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2 years ago

The sum of two numbers is 67. The larger number is 19 more than the smaller number. What are the numbers

Mathematics

1 answer:

maxonik [38]2 years ago

4 0

Answer:

32 and 35

Step-by-step explanation:

I am going to use x for the smaller number and y for the larger one.

The sum of both these numbers is 67, so the equation should be:x+y=67

Since the smaller number is three less than the larger number, that means 3 has to be added to the smaller number to make it equal in size to the larger number.

x+3=y

To solve the equation, simply plug in

x+3 for the y variable in the first equation.x+x+3=67→ Rewrite the first equation2x=64→

Subtract 3 from each side, combine like termsx=32→

Divide each side by 2The smaller number is 32, so we plug that in to the second equation to find the larger number.

32+3=yy=35

The two numbers are 32 and 35

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Katy buys 4 DVDS every 2 weeks how many DVDS will she buy in 14 weeks

liraira [26]

Answer:

28 dvds in 14 weeks

Step-by-step explanation:

4 dvds in two weeks

2 dvds in a week

14 weeks equal 28 dvds

6 0

3 years ago

Do the three points lie on one line?

padilas [110]

Answer:

Yes. No graph paper.

Step-by-step explanation:

Let's say the 3 points are A, B, C.

If A, B and C lie on one line then $m_{AB} = m_{BC} = m_{AC}$

$m_{AB} = \frac{y_{B}-y_{A} }{x_{B}-x_{A}} = \frac{2-6}{3-5} = \frac{-4}{-2} = 2\\m_{BC} = \frac{y_{C}-y_{B} }{x_{C}-x_{B}} = \frac{8-2}{6-3} = \frac{6}{3} = 2\\\\m_{AC} = \frac{y_{C}-y_{A} }{x_{C}-x_{A}} = \frac{8-6}{6-5} = \frac{2}{1} = 2\\\\$

Hence, they lie on one line.

You don't need to use a graph paper to prove it.

4 0

2 years ago

Tennis elbow is thought to be aggravated by the impact experienced when hitting the ball. The article "Forces on the Hand in the

Gnoma [55]

Answer:

Step-by-step explanation:

Hello!

The objective is to study whether there is a greater force after impacting on one- handed backhand drive in advanced tennis players than in intermediate tennis players.

Sample 1: Advanced tennis players

X₁: Force (N) on the hand just after impact on a one- handed backhand drive for an advanced tennis player.

n₁= 6

X[bar]₁= 40.29 N

S₁= 11.29

Sample 2: Intermediate players

X₂: Force (N) on the hand just after impact on a one- handed backhand drive for an intermediate tennis player.

n₂= 8

X[bar]₂= 21.40

S₂= 8.30

Assuming that both variables have a normal distribution and both population variances are equal, to compare these two populations is best to do so trough their population means using a t-test for independent samples.

If the force is greater for the advanced players than for the intermediate players, then you'd expect the population mean for the advanced players to be greater than the population mean for the intermediate players:

H₀: μ₁ ≤ μ₂

H₁: μ₁ > μ₂

α: 0.05

$t= \frac{(X_[bar]_1-X[bar]_2)-(Mu_1-Mu_2)}{Sa\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ~~t_{n_1+n_2-2}$

$Sa= \sqrt{\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} } = \sqrt{\frac{5*127.51+7*68.92}{6+8-2} }= 9.66$

$t_{H_0}= \frac{(40.29-21.40)-0}{9.66\sqrt{\frac{1}{6} +\frac{1}{8} } } = 3.62$

Using the p-value approach, the decision rule is

If p-value ≤ α, reject the null hypothesis

If p-value > α, do not reject the null hypothesis

The p-value for this test is 0.00024, it is less than the level of significance, so the decision is to reject the null hypothesis.

This means that at a 5% significance level you can conclude that the average force experienced on the hand after a one-handed backhand drive for advanced players is greater than the average force experienced on the hand after a one-handed backhand drive for intermediate players.

I hope this helps!

3 0

3 years ago

Simplify the expression 8 + (7 + x)

baherus [9]

Answer:

15 + x

Step-by-step explanation:

6 0

2 years ago

I need help! And quick!!

Aleks04 [339]

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5 0

3 years ago