A 24-foot ladder leans against a wall the base of the ladder is 9 feet from where the wall meets the ground how far up the wall does the ladder reach ?

Answer:

2√2 cm

Step-by-step explanation:

Formula to be understood :

Deriving the formula :

Solving for the length of the diagonal :

Length of diagonal

Answer:

v=2143.57

Step-by-step explanation:

4/3 x 3.14 x 8³

3.14 x 512 x 4/3

3.14 x 512=1607.68

1607.68 x 4/3=2143.57333333

round to nearest hundreth

v=2143.57

Answer:

V ≈ 2143.57= 2144

Step-by-step explanation:

[tex]v=\frac{4}{3} *3.14*8^3[/tex]

=2143.57333333

you dont need to round, so!

=2144 (if you want)

sorry for the confusion

Answer:

1516

Step-by-step explanation:

hope can help you

2000x 2%=40

9000x 5%= 450

(30000-9000-2000) x 5.4% = 1026

total tas 40+450+1026=

[tex]\textbf{(i)}\\\\~~~~~~~y= e^{3x} \sin 2x\\\\\\\implies \dfrac{dy}{dx} = \dfrac{d}{dx} \left( e^{3x} \sin 2x \right)\\\\\\~~~~~~~~~~~~=e^{3x} \dfrac{d}{dx} \sin 2x + \sin 2x \dfrac{d}{dx} e^{3x}\\\\\\~~~~~~~~~~~~=2e^{3x} \cos 2x + 3e^{3x}\sin 2x \\\\\\[/tex]

[tex]\textbf{(ii)}\\\\~~~~~~~~y = \dfrac{e^{3x}}{\cos 2x}\\\\\\\implies \dfrac{dy}{dx} = \dfrac d{dx} \left(\dfrac{e^{3x}}{\cos 2x} \right)\\\\\\~~~~~~~~~~~=\dfrac{\cos 2x \dfrac{d}{dx}\left(e^{3x} \right) -e^{3x} \dfrac{d}{dx}( \cos 2x) }{\cos^2 (2x)}\\\\\\~~~~~~~~~~~=\dfrac{3e^{3x} \cos 2x+2e^{3x}\sin2x }{\cos^2(2x)}\\\\\\~~~~~~~~~~~=\dfrac{3e^{3x} \cos 2x}{ \cos^2(2x)} + \dfrac{2e^{3x} \sin 2x}{\cos^2(2x)}\\\\\\~~~~~~~~~~~=3e^{3x}\sec (2x) + 2e^{3x}\sec (2x) \tan (2x)[/tex]

[tex]\textbf{(iii)}\\\\~~~~~~~~~y=( 3x+2)^3\\\\\\\implies \dfrac{dy}{dx} = \dfrac{d}{dx}(3x+2)^3\\\\\\~~~~~~~~~~~=3(3x+2)^2 \dfrac{d}{dx} (3x+2)\\\\\\~~~~~~~~~~~=3(3x+2)^2 \cdot 3\\\\\\~~~~~~~~~~~=9(3x+2)^2[/tex]

[tex]\textbf{(iv)}\\\\~~~~~~~~~x^2 +y^2 = 5xy\\\\\\\implies \dfrac{d}{dx}(x^2 +y^2) = 5\dfrac{d}{dx} (xy)\\\\\\\implies 2x + 2y \dfrac{dy}{dx} = 5\left(x \dfrac{dy}{dx} +y\right)\\ \\\\\implies 2x +2y \dfrac{dy}{dx} = 5x \dfrac{dy}{dx} +5y\\\\\\\implies 2y \dfrac{dy}{dx} - 5x \dfrac{dy}{dx} = 5y-2x\\\\\\\implies (2y-5x) \dfrac{dy}{dx} = 5y-2x\\\\\\\implies \dfrac{dy}{dx} = \dfrac{5y-2x}{2y-5x}[/tex]

Answer:

For rectangulasr prism

a. [tex]72cm^3[/tex]

b. [tex]108cm^{3}[/tex]

Step-by-step explanation:

For rectangulasr prism

a. Equation: Volume = length x width x height

length: 6cm

width: 4cm

height: 3cm

Volume = 6cm x 4cm x 3cm

Volume = 24cm x 3cm

b. Equation: A = 2[(width x length) + (height x length) + (heigth x width)]

A = 2[(4cm x 6cm) + (3cm x 6cm) + (3cm x 4cm)]

A = 2[(24cm) + (18cm) + (12cm)]

A = 2[(24cm) + (30cm)]

A = 2[(54cm)]

[tex]{\huge{\fcolorbox{yellow}{red}{\orange{\boxed{\boxed{\boxed{\boxed{\underbrace{\overbrace{\mathfrak{\pink{\fcolorbox{green}{blue}{Answer}}}}}}}}}}}}}[/tex]

[tex] \sf 7( \sqrt{m + 1} - 3) = 21[/tex]

we will multiply 7 with bracket

[tex] \sf 7 \sqrt{m + 1} - 21 = 21[/tex]

Now we will take (-21) on LHS to RHS

[tex] \sf 7 \sqrt{m + 1} = 21 + 21 \\ \\ \sf7 \sqrt{m + 1 } = 42 \\ \\ \sf \sqrt{m + 1} = \frac{42}{7} \\ \\ \sf \sqrt{m + 1} = 6[/tex]

Now we will do squaring both sides

[tex] \sf {( \sqrt{m + 1}) }^{2} = {(6)}^{2} \\ \\ \sf \red {m + 1 = 36}[/tex]

[tex]\sf{ 7( \sqrt{m+1} - 3)=21}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\sf{\sqrt{m+1} - 3)=\frac{21}{7}}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\sf{ 7( \sqrt{m+1} - 3)=3}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\sf{\sqrt{m+1} =6}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Get the power of 2 in both sides.

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\sf{( \sqrt{m + 1})^2 = 6^2}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\sf{m+1=36}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\sf{m=35}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

So the answer is m = 35

The number of red balls to the number of green balls is 3 : 2

The distribution of the balls is given as:

6 red, 4 green, 2 yellow and 3 blue balls

The number of red balls to the number of green balls is represented as:

Ratio = Red : Green

So, we have:

Ratio = 6 : 4

Simplify

Ratio = 3 : 2

Hence, the number of red balls to the number of green balls is 3 : 2

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The ground speed and direction of the plane is 323 kph with a directional bearing of S 22° E

To find the ground speed of the plane, we need to know what a vector is

A vector is a variable that has both magnitude and direction.

Since the airplane is headed due south with an airspeed of 300 kph, its vector is V = (-300 kph)j.

Also, the wind is blowing from the west at 120 kph. Its vector is v = (-120 kph)i

Now, the ground speed of the plane V' is the resultant vector of the airspeed and wind speed.

A resultant vector is the sum of two or more vectors.

So, V' = v + V

V' = (-120 kph)i + (-300 kph)j

So, its magnitude V' = √(x² + y²) where

So, V' = √[(-120 kph)² + (-300 kph)²]

= √[14400 kph² + 90000 kph²]

= √(104400 kph²)

= 323.11 kph

≅ 323 kph

Its direction, Ф = tan⁻¹(y/x)

Ф = tan⁻¹(-300 kph/-120 kph)

Ф = tan⁻¹(2.5)

Ф = 68.2°

From the South-line we have α = 90° - Ф = 90° - 68.2° = 21.8° ≅ 22°

So, the directional bearing of the plane is S22°E.

So, the ground speed and direction of the plane is 323 kph with a directional bearing of S 22° E

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Answer:

A on edge 2022

Step-by-step explanation:

323 kph and 22 E

Step-by-step explanation:

a) 1*7=7 (Litres);

b) 1*2*5=10 (Litres);

c) 10*0.5*1/0.5=10 (bottles)

The complete statement is 67000 pounds is equivalent to 33.5 tons

The unit is given as:

Weight = 67000 pounds

As a general rule;

1 pound = 0.0005 tons

Multiply both sides by 67000

67000 * 1 pound = 67000 *  0.0005 tons

Evaluate

67000 pounds = 33.5 tons

Hence, 67000 pounds is equivalent to 33.5 tons

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Answer:

B. -6

Step-by-step explanation:

You know immediately that it will be negative, because the temp is going down.

To find the exact answer, start by finding the difference between the two temps

82-46 = 36

since its a six day period, divide 36 by 6

36/6 = 6

so, the answer is -6

height= 8 in

length= 14 in

width= 3 in

the volume of the given rectangular prism.

[tex]v = whl[/tex]

[tex]v = 8 \times 14 \times 3[/tex]

[tex]v = 336 \: {in}^{3} [/tex]

hence, the volume of the given rectangular prism is 336 cubic inches.

answer= option D

[tex]\large\boxed{Formula: V= lbh}[/tex]

All the values are given so we'll simply have to solve.

Let's solve!

Substitute the values according to the formula.

We'll have to multiply the length, breadth and the height.

[tex]V= 14 \times 3 \times 8[/tex]

[tex]\large\boxed{V= 336 \: {in}^{3}}[/tex]

We get a whole number to the final answer so we won't have to round off.

Therefore, the volume of the given rectangular prism is 336 cubic inches.

Correct option: Option D

A probability of 1/10000 means that only one person can get the Pick 4 lottery among 10000 pickers.

The term probability has to do with the chance that an event will occur or not. Usually probability is expressed as a fraction.

The meaning of the saying that the  probability of picking the winning 4-digit number in a Pick 4 lottery is 1/10000 is that only one person can get the Pick 4 lottery among 10000 pickers.

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Answer:

[tex]0.33[/tex]

Step-by-step explanation:

There are 6 sides on dice, therefore the sample space would be 6 (the sample space is the denominator). We were asked to find the probability of getting a 1 or a 6. Since we were given 2 options 1 or 6, it therefore means that we are trying to find the probability of the dice rolling on 2 out of the 6 sides it has. Therefore the probability would be:

[tex] \frac{2}{6} \: or \: \frac{1}{3} [/tex]

A third as a decimal is

[tex]0.33[/tex]

Answer:

True, (-∞, ∞)         3 ≤ 8

Step-by-step explanation:

−8 + 11 ≤ −3 + 11

3 ≤ 8

Answer:

    18. 0.25

    19. 0.33

Step-by-step explanation:

Problem 18

Problem 19

Answer:

SA = 2,400 cm²

Step-by-step explanation:

Surface Area (SA) of a cuboid: 2(lw) + 2(wh) + 2(hl)

SA = 2(lw) + 2(wh) + 2(hl)

Substitute the values above and multiply:

SA = 2(lw) + 2(wh) + 2(hl)

SA = 2(20)(20) + 2(20)(20) + 2(20)(20)

SA = 2(400) + 2(400) + 2(400)

SA = 800 + 800 + 800

SA = 2,400 cm²

Final answer: 2,400 cm²

Hope this helps!

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

[tex] \large \sf \underline{Direction:}[/tex]

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

[tex] \large \sf \underline{Answer:}[/tex]

[tex] \qquad \qquad \huge \bold{2,400cm^{2} }[/tex]

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

[tex] \large \sf \underline{Solution:}[/tex]

[tex] :\sf{SA=2(lw)+2(wh)+2(hl)}[/tex]

[tex]:\sf{SA=2(20)(20)+2(20)(20)+2(20)(20)}[/tex]

[tex]:\sf{SA=2(400)+2(400)+2(400)}[/tex]

[tex]:\sf{SA=800+800+800}[/tex]

[tex]\therefore\sf\underline{SA = \pmb{2,400cm^{2} }}[/tex]

Hence, the surface area that you are looking for is 2, 400cm².

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

Answer:

The answer can be seen in the image attached to this message (containing the full steps).

short: 27cm

long: 36cm

hypotenuse: 45cm

Step-by-step explanation:

The image attached to this message contains explained steps.

[tex]\text{Given that,} ~ x-y = 5~ \text{amd}~ xy = 4\\\\\text{Now,}\\\\x^3 -y^3\\\\=(x-y)(x^2 +xy+y^2)\\\\=(x-y)[(x-y)^2 +2xy +xy]\\\\=(x-y)[(x-y)^2 +3xy]\\\\=5(5^2+3\cdot 4)\\\\=5(25+12)\\\\=5(37)\\\\=185[/tex]

Answer:

A, Yes because each t value is paired with exactly one number of gallons.

Step-by-step explanation:

Simply perform the vertical line test. On a graph, draw a vertical line, and if the line crosses the graph exactly once, it is a function. See the diagram below. Hope it helps, have a fantastic day.

Answer:

a

Step-by-step explanation:

because i am built diffrent thats why

Answer:

The y-intercept is 4

Step-by-step explanation:

You find the y-intercept by finding where x is zero. In the table, when x=0 the y=4. The y-intercept is 4. The graph of the function crosses the x-axis at the point (0,4).

Answer:

4

Step-by-step explanation:

the y-intercept is the y-coordinate where the line intersects the facis.So if we want to figure out the intercept,we're going to set x=0 and sdue for Y.

Answer:

Step-by-step explanation:

Using the t-distribution, it is found that the desired measures are given as follows:

At the null hypotheses, it is tested if the mean is of 63.5, that is:

[tex]H_0: \mu = 63.5[/tex]

At the alternative hypotheses, it is tested if the mean is less than 63.5, that is:

[tex]H_1: \mu < 63.5[/tex]

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

The values of the parameters are given as follows:

[tex]\overline{x} = 56.3, \mu = 63.5, s = 13.2, n = 62[/tex]

Hence, the test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{56.3 - 63.5}{\frac{13.2}{\sqrt{62}}}[/tex]

t = -4.29.

We have a left-tailed test, as we are testing if the mean is less than a value, with 62 - 1 = 61 df and t = -4.29. Hence, using a t-distribution calculator, the p-value is of 0.

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Answer:

$175

Step-by-step explanation:

Original Price = $140

Mark up (% increase) = 25%

Selling Price = Original Price (1 + Mark up)

Answer:

V = 2143.57

Step-by-step explanation:

To find the volume of a sphere you need to use this formula:

[tex]V = \frac{4}{3}\pi r^{3}[/tex]

r = radius

Solve:

You need the radius from the diameter. Divide 16/2 which is

8.

[tex]V = \frac{4}{3}(3.14) 8^{3}[/tex]

V = 2143.57

Answer:

Let x be the total fund

[tex] \frac{3x}{5} + \frac{2}{3}(x - \frac{3x}{5} ) + 8 = x [/tex]

3x/5 + 2/3(2x/5) + 8 = x

3x/5 + 4x/15 + 8 = x

9x/15 + 4x/15 + 120/15 = 15x/15

9x+4x+120=15x

-2x= -120

x=60£

Step-by-step explanation:

let's explain this a bit.

when the exterior angle is a certain size, then the interior angle is 180 - that exterior angle.

in our case the exterior angle is half of a right angle, so it is 90/2 = 45°.

the corresponding interior angle is 180-45 = 135°.

the sum of all angles inside a triangle is always 180°.

so,

x + 2x + 135 = 180

3x = 45

x = 15°

2x = 30°

so, the 3 interior angles are

135°, 15°, 30°

Answer:

4x² - 43x - 106

Step-by-step explanation:

4(x - 5)²– 3(x - 2)

4(x - 5)(x - 5) - 3 (x - 2)

distribute

4(x(x - 5) - 5(x - 5)) - 3 (x - 2)

4(x² - 5x - 5x - 25) - 3 (x - 2)

                                 ↓

combine like terms  ↓

4(x² - 10x - 25) (((      ↓

distribute again        ↓

4x² - 40x - 100          ↓

                                 ↓

distribute          ↔    ↓

4x² - 40x - 100 - 3 (x - 2)

4x² - 40x - 100 - 3x + 6

add

4x² - 40x - 106 - 3x

combine

4x² - 43x - 106

The amount that was invested in the first fund is $8300.

The amount that was invested in the second fund is 3700.

0.09a + 0.03b = $858 equation 1

0.1a + 0.01b = $867  equation 2

Where:

Multiply equation 2 by 0.9:

0.09a + 0.009b = 780.30 equation 3

Subtract equation 1 from equation 3

0.021b = 77.70

Divide both sides by 0.021

b = $3700

Substitute for b in equation 1: 0.09a + 0.03(3700) = $858

0.09a + 111 = 858

a = (858 - 111) / 0.09

a = $8300

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