} =8.4 represent the population standard deviation for the sample 1

\sigma_{2}=7.6 represent the population standard deviation for the sample 2

n_{1}=80 sample size for the group 1

n_{2}=70 sample size for the group 2

z would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the means for the two groups are the same, the system of hypothesis would be:

H0:\mu_{1}-\mu_{2} =0

H1:\mu_{1} -\mu_{2} \neq 0

If we analyze the size for the samples both are greater than 30 and we know the population deviations so for this case is better apply a z test to compare means, and the statistic is given by:

z=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}} (1)

z-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

First we need to calculate the mean and deviation for each sample, after apply the formulas (2) and (3) we got the following results:

And with this we can replace in formula (1) like this:

z=\frac{104-\bar 106}{\sqrt{\frac{8.4^2}{80}+\frac{7.6^2}{70}}}}=-1.53

7 0
3 years ago
Which of the following is the solution to 9|x +4|>54 ?
horsena [70]

Answer:

x>2 or x<-10

Step-by-step explanation:

9|x +4|>54

Divide each side by 9

9/9|x +4|>54/9

|x +4|>6

There are two solutions, one positive and one negative

x+4 >6  or x+4 < -6

Subtract 4 from each side

x+4-4 >6-4   or x+4-4 < -6-4

x>2 or x<-10

4 0
2 years ago
A rocket is launched from the ground and travels in a straight path. The angle of inclination of the rocket's path is 1.2 radian
gladu [14]

Answer:

a)S=2.57

b)H=203.2yard

c)X=121.79yards

Step-by-step explanation:

From the question we are told that:

Angle \theta=1.2=68.755^o

a)

Generally the equation for Slope is mathematically given by

 S=tan \theta

 S=tan 68.755

 S=2.57

b)

Given the right Angle triangle with horizontal distance x=85yard

Generally the equation for Height traveled is mathematically given by

 H=tan\theta*x

 H=2.57*85

 H=218.45

 H=203.2yard

c)

Generally the equation for Horizontal Distance traveled at 313 height traveled is mathematically given by

X=\frac{313}{tan65.75}

X=\frac{313}{2.57}

X=121.79yards

3 0
2 years ago
I need to buy some cardboard to build a box 12 inches long, 8 inches wide and 10 inches high. How much cardboard is needed to bu
Sliva [168]

Answer:

960

Step-by-step explanation:

you have to multiply 12*8*10

12*8=96

96*10=960

7 0
3 years ago
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