What is the solution to the given system of equations?​

9514 1404 393

Answer:

  row 13

Step-by-step explanation:

The sum of row n is 2^n, so the row number with a particular sum is ...

  2^n = sum

  n·log(2) = log(sum)

  n = log(sum)/log(2)

The row with sum 8192 is ...

  n = log(8192)/log(2) = 13

The row of Pascal's triangle that has a sum of 8192 is row 13.

9514 1404 393

Answer:

  $55,085.44

Step-by-step explanation:

The formula for the account balance is ...

  A = P(1 +r/n)^(nt)

where principal P is invested at annual rate r compounded n times per year for t years. Using the given values, we find the balance to be ...

  A = $21,000(1 +0.082/2)^(2·12) = $21,000(1.041^24) ≈ $55,085.44

The balance is $55,085.44 after 12 years.

Answer:

87.5%

Step-by-step explanation:

Complete question  -

75% of the people who eat at Doug's Diner order fish and 90% of the people who order fish also order fries. Given that 80% of all people who eat at Doug's order fries, what is the probability that a randomly chosen customer orders fries without fish?

Solution

Given

People who order fish at the Doug's Diner  = 75%

Out of this 75%, 90% also order  fries which means that nearly 67.5% ordered fries with the fish.

Given that, 80% of people dining at Doug's Diner order fries

Then percentage or people who ordered only fires and no fish = 80% - 67.5% = 12.5%

The probability of customers who ordered fish = 100 - 12.5% = 87.5%

Answer:                                              6666666667

-2.06666666667 to a fraction is : 2 ----------------------

                                                            100000000000

Step-by-step explanation:

Have a nice day :)

Answer:

The p-value of the test is 0.1611>0.01, which means that there is not significant evidence at the 1% significance level that less than 34% of fathers take no responsibility for child care

Step-by-step explanation:

A journal article reports that 34% of fathers take no responsibility for child care. A group of fathers believes that this estimate is too high.

At the null hypothesis, we test if the proportion is of at least 34%, that is:

[tex]H_0: p \geq 0.34[/tex]

At the alternative hypothesis, we test if the proportion is less than that, that is:

[tex]H_1: p < 0.34[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.34 is tested at the null hypothesis:

This means that [tex]\mu = 0.34, \sigma = \sqrt{0.34*0.66}[/tex]

In a random sample of 80 fathers, it was found that 23 of those fathers take no responsibility for child care.

This means that [tex]n = 80, X = \frac{23}{80} = 0.2875[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.2875 - 0.34}{\frac{\sqrt{0.34*0.66}}{\sqrt{80}}}[/tex]

[tex]Z = -0.99[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion below 0.2875, which is the p-value of Z = -0.99.

Looking at the Z-table, Z = -0.99 has a p-value of 0.1611.

The p-value of the test is 0.1611>0.01, which means that there is not significant evidence at the 1% significance level that less than 34% of fathers take no responsibility for child care

Answer:

g(a + 1) - g(a - 1) = 4a

Step-by-step explanation:

g(x) = x^2 + 5,

when x = a+1, g(a+1) = (a+1)^2 + 5.

when x = a-1, g(a-1) = (a-1)^2 +5.

g(a+1)-g(a-1) = (a+1)^2 + 5 - [(a-1)^2 + 5]

= a^2 + 2a + 1 + 5 - [a^2 - 2a + 1 + 5]

= 4a

Answer:

The answer is the second graph, Option 2

Step-by-step explanation:

[tex]\frac{( \csc x+1)( \csc x-1)}{ \csc ^2x} = \frac{ { \csc }^{2} x - 1}{ \csc^{2} x} \\ = 1 - \sin^{2} x = \cos^{2} x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

b. Since csc theta = 1/sin theta, we can multiply both sides by sin theta and you will end up with

[tex] \cos^{2} \theta + \sin^{2} \theta = 1[/tex]

which is an identity.

9514 1404 393

Answer:

  4

Step-by-step explanation:

2/3 = 4/6

There are four 1/6-cup servings of rice in 4/6 cups of rice.

Answer:

37.194574

Step-by-step explanation:

Answer:

$66.3

Step-by-step explanation:

price of a ticket without discount = $78

discount  % = 15%

discount amount = ?

price of a discounted ticket = ?

discount amount = discount% of price of a original ticket

=15/100 * $78

=$1170/100

=$ 11.7

price of the discounted ticket = $78 - $11.7

=$66.3

The discounted price of the stadium's normal ticket is  $66.3

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A stadium's normal ticket price is $78 and As a special promotion they offer 15% off.

Therefore, The discounted price of the ticket should be (100 - 15)% = 85% of the original price which is,

= (85/100)×78.

= $66.3 is the discounted price.

learn more about percentages here :

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Answer:

Step-by-step explanation:

Answer:

[tex] - 10x + 2y = - 28 - - - (a) \\ - 13x + 3y = - 40 - - - (b) \\ 3 \times (a) - 2 \times (b) : \\ - 4x + 0y = - 4 \\ x = 1 \\ ( - 10 \times 1) + 2y = - 28 \\ 2y = - 18 \\ y = -9[/tex]

answer: ( 1, -9 )

Answer:

4

Step-by-step explanation:

2(y-4)

=2y-8

2y=8

y=8/2

y=4

Hope it helps ☺️

Answer:

B) mix number

Answer:

x=7

Step-by-step explanation:

take 30 degree as reference angle

using sin tan rule

tan 30=opposite/adjacent

[tex]\frac{1}{\sqrt{3} }[/tex]=x/[tex]7\sqrt{3}[/tex]

[tex]\frac{1}{\sqrt{3} }[/tex] *[tex]7\sqrt{3}[/tex]

[tex]7\sqrt{3} /\sqrt{3}[/tex]

7=x

Answer:

c) it appears to be sound because the data are not biased in anyway.

Step-by-step explanation:

From the information given regarding the sample selection method , the size, the larger sample from which the survey subject were selected, we can conclude that the data is sound and not in anyway biased. The subject were selected from a reputable market research firm, which means the subjects were chosen from a larger sample which is reliable and not just a voluntary pool of subjects. Also, the selection process is randomized. Based on these, there are no flaws which are likely to cause the introduction of bias into the sample selected. Hence, the data is sound and not in any way biased.

Answer:

Step 1

Step-by-step explanation:

18 − (3x + 5) = 8

Step 1: 18 − 3x + 5 = 8

Correct Step 1: 18 - 3x - 5 = 8

Step 2: -3x + 23 = 8

Step 3: -3x = -15

Step 4: x = 5

The distributive property was applied incorrectly on Step 1.

Answer: Step 1

Step-by-step explanation:

(1.00)³⁶⁵

=1

1 power any natural number is 1

Answer:

1

Step-by-step explanation:

(1.00)^365

it means to multiply (1 .00) 365 times

Answer:

4. 18 cm^2

5. 24 cm^2

6. 12 cm^2

SA: 108 cm^2

Step-by-step explanation:

Answer:

Surface area is 108

1.  18

4. 18

2. 12

6.  12

3. 24

5. 24

Step-by-step explanation:

1. 3 x 6 = 18

4. 3 x 6 = 18

2. 4 x 3 = 12

6. 4 x 3 = 12

3. 4 x 6 = 24

5. 4 x 6 = 24

Answer:

B

Step-by-step explanation:

Answer:

B EDGE

Step-by-step explanation:

Answer:

141 bunches, 7 flowers left

Step-by-step explanation:

Number of bunches of flowers that can the florist make is 23 flowers

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Here, we have,

If 60% of the flowers in a bunch are lilies,

then there are 40 x 0.6 = 24 lilies in each bunch.

That means there are 40 - 24 = 16 roses and carnations in each bunch.

The ratio of carnations to roses = 3 : 5

Let's call the number of carnations in each bunch "3x" and the number of roses in each bunch "5x". That means

3x + 5x = 16 (the total number of carnations and roses)

8x = 16

x = 2

So there are 3 x 2 = 6 carnations in each bunch.

If the florist has only 140 carnations, they can make 140 / 6 = 23.333... bunches of flowers. However, since they can't make a fraction of a bunch, the florist can only make 23 bunches of flowers.

Learn more about ratio here

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complete question:

A florist is making some bunches of flowers for a wedding. Each bunch contains some carnations, roses, and lilies. Each bunch is the same. - A bunch contains 40 flowers -60% of the flowers are lilies The ratio of carnations to roses is 3:5 The florist only has 140 carnations. How many bunches of flowers can the florist make?​

Assuming the curve is

y = cos(x) - √3 sin(x)

differentiate once to get dy/dx, which gives the slope of the tangent line to y at some point x. The derivative is

dy/dx = -sin(x) - √3 cos(x)

The tangent line is horizontal when the derivative is 0, so you end up having to solve

-sin(x) - √3 cos(x) = 0

sin(x) = -√3 cos(x)

sin(x)/cos(x) = tan(x) = -√3

x = arctan(-√3) + nπ

(where n is an integer)

x = -arctan(√3) + nπ

x = -π/3 + nπ

You get two solutions in the interval [0, 2π] when n = 1 and n = 2, for which

x = 2π/3   or   x = 5π/3

===================================================

Explanation:

16/31 represents the probability of picking a white marble

This is because there are 16 white out of 15+16 = 31 total.

---------

After we make a first selection, we have 16-1 = 15 white marbles left out of 31-1 = 30 marbles overall. The probability of selecting another white marble is 15/30 = 1/2.

Multiply those two fractions:

(16/31)*(1/2) = (16*1)/(31*2) = (2*8)/(31*2) = 8/31

which represents the probability of selecting two white marbles in a row, such that we don't put the first one back (and there's no replacement).

Answer:

Step-by-step explanation:

Equations according the given:

Solve for q by substitution:

Find the value of d:

Nathaniel has 10 dimes and 4 quarters