Write an equation in slope-intercept form for the line with y-intercept 7 and slope
-3

If the sample mean is 51,sample size is 21 , sample standard deviation is 15 and confidence level is 95% then the lower bound is 45.35 and upper bound is 56.65.

Given sample mean of 51, sample size of 21, sample standard deviation be 15 and confidence level be 95%.

We are required to find the upper bound and lower bound.

We have to use t test as the sample size is less than 30.

Margin of error is the difference between calculated figures and real figures.

Margin of error= standard deviation* critical value of t

Critical value of t at 0.05 significance level with degree of freedom 20   [21-1] is 1.7247.

Margin of error=1.7247*15/4.5826

(4.5826 is the square root of 21)

=5.6454

Upper bound=51+5.6454

=56.6454

Lower bound=51-5.6454

=45.3546

After rounding off they will be 56.65 and 45.35.

Hence if the sample mean is 51,sample size is 21 , sample standard deviation is 15 and confidence level is 95% then the lower bound is 45.35 and upper bound is 56.65.

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Answer:

Assume you are working with a standard deck of 52 cards. There are 13 cards (2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, and ace) in each of four suits

and spades).

What is P(Jack Heart) if you draw one card? 13

2x3 i think maybe yes

The quantity of each concentrations of 3% and 9% needed to get the desired concentration is 54 milliliters and 27 milliliters respectively

Let

x + y = 81

0.03x + 0.09y = 81 × 5%

0.03x + 0.09y = 4.05

x + y = 81

0.03x + 0.09y = 4.05

From (1)

x = 81 - y

0.03x + 0.09y = 4.05

0.03(81 - y) + 0.09y = 4.05

2.43 - 0.03y + 0.09y = 4.05

- 0.03y + 0.09y = 4.05 - 2.43

0.06y = 1.62

y = 1.62/0.06

y = 27

x = 81 - y

x = 81 - 27

x = 54

Simultaneous equation:

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Answer:  [tex]y=\frac{13}{2} x+3[/tex]

Step-by-step explanation:

Remember the point-slope equation which is [tex]y-y_{1} = m(x-x_{1} )[/tex]  where[tex](x_{1} , y_{1} )[/tex] is your point and [tex]m[/tex] is your slope.

Given that we substitute what you have:

[tex]y-(-10) =\frac{13}{2} (x - (-2))[/tex]

Minus and minus give us positive:

[tex]y+10 =\frac{13}{2} (x +2)[/tex]

Multiply slope into the parenthesis:

[tex]y+10= \frac{13}{2}x + \frac{13}{2}*2\\[/tex]

Calculate it:

[tex]y+10= \frac{13}{2}x +13[/tex]

Isolate the [tex]y[/tex] by subtracting 10 from both sides:

[tex]y=\frac{13}{2} x + 13 -10[/tex]

Your final equation is:

[tex]y=\frac{13}{2} x +3[/tex]

Hope this makes sense!

And here's the graph to prove that the line actually goes through the point [tex](-2,-10)[/tex]:

Answer:

26 - R = C

3 cars

Step-by-step explanation:

26-R = C

26-23 = 3

Answer: B

Step-by-step explanation: Trust me bro

The value of x according to the given task is; 12.

It follows from the task content that the value of x is to be determined.

Since, lines AB and BC are both tangent to the circle and they both share a point of intersection; it follows that;

5x = 3x +24

2x = 24

x = 24/2

x = 12.

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Answer:

z=16

Step-by-step explanation:

10=z-6

10+6=z-6+6

16=z

Answer:

10=z-6

or, z= 10+6

or, z = 16

the vale of y is 16

Answer: D

Step-by-step explanation:

The graph is narrower, so the coefficient of [tex]x^2[/tex] has an absolute value more than 1.

Also, because g(x) opens down, the coefficient of [tex]x^2[/tex] is negative.

This leaves D as the answer.

The price elasticity of demand is 1.90.

Price elasticity of supply measures the responsiveness of quantity supplied to changes in price of the good. It is expected that quantity supplied would be positively related to the price of the good.

Price elasticity of supply = percentage change in quantity supplied / percentage change in price

55% / 29% = 1.90

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Answer:

From least to most likely:

Event 4, Event 2, Event 3, Event 1

Step-by-step explanation:

Event 1 has a 100% chance because there are only red and orange marbles in the bag.

In event 2, there are 4 orange marbles in the bag, giving us a (4/20) chance. This is 20%

In event 3, there are 2 orange marbles of 8 total, giving us an (2/8) chance. This is 25%

Lastly, there are no purple marbles in either bag, giving us a 0% chance of this occurring.

The expression that would be simplified to be a multiplicative identity is 2^0

The complete question is added as an attachment

Multiplicative identities are represented as:

a * 1 = a

This means that the definition of multiplicative identities is the product of a number and 1

From the list of options, we have

2^0

When the exponent of a non-zero number is 0, the result is 1.

This means that

2^0 = 1

Hence, the expression that would be simplified to be a multiplicative identity is 2^0

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Answer:

150 student tickets and 375 adult tickets

Step-by-step explanation:

Let x = # of student tickets sold, and y = # of adult tickets sold.

Total of 525 tickets were sold, so the first equation is x + y = 525. The register gained $8325, so 10.50x + 18y = 8235 is the second equation.

x + y = 525

10.50x + 18y = 8325

18x + 18y = 9450

10.50x + 18y = 8325

7.5x = 1125

x = 150

150 + y = 525

y = 375

Answer:

(I've marked the lines considered functions with a check mark)

Step-by-step explanation:

Answer:

the slope is 5 and the y intercept is 5

Step-by-step explanation:

I think that you meant to write y = 6x + 5.

y = mx + b

The number in in the m spot is the slope and the number in the b spot is the y intercept.

Substitute [tex]u=x^2+4[/tex] and [tex]du=2x\,dx[/tex]. Then the integral transforms to

[tex]\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \int \frac{du}{u^3}[/tex]

Apply the power rule.

[tex]\displaystyle \int \frac{du}{u^3} = -\dfrac1{2u^2} + C[/tex]

Now put the result back in terms of [tex]x[/tex].

[tex]\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \left(-\dfrac1{2u^2} + C\right) = -\dfrac1{4u^2} + C = \boxed{-\dfrac1{4(x^2+4)^2} + C}[/tex]

Answer:

-8 x^2
1.25 x^2
1/2 x^2

Step-by-step explanation:

They are like terms because they have the same variable x^2, yx^2 is not the same because it has the variable y

Answer:

the 2nd, 3rd and 4th options (all with x²)

Step-by-step explanation:

"like terms" means the exactly same variable(s) with exactly the same exponents of these variables.

constants in the terms can be different and even have different signs.

5yx² is not "like", because of the additional y variable.

The required equation for a line passing through point A and perpendicular to BC exists 2y + 5x = 31.

First, we must obtain the slope of the line perpendicular to BC

Given the coordinates B(7,5), and C(2,3)

Get the slope BC, exists

[tex]$m_{BC} = \frac{3-5}{2-7}[/tex]

= -2/-5 = 2/5

The slope of the line perpendicular to BC will be -5/2.

The slope of the required line in point-slope form exists expressed as;

[tex]$y - y_0 = m(x - x_0)[/tex]

m = -5/2

[tex](x_0, y_0) = (3, 8)[/tex]

Substitute the values into the formula we get

y - 8 = (-5/2)(x - 3)

2(y - 8) = (-5)(x - 3)

2y - 16 = (-5x + 15)

2y + 5x = 15 + 16

2y + 5x = 31

Therefore the required equation for a line passing through point A and perpendicular to BC exists 2y + 5x = 31.

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Answer:

5:3:2

Step-by-step explanation:

see image

Jarek gets half. Then from the other half, Jerzy gets 3 pieces of 5 and Justyn gets the leftover 2 pieces. But Jarek's piece is all 5 pieces of the first half.

Jarek 5 parts:

Jerzy 3 parts:

Justyn 2 parts

5:3:2

see image

In the given diagram, the length of CD is 12.7 cm

From the question, we are to determine the length of CD

First, we will calculate the length of CB

From the Pythagorean theorem,

|CA|² = |CB|² + |BA|²

12² = |CB|² + 6²

144 = |CB|² + 36

|CB|² = 144 - 36

|CB|² = 108

|CB| = √108

|CB| = 6√3 cm

Now, to find CD

Using SOH CAH TOA

sin55° = |CB| / |CD|

sin55° = 6√3 / |CD|

|CD| = 6√3 / sin55°

|CD| = 12.7 cm

Hence, the length of CD is 12.7 cm

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Answer:

b)14/3 or 4 2/3  C) 256/15 or 14 1/15

Step-by-step explanation:

In the second fraction, the "of" means to multiply

Answer:

#b

[tex] \displaystyle{ \pmb{ \pink{3 \frac{1}{5} \times 3 \frac{1}{2} \div 2 \frac{2}{5} }}}[/tex]

[tex]\frak{SOLUTION:}[/tex]

[tex]\displaystyle \frak{Here,}[/tex]

[tex]\displaystyle{3 \frac{1}{5} \times 3 \frac{1}{2} \div 2 \frac{2}{5} }[/tex]

[tex] = \displaystyle{ \frac{16}{5} \times \frac{7}{2} \div \frac{12}{5} }[/tex]

[tex]=\displaystyle{ \frac{16}{5} \times \frac{7}{2} \times \frac{5}{12} \frak{(Performing division)} }[/tex]

[tex]\displaystyle{ = \frac{ \cancel{16} \: {}^{2} \times 7 \times \cancel5}{ \cancel5 \times \cancel 2 \times 12} }[/tex]

[tex]\displaystyle{ = \frac{8 \times 7}{12} }[/tex]

[tex] =\displaystyle{} \frac{56}{12} [/tex]

[tex]\displaystyle{ = \frac{ \cancel2 \times \cancel2 \times 2 \times 7}{ \cancel2 \times \cancel 2 \times 3} }[/tex]

[tex]\displaystyle{ = \frac{14}{3} \frak {\: or} \: 4 \frac{2}{3} } [/tex]

#c

[tex]\displaystyle{\pmb{ \pink{2 \frac{2}{3} \div \frac{1}{2} \: of \: 3 \frac{1}{5} }}}[/tex]

[tex]\displaystyle{ \frak{SOLUTION:}}[/tex]

[tex]\displaystyle \frak{Here,}[/tex]

[tex] \displaystyle{2 \frac{2}{3} \div \frac{1}{2} \: of \: 3 \frac{1}{5} }[/tex]

[tex]\displaystyle{ = \frac{8}{3} \div \left( \frac{1}{2} \times \frac{16}{5} \right)\frak{(Performing "of")}}[/tex]

[tex] = \displaystyle{ \frac{8}{3} \div \left( \frac{1 \times \cancel{16} \: {}^{8} }{ \cancel2 \times 5} \right) }[/tex]

[tex]\displaystyle{ = \frac{8}{3} \div \frac{8}{5} }[/tex]

[tex]\displaystyle{ = \frac{8}{3} \times \frac{5}{8} \frak{(Performing \: division)} }[/tex]

[tex]\displaystyle{ = \frac{ \cancel8}{3} \times \frac{5}{ \cancel8} }[/tex]

[tex] = \displaystyle{ \frac{5}{3} \frak{ \: or \: }1 \frac{2}{3} }[/tex]

Answered by :

[tex]\frak{\pink{seolleaphrodite}}[/tex]

The amount that will be in the account after 30 years is $162,272.32.

When an amount is compounded annually, it means that once a year, the amount deposited and the interest already accrued increases in value. Compound interest leads to a higher value of deposit when compared with simple interest, where only the amount deposited increases in value once a year.

The formula that can be used to determine the future value of the yearly deposit of $4,000 in 30 years is : annuity factor x yearly deposit

Annuity factor = {[(1+r)^n] - 1} / r

Where:

$4000 x [{(1.02^30) - 1} / 0.02] = $162,272.32

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[tex]x {}^{(1)} = - 3 \: \: \: \: \: \: x {}^{(2)} = - 1[/tex]

Answer:

The answer is circle.

Step-by-step explanation:

For all the rest of the shapes, we use certain base x height formulas.  Square uses base x height along with parallelograms and trapezoids. For a triangle, we use [tex]\frac{base x height}{2}[/tex]. Though, for a circle, we use the formula  [tex]\pi r^{2}[/tex] where r= radius.

Answer:

A. The reference angle measures 78 degrees

Answer: B

Step-by-step explanation:

The parabola has an open hole at x=2, and the line has a closed hole at x=2.

This means the top part of the function should have domain [tex]x < 2[/tex], and the second part of the function should have domain [tex]x \geq 2[/tex].

This eliminates everything except for B.