Using the set of numbers find the mean ( rounded to the nearest tenth ) , median , mode and range.

Answer:

The equation of the line that passes through the point (4,6) with a slope of -6

is y=-6x+30

Step-by-step explanation:

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

To start, you know what m is; it's just the slope, which you said was -6. So you can right away fill in the equation for a line somewhat to read:

y=-6x+b.

Now, what about b, the y-intercept?

To find b, think about what your (x,y) point means:

(4,6). When x of the line is 4, y of the line must be 6.

Because you said the line passes through this point, right?

Now, look at our line's equation so far: . b is what we want, the -6 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the point (4,6).

So, why not plug in for x the number 4 and for y the number 6? This will allow you to solve the particular line that passes through the point you gave!.

(4,6). y=mx+b or 6=-6 × 4+b, or solving for b: b=6-(-6)(4). b=30.

The area should be 47.5 CM.

Answer:

Step-by-step explanation:

The figure you see here is a trapezoid.

Area = \(\frac{(a + b)h}{2}\) = \(\frac{(6 + 13)(5)}{2}\) = \(\frac{(19)(5)}{2}\) = \(\frac{95}{2}\) = 47.5 cm

Answer:

B: 5/13

Step-by-step explanation:

pythagoras theorem: a^2 + b^2 (sides) = c^2 (hypotenuse)

a^2 + 12^2 = 13^2

a^2 + 144 = 169

a^2 = 25

a = 5

sin = opp/hyp

sin 5/13

Hope this helps

Answer:

sa =45

vol = 6000.

I hope it helps. and if you can, give me the brainlist

By solving a system of equations, we conclude that Kelli's speed on still water is 6.1km/h

Let's say that the speed of Kelli in still water is S. And we know that the speed of the river is 5km/h.

When she swims upstream, her velocity is:

(S - 5km/h)

When she swims downstream, her velocity is:

(S + 5km/h)

With the given information, we can write for a distance D:

(S - 5km/h)*1h = D

(S + 5km/h)*6min = D

First, let's rewrite 6 minutes into hours.

1 hour = 60min

6 min = 6/(60) hours = 0.1 hours

Then the system of equations that we need to solve is:

(S - 5km/h)*1h = D

(S + 5km/h)*0.1h = D

D is the same distance in both cases, then we can write:

(S - 5km/h)*1h = (S + 5km/h)*0.1h

Now we can solve this for S.

S*1h - 5km = S*0.1h + 0.5km

S*1h - S*0.1h = 5km + 0.5km

S*(0.9h) = 5.5km

S = 5.5km/0.9h = 6.1km/h

Kelli's speed on still water is 6.1km/h

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Answer:

1.894

3.169

2.064

3.690

Step-by-step explanation:

A.) 90% ; sample size = 8

Degree of freedom, df = n - 1

t(1 - α/2, 7) = t0.05, 7 = 1.894

B.) 99% ; sample size = 11

Degree of freedom, df = n - 1

t(1 - α/2, 10) = t0.005, 10 = 3.169

C.) 95% ; sample size = 25

Degree of freedom, df = n - 1

t(1 - α/2, 24) = t0.025,24 = 2.064

(D.) 99.5% and sample size 10.

Degree of freedom, df = n - 1

t(1 - α/2, 9) = t0.0025,9 = 3.690

Based on the given information, we have a square pyramid with points M and N being the midpoints of the edges of one face. and forms a parallelogram. Option D

Since the base of the pyramid is a square, the cross section will consist of a square shape. Additionally, since the slice is made through the midpoints of the edges of the face, the resulting cross section will have parallel sides.

Considering these characteristics, we can conclude that the shape of the resulting cross section is a parallelogram. A parallelogram is a quadrilateral with opposite sides parallel. In this case, the opposite sides of the square cross section will be parallel, as the slice passes through the midpoints of the edges.

Therefore, the correct answer is D. parallelogram.

It's important to note that a triangular prism is not the correct answer because a triangular prism is a three-dimensional figure with two triangular bases and three rectangular faces. The cross section resulting from the given slice will not have the characteristics of a triangular prism. Option D.

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Answer:

1. 7.3

2. 33.3

3. 21.3

4. 31.9

5. 25.6

6. 11.0

7. 42°

8. 64°

9. 13°

10. 51°

Step-by-step explanation:

make sure if you're using a math calculator that it is in degree mode.

SIN, COS, OR TAN. SOH CAH TOA. Sin is Opposite/hypotenus.

Cos is Adjacent(next to it)/hypotenus.

Tan is Opposite/Adjacent.

~~

PROBLEM 1:

So we have 63°, 16 as hypotenus, and x as one of the legs.

1. Figure out whether it is Sin, Cos, or Tan. (It's adj and hyp. of the angle degree (63° listed so it's cos.)

2. Once you set it up, it is Cos 63°= x/16 then flip it around. which makes it 16 COS 63= X.

3. Input it into your calculator as 16cos(63, then it will give you.. 7.263847996

4. Don't forget to round to the nearest tenth, which gives you

x = 7.3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 2:

Given: 39°, 27 is opposite of the °, and adj is x. So this is Tan.

1. Set it up, Tan 39° = 27/x can't solve this way so fix it.

2. rewritten as X = 27/tan39

3. round ur answer.

x = 33.3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 3:

Given: 49°, adj is 14, hyp is x. So this is Cos.

1. Set up according to CAH, Cos 49=(14/x).

We can't solve it this way since the X is on the bottom. So we have to fix it!

2. Turns into X Cos 49 = 14, which then turns into X= 14/cos49.

3. Put it in your calculator as 14 DIVIDED BY cos 49. ( Put image example)

4. Round.

x= 21.3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 4:

Given: 15°, 33 hyp, adj x. Which is Cos.

1. Cos 15= x/33 and rewrite.

2. Input as 33 cos(15 into calculator = 31.875...

3. Round to tenth.

x = 31.9

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 5:

Given: 52°, 20 adj of °, and x opp of °. Will use TAN.

1. Tan 52° = x/20

2. 20 Tan(52 into calculator

3. Round

x = 25.6

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 6:

Given: 27°, opp of ° is 5, hyp is x. Will use Sin.

1. Write out as I have the last few times, Sin 27 = 5/x rewrite cause x can't be at the bottom.

2. Input into calculator as: 5/sin 27 which equals 11.01...

3. Round.

x = 11.0

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 7:

Given: x°, 6 as hyp, 4 opp. now we have to solve this different since we don't know the degree. Now when we input into the calculator you will press 2nd, then sin/cos/tan so it will be negative this is depending on which one ur solving for.

We will be using SIN, x is still a °.

1. Sin X = 4/6 Rewrite.

2. X= Sin^-1 (4/6)

Make sure ur sin is negative in calculator when doing this.

3. It SHOULD give you 41.81, round.

x = 42°

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 8:

Given: x°, 29 opp, 14 adj. TAN.

1. Tan x°= 29/14 or..

2. X = Tan^-1(29/14) solve..

3. gives u 64.23.... round.

x = 64°

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 9:

Given: x°, hyp 54, opp 12. SIN

1. Sin x°=(12/54)

2. X= Sin^-1(12/54) solve. (dont put x= into calculator.)

3. Don't Forget to round, answer unrounded: 12.839..

x = 13°

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 10:

Given: x°, adj 25, hyp 40. COS

1. Cos x°=25/40 rewrite.

2. X= Cos^-1(25/40) Solve.

3. Round.

X= 51°

Answer:

down below

Step-by-step explanation:

3,487, 651

(3 x 1,000,000) + (4 x 100,000) + (8 x 10,000) + ( 7 x 1,000) + (6 x 100 ) +

(5 x 10) + (1 x 1)

The tangent line at that point is:

y = (-3/25)*x + 6/5

so m = -3/25, and b = 6/5

To find the slope at that point, we need to evaluate the derivative at that point.

y = 3/x

The derivative is:

y' = -3/x²

When x = 5, we have:

y' = -3/5² = -3/25

So that is the slope, m.

Now let's find the line.

The line must pass trhough the point (5, 3/5), then:

3/5 = (-3/25)*5 + b

3/5 = -3/5 + b

3/5 + 3/5 = b

6/5 = b

The equation of the line is:

y = (-3/25)*x + 6/5

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Answer:

C is correct

Step-by-step explanation:

10/12=0.83...

2/3=0.66...

2/3<10/12

Answer:

C

Step-by-step explanation:

Why the others are incorrect:

A: \(\frac{2}{10} > \frac{3*2}{5*2}\) → \(\frac{2}{10} > \frac{ 6}{10}\) This statement/comparison is false

B : \(\frac{2*2}{4*2} > \frac{4}{8}\) → \(\frac{4}{8} > \frac{4}{8}\) This statement/comparison is false

D:\(\frac{9}{12} < \frac{3*2}{6*2}\) → \(\frac{9}{12} < \frac{6}{12}\) This statement/comparison is false

C: \(\frac{2*4}{3*4} < \frac{10}{12}\) → \(\frac{8}{12} < \frac{10}{12}\) This statement/comparison is true

The computation of the increased in salary is $500.

Here, we have,

Explanation:

Data provided in the question

Salary for the first year = $50,000

CPI increase during the year = 4%

Overstated inflation = 1% i.e. 5%

The computation of the increased in salary is shown below:

= Salary of the first year × inflation rate - salary of the first year × CPI increase during the year

= $50,000 × 5% - $50,000 × 4%

= $2,500 - $2,000

= $500

Hence, The computation of the increased in salary is $500.

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complete question:

Mark's wage contract specifies a $50,000 salary for the first year, and specifies a salary increase equal to the percentage increase in the CPI during the second year. The increase in the CPI during the year was 4.0%. If the CPI overstates inflation by 1.0% (that is, the actual price increase was 3% and not 4%), at the end of the first year Mark's salary increased by $________ more than it would have without the upward bias.

Answer:

The system of inequalities representing the situation above is given as:

Number of ink drawings x ≥ 0

Number of water colors ≥ 0

Number of preparation time: 0.3x + 0.5y ≤ 120

Number of packaging time: 0.2x + 0.2y ≤ 60

Step-by-step explanation:

They volunteered to spend:

Number of hours for preparation = 120

Number of hours for packaging = 60

Number of hours to prepare ink drawing = 0.3

Number of hours to prepare water colour = 0.5

Number of hours it takes to package each card = 0.2

x = number of ink drawings

y = number rod water colour

The system of inequalities representing the situation above is given as:

Number of ink drawings x ≥ 0

Number of water colors ≥ 0

Number of preparation time: 0.3x + 0.5y ≤ 120

Number of packaging time: 0.2x + 0.2y ≤ 60

Option d is the correct option

The number of items on their grocery shopping list given the percentage already bought is 20 items.

Percentage of items bought already= 60%

Number of items bought already= 12

Total number of items on the list= x

Number of items bought already = Percentage of items bought already × Total number of items on the list

12 = 60% × x

12 = 0.6 × x

12 = 0.6x

divide both sides by 0.6

x = 12/0.6

x = 20 items

Hence, there are a total of 20 items on their grocery list.

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Answer:

-5+√2 and -5-√2

Step-by-step explanation:

With the quadratic formula:

\(\displaystyle x^2 + 10x + 25 = 2\\\\x^2+10x+23=0\\\\x=\frac{-10\pm\sqrt{10^2-4(1)(23)}}{2(1)}=\frac{-10\pm\sqrt{100-92}}{2}=\frac{-10\pm\sqrt{8}}{2}=\frac{-10\pm2\sqrt{2}}{2}=-5\pm\sqrt{2}\)

We can also complete the square (which is faster):

\(x^2+10x+25=2\\(x+5)^2=2\\x+5=\pm\sqrt{2}\\x=-5\pm\sqrt{2}\)

The transformation that is used is a translation of 3 units upwards.

Numerous different coordinate systems can be used to describe geometrical figures.

From the diagram of the graph we can see that the transformation that is used is translation of 3 units upwards.

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Answer:

\( f'(x) = \frac{2{x}^{2}}{ \sqrt[3]{( {x}^{3} - 8) } }\)

Step-by-step explanation:

\(f(x) = ( {x}^{3} - 8)^{ \frac{2}{3} } \\ \\ f'(x) = \frac{2}{3} ( {x}^{3} - 8)^{ \frac{2}{3} - 1 } (3 {x}^{2} - 0) \\ \\ f'(x) = \frac{2}{3} ( {x}^{3} - 8)^{ \frac{2 - 3}{3} } \times 3 {x}^{2} \\ \\ f'(x) = 2{x}^{2}( {x}^{3} - 8)^{ \frac{ - 1}{3} } \\ \\ f'(x) = \frac{2{x}^{2}}{( {x}^{3} - 8)^{ \frac{ 1}{3} } } \\ \\ \huge \red{ \boxed{ f'(x) = \frac{2{x}^{2}}{ \sqrt[3]{( {x}^{3} - 8) } } }}\)

Answer: A

because slope are

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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The value of the scale factor is 3. Then the height and area of the triangle ΔABC will be 9 ft and 54 square ft.

Dilation means the changing of the size of the object without changing the shape. The size of the object may be increased or decreased based on the scale factor.

The area of the triangle ΔDEF is 6 square ft. And the base length of the triangle ΔDEF is 4 ft.

The area of the triangle is given as

\(\rm Area = \dfrac{1}{2} \times bh\\\\\)

Then the height of the triangle ΔDEF will be

\(\rm 6 = \dfrac{1}{2} \times 4 \times h\\\\h = \dfrac{12}{4}\\\\h = 3\)

Then the scale factor will be

\(\rm SF = \dfrac{12}{4} = 3\)

Then the height of the triangle ΔABC will be

\(\rm \dfrac{H}{3} = 3\\\\H \ = 9\)

Then the area of the dilated triangle ΔABC will be

\(\rm Dilated \ Area = \dfrac{1}{2} \times 12 \times 9\\\\Dilated \ Area = 54 \ ft^2\)

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Step-by-step explanation:

log(79) = 1.897627091... ≈ 1.90

Answer:

$18.51

Step-by-step explanation:

23.42×.21= 4.91 then 23.42-4.91= your sale price which is $18.51

Answer:

smallest whole number is 0 so product of 0 is 0

smallest natural number is 1 so product of 1 is 1

Answer:

(0,4)

Step-by-step explanation:

use midpoint formula

Answer:

see below

Step-by-step explanation:

\(l=\frac{360-2(85)}{2}=180-85 = 95\)

\(m=\frac{360-2(30+95)}{2}=180-125 = 55\)

\(n=180-95=85\\p=360-(30+95+85+55)=95\\q=180-30-95=55\)

There are 120 different combinations of 3 programmers that can be chosen to transfer to the new department

From the question, we have

Total number of programmers, n = 10

Numbers to programmers to select, r = 3

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 10 and r = 3

Substitute the known values in the above equation

Total = ¹⁰C₃

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 10!/(7! * 3!)

Evaluate

Total = 120

Hence, the number of ways is 120

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The total budget for their student film $800

11% of total budget = (11/100) * total budget

= 0.11 * total budget

Let P be the amount the group spent on props.

Now we can write the equation:

P = 0.11 * total budget

We also know that this group spent $712 on equipment. Let E be the amount they spent on equipment.

So it looks like this:

E=$712

Your total budget is the total cost of your equipment and props. This can be written as:

Total Budget = E + P

Plugging in the E and P values, we get:

Total Budget = $712 + 0.11 * Total Budget

Simplifying this equation, we get:

0.89 * total budget = $712

Dividing both sides by 0.89 gives:

Total budget = $800

So her student film had a total budget of $800. 

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Answer:

5/7

Step-by-step explanation:

You find a slope by using the equation y2-y1/x2-x1.

In this case: 15-5/21-7

10/14

5/7