Group the terms with variables on one side of the equal sign, and simplify.
8t −15 = 32t

Answer:

M=3ft

Step-by-step explanation:

Use trigonometric ratio Sin to get M which is the opposite side of the given angle of 30°

[tex]sin = \frac{opp}{hyp} [/tex]

[tex]sin30 = \frac{m}{6} [/tex]

Multiply 6 on both sides:

[tex]6sin30 = m[/tex]

Use a calculator:

3=M

or..

use special angles:

Sin30=0.5

6×0.5=3

Therefore M is 3 ft

Answer:

80

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

substitute m = 5 and n = 29 into the expression

n - 4m

= 29 - 4(5)

= 29 - 20

= 9

Answer:

answer is 9/16 (9 over 16) Decimal form 0.5625

Step-by-step explanation:

Check the picture below.

the area of the triangle whose base is AC and height is BD, is the same area of the triangle whose base is AB and altitude is BC, namely

[tex]A=\cfrac{1}{2}(\stackrel{b}{6})(\stackrel{h}{6})\implies 18[/tex]

Answer:

1/1000, 0.001

1/1000

Convert the negative exponent of base 10 into decimal: move to the left thrice

=0.001

Answer:

1) $181.40

2) $100

3) $81.40

Step-by-step explanation:

Interest rate is 1.5% which mans that the decimal multiplier is 1.015.

1) To find for 40 yrs we do:

40 yrs = 100 x [tex]1.015^{40}[/tex]

           =  $181.40

2) He contributed $100

3) He gained $181.40 - $100

   = $81.40

Answer:

143 50

Step-by-step explanation:

I hope it helps pa brainlest po

Answer:

Alice's age = 5 years

Malice's age = 5 years

Bob's age = 5+8 =13 years

Step-by-step explanation:

Let x be the age (in years of Alice and Malice (They have the same age because they are twins).

Age of Bob: x+8  (because he is 8 years older than the twins).

Then the sum of their three ages is 23:

x (Alice's age) + x (Malice's age) +(x+8 ) (Bob's age)= 23

2x + ( x+8) = 23

3x+8 = 23

3x = 15

(3x)/3 = 15/3

x = 5

So ...

Alice's age = 5 years

Malice's age = 5 years

Bob's age = 5+8 =13 years

if this helped you say meow

i may be wrong but i think you should divide 2.4% by the 15000 wicth  is

0.00000016 or just 0.16 or maybe  muptication 2.4% x15000 whicth is 360 hope this helps :D

To solve this problem, we just have to use trigonometric ratios and apply which of the ratios is needed here and proceed to solve. The value of side AC is 2.85 units

In the given diagram, we have the value of angle and hypothenuse and we are required to find the adjacent side of the triangle.

Data;

Let's use cosine rule for this.

[tex]cos\theta = \frac{adjacent}{hypothenuse}[/tex]

Proceed to substitute the values into the equation and solve.

[tex]cos 32.9 = \frac{AC}{3.4} \\AC=3.4cos32.9\\AC = 2.85[/tex]

From the calculations above, the value of side AC is 2.85 units

Learn more on trigonometric ratio here;

https://brainly.com/question/11967894

#SPJ1

This line is fairly close to the majority of the points shown. Unfortunately there's an outlier left out, but it isn't too far from the main cluster. The further the outlier is, the more pull it will drag the line away from the main cluster.

Line Q

Q is correct

Answer:

No

Step-by-step explanation:

Identify the equation for the circle

[tex](x-h)^2+(y-k)^2=r^2\\(x-2)^2+(y-13)^2=5^2\\(x-2)^2+(y-13)^2=25[/tex]

Check if (2,-11) is a point on the circle

[tex](x-2)^2+(y-13)^2=25\\(2-2)^2+(-11-13)^2=25\\0^2+(-24)^2=25\\576\neq25[/tex]

Since both sides of the equation are not equal to each other, then (2,-11) is not a point on the circle.

Federal agencies have the power to enforce those laws through regulation. State lawmakers, in turn, make laws that typically supplement federal legislation. State government regulation examples include setting a higher minimum wage than the federal requirement

Adding extra tax for Imported goods rather than Built in country goods

Look at a situation

Step-by-step explanation:

area of quadrilateral = sum of area of triangles

area of triangle ADC = .5 * b * h

= .5 * 12 * 5 = 30 km^2

area of ∆ABC = .5 * sinx* ab* ac

= .5 * sin 30 * 3* 13 = 39/4 = 9.75 km^2

area of quadrilateral = 39.75 km^2

total cost =$ 397.5 million

The total cost of the piece of land for which James, John and Jane decided to buy a piece of land is 1,200,000.

Total cost or the final cost is the summation of all the cost spend while buying any good or taking any service.

James, John and Jane decided to buy a piece of land. James paid 3/5 of the total cost while John paid 3/8 of the reminder.  Thus, the fraction of amount paid by Jane is,

[tex]x=1-\dfrac{3}{5}-\dfrac{3}{8}\\x=\dfrac{40-24-15}{40}\\x=\dfrac{1}{40}[/tex]

The Jane paid, 30000 of total cost which is 1/40 part of it. Thus, the total cost of the piece of land is,

[tex]\dfrac{1}{40}x=30000\\x=30000\times40\\x=1200000[/tex]

Thus, the total cost of the piece of land for which James, John and Jane decided to buy a piece of land is 1,200,000.

Learn more about the total cost here;

https://brainly.com/question/25109150

#SPJ1

Step-by-step explanation:

3.

the left cup is the summary of 2 cylinders.

the right cup is just a cone.

the volume of a cone is

pi×r²×h/3 = pi×3.5²×6/3 = pi×12.25×2 = pi×24.5 =

= 76.93 in³

the volume of a cylinder is

pi×r²×h

the first cylinder is

pi×3²×1.5 = pi×9×1.5 = pi×13.5 = 3.14×13.5 = 42.39 in³

the second cylinder is

pi×2²×2.25 = pi×4×2.25 = pi×9 = 28.26 in³

in total the cup has

42.39 + 28.26 = 70.65 in³

so, the cone has the larger volume by 6.28 in³ ≈ 6 in³.

that would be 3.479827 fl.oz. ≈ 3 fl.oz. of water.

I have no idea on what scale you need to quantify the amount of water. I just guessed.

2.

here we need the surface area.

the object consists of a large prism (or block) and a cylinder.

we don't need the bottom area for neither, as the cylinder is simply on top of the prism, and its bottom is not going to be painted either.

we need 5 sides of the prism :

front and back

left and right

top (and we need the full top, because the area the cylinder is covering up is the same area for the top of the cylinder).

and the we need to add only the side wall of the cylinder the "mantle".

so,

front and back rectangles are 10×3 × 2 = 60 in²

left and right rectangles are 10×3 × 2 = 60 in²

the top rectangle (square) is 10×10 = 100 in²

the cylinder mantle is

circumference of the circle × height

2×pi×r×h = 2×pi×4×6 = 3.14×48 = 150.72 in²

so, in total we have

60 + 60 + 100 + 150.72 = 370.72 in² ≈ 371 in²

Answer:

Question 2: 320.48 in^2

Question 3: 6.28 in^3

Step-by-step explanation:

Question 2)

The question tells us that the shape will be covered in paint. This means that we need to find the surface area instead of volume. In the question, I’ll find the surface area of the two individual shapes (The cylinder and the rectangular prism) and take away parts that will not be covered in paint.

Rectangular Prism

1. ((10x10)+(10x3)+(10x3))x2 — All rectangular prisms have 2 sides with the same area. Since there are 6 sides total, all we need to do is find 3 sides of different sizes and multiply them by 2. The number we get is 320 in^2.

2. We will not be painting the bottom, so we can take the area of the bottom away. The area of the bottom is 10x10, which is 100. 320 - 100 is 220 in^2.

3. We are also not painting the area where the cylinder is touching the top (The circle-shaped area). The formula of finding the area of a circle is radius x radius x pi. Since the radius is 4 and pi can be rounded to 3.14, the area of the circle will be 4x4x3.14, which is 50.24 in^2. We can take that away from 220, so 220 - 20.24 is 169.76 in^2.

Cylinder

1. 4x4x3.14 — We know that one side of the cylinder (The base) will not be painted, so all we need to do is find the area of one of the bases. Radius x Radius x pi, in this case, is 50.24 in^2.

2. (((4+4)x3.14)x6) — Now we need to find the area of the side of the cylinder. The area of the side is base x height. The base length is the perimeter of the circle. The equation of the circle perimeter is (radius + radius) x pi. In numbers, it will be 8x3.14 which is 25.12. The height of the side is 6, so the equation will be 25.12 x 6, which is 150.72.

3. The surface area of the cylinder (excluding the base at the bottom) is 150.72 in^2.

Since the rectangular prism and the cylinder is stuck together and is considered as a whole, we add the two numbers together. 169.76 + 150.72 = 320.48 in^2!

Question 3)

The amount of water the cups can hold is the same size as the volume of individual cups. In order to find out the amount of water each cup can hold, we need to find the volume first.

Cup #1

1. (2x2x3.14)(2.25) — This is the base times the height of the bottom cylinder. The formula to find a circle is radius x radius x pi, and the height was 2.25. The volume of this shape will be 28.26 in^3.

2. (3x3x3.14)(1.5) — The area of the bottom is radius x radius x pi, and the height was 1.5 If we multiply all of these numbers together, we get 42.39 in^3.

3. Now that we found the two cylinders of the first cup, we can add them together. 28.26 + 42.39 = 70.65.

4. The area of cup #1 is 70.65 in^3.

Cup #2

1. (3.5 x 3.5 x 3.14)(6)(1/3) — The formula for finding the area of a cone is base x height x 1/3. The area of the base is radius x radius x pi, and the height is 6. Then we multiply by 1/3 (or divide by 3). Then, we get 76.93 in^3.

2. The volume of cup #2 is 76.93 in^3.

The question asks: How much more water will the larger cup hold?

Comparing 70.65 in^3 (First cup) and 76.93 in^3 (Second cup), we know that the second cup is bigger. To find the difference in the amount of water it can hold, we can subtract 70.65 from 76.93. This equals 6.28 in^3.

The final answer for Question 3 will be 6.28 in^3!

Answer:

volume = 216cm

Step-by-step explanation:

V = (1/2) × b × h × l

V = 1/2 × 6 × 8 × 9

v=216

Answer:

216 cubic centimeters

Step-by-step explanation:

To calculate the volume of a triangular prism, we can use the formula:

V = (length x width x height) / 2

To solve this problem, in particular, all we have to do is substitute the values:

V = (8 x 6 x 9) / 2

V = 216 cubic centimeters

Hope this helps!!

Answer:

y - 5 = 3(x + 7)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = 3 and (a, b ) = (- 7, 5 ) , then

y - 5 = 3(x - (- 7) ) , that is

y - 5 = 3(x + 7)

The approximate probability that the 5 bushels will have a mean weight of more than 90 pounds is 0.41

The given parameters are:

Mean, μ = 89.46

Standard deviation, σ = 2.31

The z-score at x = 90 is calculated using

[tex]z = \frac{x - \mu}{\sigma}[/tex]

This gives

[tex]z = \frac{90 - 89.46}{2.31}\\[/tex]

Evaluate

z = 0.234

The probability is then calculated as:

P(x >90) = P(z > 0.234)

From z table of probabilities, we have:

P(x >90) = 0.41

Hence, the approximate probability that the 5 bushels will have a mean weight of more than 90 pounds is 0.41

Read more about probability at:

https://brainly.com/question/251701

#SPJ4

Answer:

multiply the number with 4

Step-by-step explanation:

2 8 32 128

2x4 =8

8×4=32

32×4=128

128×4=512

[tex]\text{First term,}~ a =2\\\\\text{Common ratio,}~ r = \dfrac{8}2 = 4\\\\\text{Nth term} = ar^{n-1}\\\\\text{7th term} = 2 \cdot 4^{7-1} = 2 \cdot 4^6=8192\\ \\\text{Hence, the 7th term in the geometric series is 8192.}[/tex]

Answer:

0.0064

Step-by-step explanation:

Probability (2 sets of twins) :

Answer:

[tex]\displaystyle x=\biggr\{\frac{\pi}{6},\frac{11\pi}{6}\biggr\}[/tex]

Step-by-step explanation:

[tex]\displaystyle 5\cos x-\sqrt{3}=3\cos x;\:0\leq x < 2\pi\\\\5-\frac{\sqrt{3}}{\cos x}=3\\ \\-\sqrt{3}\sec x=-2\\\\\sec x=\frac{2}{\sqrt{3}}\\\\\sec x=\frac{2\sqrt{3}}{3}\\ \\\cos x=\frac{3}{2\sqrt{3}}\\ \\\cos x=\frac{3\sqrt{3}}{6}\\ \\\cos x=\frac{\sqrt{3}}{2}\\\\x=\biggr\{\frac{\pi}{6},\frac{11\pi}{6}\biggr\}[/tex]

Answer:

[tex]\log_{9}4\approx 0.631[/tex]

Step-by-step explanation:

The change of base formula we can use is

[tex]\log_{b}a=\frac{\log{a}}{\log{b}}[/tex]

Not all calculators will allow the user to directly enter the logarithms with a given base, so the change of base can be used for all calculators, which use the common log.

Common logs have a base of 10.

Let's convert your expression:

[tex]\log_{9}4=\frac{\log4}{\log9}[/tex]

Using our calculator, we will compute log 4 divided by log 9:

[tex]\frac{\log4}{\log9}\approx0.631[/tex].

Using a proportional relationship, it is found that when x = -7, the value of y will be of y = 6.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

When y varies inversely with x, the rule is given by:

[tex]y = \frac{k}{x}[/tex]

y = −3 when x = 14, hence we use this to find k.

[tex]-3 = \frac{k}{14} \rightarrow k = -42[/tex]

Then:

[tex]y = -\frac{42}{x}[/tex]

Then when x = -7, y = -42/-7 = 6.

More can be learned about proportional relationships at https://brainly.com/question/10424180

#SPJ1

The classification of the shapes into the categories described is as follows;

Plane shapes have peculiar characterization in each case. A triangle can either be isosceles (2 sides of equal length) or right (90⁰ angle measure).

Rectangles, squares and Parallelograms all have parallel sides.

Read more on plane shapes;

https://brainly.com/question/2644832

#SPJ1

Answer:

x = 10

Step-by-step explanation:

The sum of the angles of a triangle is 180 degrees

6x-6 + 7x+1 +55 = 180

Combine like terms

13x+50=180

Subtract 50 from each side

13x+50-50=180-50

13x = 130

Divide by 13

13x/13 =130/13

x = 10

The answer is A!

From this, we will get the equation

(13x -5) + 55 = 180

+ 5 on both sides

13x + 55 = 185

-55 on both sides

13x = 130

Divide by 13 on both sides

x = 10

Answer:

The answer is D I hope this helps

The required domain for the function given on the graph represents the exponential function is x ≥ 1. Option C is correct.

Given that,
A graph of a function is shown that has 3 distinct functions for its domain, we have to determine which of these 3 functions shows an exponential function.

The function which is in format f(x) =   where, a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).  

Since, as we can see throughout the graph the graph constantly decreases to -4 and then shows a parabolic function from -4 to 0.9 afterward it starts increasing exponentially.

Thus, the required domain for the function given on the graph represents the exponential function is x ≥ 1. Option C is correct.

Learn more about exponential function here:

brainly.com/question/15352175

#SPJ5

Answer:

200

Step-by-step explanation:

(6 × 10^5) / (3 × 10^3) = 6/6 × 10^5/10^3 = 2 × 10^2 = 200

Answer:

200

Step-by-step explanation:

(6 × 10^5) / (3 × 10^3) = 6/6 × 10^5/10^3 = 2 × 10^2 = 200