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1 year ago

The sum of a three-digit number and one-digit number is 731. The product of the numbers is 2,908. What are the numbers?

Mathematics

1 answer:

miss Akunina [59]1 year ago

7 0

Solving a system of equations we can see that the two numbers are 727 and 4

<h3></h3><h3>How to find the two numbers?</h3>

Let's define x as the 3-digit number and y as the one-digit number.

Then we know that the sum is equal to 731:

x + y = 731

And the product is equal to 2,908, then:

x*y = 2,908

So we have a system of equations:

x + y = 731

x*y = 2,908

Isolating x on the first equation gives:

x = 731 - y

Now we can replace that in the other equation to get:

(731 - y)*y = 2,908

Now we can solve this quadratic equation to find the value of y.

731*y - y^2 = 2,908

-y^2 + 731*y - 2,908 = 0

The solutions are:

y = (-731 ± √( 731^2 - 4*(-2,908)*(-1))/(-2)

y = (-731 ± 723)/-2

Now, y is an one digit number, then:

y = (-731 + 723)/-2 = 4

And x will be the 3 digit number:

x = 731 - x = 731 - 4 = 727

So the two numbers are 727 and 4

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If you bought a stock last year for a price of $67, and it has risen 12% since then, how much is the stock worth now, to the nea

lisabon 2012 [21]

Answer:$75.04

Step-by-step explanation:

last year price=$67

12% of 67

12/100 x 67

(12 x 67) ➗ 100

804 ➗ 100=8.04

Since it has risen by 12%

There new price is 67+8.04=75.04

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3 years ago

Rewrite 1−2 sin ^2 (22.5∘) using a double-angle identity.

attashe74 [19]

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Cos (2a) = 1-2 Sin^2(a)

Therefore :<span>1−2 sin ^2 (22.5∘) = Cos(2a)
= Cos (2 * 22.5) = Cos 45</span>

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3 years ago

Bruce pitches for his little brother's baseball team. He has observed that the number of pitches a batter hits varies and is giv

liberstina [14]

Hello!

If Bruce observes that the number of pitches a batter hits varies and is given by the function f(x)=x-11, and the batters get {4, 12, 14, 27, 42}, then Bruce threw {15, 23, 25, 38, 53} pitches. We get this solution set by adding 11 to each element in the set {4, 12, 14, 27, 42}.
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6 0

3 years ago

Suppose that the population mean for income is $50,000, while the population standard deviation is 25,000. If we select a random

Fudgin [204]

Answer:

Probability that the sample will have a mean that is greater than $52,000 is 0.0057.

Step-by-step explanation:

We are given that the population mean for income is $50,000, while the population standard deviation is 25,000.

We select a random sample of 1,000 people.

<em>Let </em> $\bar X$ <em> = sample mean</em>

The z-score probability distribution for sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean = $50,000

$\sigma$ = population standard deviation = $25,000

n = sample of people = 1,000

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, probability that the sample will have a mean that is greater than $52,000 is given by = P( $\bar X$ > $52,000)

P( $\bar X$ > $52,000) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{52,000-50,000}{\frac{25,000}{\sqrt{1,000} } }$ ) = P(Z > 2.53) = 1 - P(Z $\leq$ 2.53)

= 1 - 0.9943 = 0.0057

<em>Now, in the z table the P(Z </em> $\leq$ <em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 2.53 in the z table which has an area of 0.9943.</em>

Therefore, probability that the sample will have a mean that is greater than $52,000 is 0.0057.

5 0

2 years ago

Matrix a is a 6 × 5 matrix. which order of matrix can be multiplied by matrix a to create matrix ab?

mezya [45]

Order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.

<h3>What is a matrix?</h3>

A matrix is a rectangular array or table of numbers, symbols, or expressions that are organized in rows and columns to represent a mathematical object or an attribute of such an object in mathematics.
For instance, consider a matrix with two rows and three columns.

To find the order of matrix:

We must first check the dimension of two matrices, say matrix A by matrix B, before we may multiply them.
Multiplication is achievable if the number of columns in the first matrix, A, equals the number of rows in the second matrix.
Dimension is assigned to the provided matrix: 6 × 5
This means the given matrix contains six rows and five columns.
As a result, the second matrix MUST have 5 rows in order for multiplication to be POSSIBLE.
The only matrix with 5 rows among the above alternatives is the matrix with dimension (B) 5 × 6.

To prove:

In other words, the inner products of the dimensions should be equal.
That is; (a × b)(b × a) is possible but (a ×b)(c × b) is impossible.
The dimensions of the matrix are given by, row × column.

Therefore, order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.

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7 0

2 years ago