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3 years ago

The sum of two numbers is 51 and the difference is 1 . What are the numbers?

Mathematics

2 answers:

Art [367]3 years ago

6 0

Answer:

-52 and 53

Step-by-step explanation:

adell [148]3 years ago

4 0

26 and 25. 26+25=51 and 26-25=1

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Write an equation of the line with a slope of −1/2 and a y-intercept of 1.

masha68 [24]

Answer:

y=-1/2x+1

Step-by-step explanation:

y=mx+b

5 0

3 years ago

In around of golf, the lowest score wins. At the end of a round you have score -3 and your friend has score -4. Who won the roun

scoray [572]

Answer: The friend won the round.

Step-by-step explanation:

We want to find the lowest score.

The lowest score means the smallest value.

With intergers, as the number gets farther away from zero to the left, the smaller the value is. The middle number is zero on a number line. The numbers to the left of zero are negative. The number to the write of zero are positive.

As you move to the left on the number line, the numbers get smaller. As you move to the right on a number line, the values get bigger

Since -4 is farther away from zero to the left on a number line than -3, -4 is smaller.

Hence -4 is smaller than -3. -4 is one more to the left than -3 so -4 is smaller than -3.

Hence the friend won the round.

3 0

3 years ago

I know you want to answer this question.

Alik [6]

Answer:

D. x = 3

Step-by-step explanation:

$\frac{1}{2} ^{x-4}$ - 3 = $4^{x-3}$ - 2

First, convert $4^{x-3}$ to base 2:

$4^{x-3}$ = $(2^{2})^{x-3}$

$\frac{1}{2} ^{x-4}$ - 3 = $(2^{2})^{x-3}$ - 2

Next, convert $\frac{1}{2} ^{x-4}$ to base 2:

$\frac{1}{2} ^{x-4}$ = $(2^{-1})^{x-4}$

$(2^{-1})^{x-4}$ - 3 = $(2^{2})^{x-3}$ - 2

Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

$(2^{-1})^{x-4}$ = $2^{-1*(x-4)}$

$2^{-1*(x-4)}$ - 3 = $(2^{2})^{x-3}$ - 2

Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

$(2^{2})^{x-3}$ = $2^{2(x-3)}$

$2^{-1*(x-4)}$ - 3 = $2^{2(x-3)}$ - 2

Apply exponent rule: $a^{b+c}$ = $a^{b}$ $a^{c}$ :

$2^{-1(x-4)}$ = $2^{-1x}$ * $2^{4}$ , $2^{2(x-3)}$ = $2^{2x}$ * $2^{-6}$

$2^{-1 * x}$ * $2^{4}$ - 3 = $2^{2x}$ * $2^{-6}$ - 2

Apply exponent rule: $(a^{b})^{c}$ = $a^{bc}$ :

$2^{-1x}$ = $(2^{x})^{-1}$ , $2^{2x}$ = $(2^{x})^{2}$

$(2^{x})^{-1}$ * $2^{4}$ - 3 = $(2^{x})^{2}$ * $2^{-6}$ - 2

Rewrite the equation with $2^{x} = u$ :

$(u)^{-1}$ * $2^{4}$ - 3 = $(u)^{2}$ * $2^{-6}$ - 2

Solve $u^{-1}$ * $2^{4}$ - 3 = $u^{2}$ * $2^{-6}$ - 2:

$u^{-1}$ * $2^{4}$ - 3 = $u^{2}$ * $2^{-6}$ - 2

Refine:

$\frac{16}{u}$ - 3 = $\frac{1}{64}$ $u^{2}$ - 2

Add 3 to both sides:

$\frac{16}{u}$ - 3 + 3 = $\frac{1}{64}$ $u^{2}$ - 2 + 3

Simplify:

$\frac{16}{u}$ = $\frac{1}{64}$ $u^{2}$ + 1

Multiply by the Least Common Multiplier (64u):

$\frac{16}{u}$ * 64u = $\frac{1}{64}$ $u^{2}$ + 1 * 64u

Simplify:

$\frac{16}{u}$ * 64u = $\frac{1}{64}$ $u^{2}$ + 1 * 64u

Simplify $\frac{16}{u}$ * 64u:

1024

Simplify $\frac{1}{64}$ $u^{2}$ * 64u:

$u^{3}$

Substitute:

1024 = $u^{3}$ + 64u

Solve for u:

u = 8

Substitute back u = $2^{x}$ :

8 = $2^{x}$

Solve for x:

x = 3

4 0

3 years ago

A random sample of 5120 permanent dwellings on an entire reservation showed that 1627 were traditional hogans.

krek1111 [17]

Answer:

a) $\hat p=\frac{1627}{5120}=0.3178$

b)The 99% confidence interval would be given by (0.301;0.355)

Step-by-step explanation:

1) Notation and definitions

$X=1627$ number of permanent dwellings on the entire reservation that are traditional hogans.

$n=5120$ random sample taken

$\hat p=\frac{1627}{5120}=0.318$ estimated proportion of permanent dwellings on the entire reservation that are traditional hogans.

$p$ true population proportion of permanent dwellings on the entire reservation that are traditional hogans.

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".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

Part a

The point of estimate for p=the proportion of all permanent dwellings on the entire reservation that are traditional hogans is given by:

$\hat p=\frac{1627}{5120}=0.3178$

Part b

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58$

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

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

If we replace the values obtained we got:

$0.318 - 2.58\sqrt{\frac{0.318(1-0.318)}{5120}}=0.301$

$0.318 + 2.58\sqrt{\frac{0.318(1-0.318)}{5120}}=0.335$

The 99% confidence interval would be given by (0.301;0.355)

8 0

3 years ago

2x + y = -3<br> What’s the solution?

Ede4ka [16]

Y= -3 - 2x because all you have to do is move the 2x over to have an x and a y on different sides, and in order to do that you do the opposite so since it is a positive 2, you subtract it and make it negative

7 0

3 years ago

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