Let $a_1, a_2, a_3, \dots$ be a non-constant arithmetic sequence. Suppose that $a_4, a_7, a_{12}$ form a geometric sequence. If $a_7 = 30$, what is $a_1$?

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:

    18. 0.25

    19. 0.33

Step-by-step explanation:

Problem 18

Problem 19

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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Answer:

$5×30days= $150 for the whole month

Answer: $90 saved

Step-by-step explanation:

8 - 5 = $3 dollars saved each day

Multiply daily amount saved by number of days

$3 × 30 = $90 saved

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

Fatima's claim that she has 0.413 kilogram of rose petals left is wrong

The given parameters are:

The amount left is the difference between the amount purchased and the amount used.

So, we have:

Remaining  = 0.454 + 0.056 - 0.02 - 0.095

Evaluate

Remaining  = 0.395

This means that the remaining amount is 0.395kg, not 0.413 kg

Hence, Fatima's claim that she has 0.413 kilogram of rose petals left is wrong

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Answer: she is left with 0.395 kilogram of rose pedals

Step-by-step explanation: she misalinged the first step,

0.454 - 0.02 = 0.434 + 0.056 = 0.490 - 0.095 = 0.395

The corresponding sides and angles of the both triangle would be congruent to each other.

An equation is an expression that shows the relationship between two or more numbers and variables.

△MNP is the image of △JKL after a reflection in the x-axis. Therefore, both triangles would be congruent.

The corresponding sides and angles of the both triangle would be congruent to each other.

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Answer:

x ≥ -42

Step-by-step explanation:

[tex]\frac{x}{7} > =-6[/tex]

[tex]\frac{x}{7}\cdot 7 > =-6\cdot 7[/tex]

[tex]\frac{1}{7}\cdot 7x > =-6\cdot 7[/tex]

[tex]x > =-6\cdot 7[/tex]

[tex]x > =-42[/tex]

Shortcut

• Multiply positive 7 by negative 6 to find x as a shortcut.

Answer:

The answer is (-100).

Step-by-step explanation:

Now,

x/5 + 6 = -14

Cross multiplication

x + 5 × 6 ÷ 5 = -14

x + 30/5 = -14

Multiply 5 both sides we get,

x + 30/5 × 5 = -14 × 5

x + 30 = -70

x + 30 – 30 = -70 – 30

x = -100

Thus, The value of x is (-100).

Answer:

[tex]\huge\boxed{\sf x = -100}[/tex]

Step-by-step explanation:

Given Equation:

x/5 + 6 = -14

Subtract 6 to both sides

x/5 = -14 - 6

x/5 = -20

Multiply 5 to both sides

x = -20 × 5

x = -100

[tex]\rule[225]{225}{2}[/tex]

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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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

[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

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:

$175

Step-by-step explanation:

Original Price = $140

Mark up (% increase) = 25%

Selling Price = Original Price (1 + Mark up)

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:

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:

True, (-∞, ∞)         3 ≤ 8

Step-by-step explanation:

−8 + 11 ≤ −3 + 11

3 ≤ 8

Answer:

-7.

Step-by-step explanation:

Using the Remainder Theorem :

If  f(x) is divided by x-1 then the remainder is f(1), so

The required remainder

= f(1) =  2(1)^3 - 5(1)^2 + (-1) - 3

= 2 - 5 - 1 - 3

= -7.

Answer:

remainder = -5

Step-by-step explanation:

Divide using long division:

[tex]\large \begin{array}{r}2x^2-3x-2\phantom{)}\\x-1{\overline{\smash{\big)}\,2x^3-5x^2+x-3\phantom{)}}}\\\underline{-~\phantom{(}(2x^3-2x^2)\phantom{-b))))))}}\\0-3x^2+x-3\phantom{)}\\ \underline{-~\phantom{()}(-3x^2+3x)\phantom{-b}}\\ 0-2x-3\phantom{)}\\\underline{-~\phantom{()}(-2x+2)}\\ -5\end{array}[/tex]

The area of the training field is 5606.48 m².

Area can be defined as the region bounded by a plane shape.

To calculate the area of the training field, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the area of the training field is 5606.48 m².

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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)]

Answer:

711001392

321000759

Step-by-step explanation:

hope it helps ^o^

Type such digits that's are correlated to both numbers but they are not present in both rather than present in one.

They can be 2 and 7 or 5 and 9

You can write other one also

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.

Answer:

232

Step-by-step explanation:

→ Find the percentage multipier

( 100 + 45 )÷ 100 = 1.45

→ Multiply this by the original amount

1.45 × 160 = 232

Answer: 1/6

Step-by-step explanation:

Since there’s only one side on the dice that has two on it out of six sides it has to be 1/6.

[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]

(a)The domain of the function is, [tex]\rm x \geq -c^2 \ x\neq0[/tex]

(b)The given function is discontinuous at x=0.

Domain is the set of values for which the given function is defined. Range is the set of all values which the given function can output.

The standard function is;

[tex]\rm f(x)= \frac{\sqrt{x+c^2-c} }{x} , c > 0[/tex]

The domain of the given function is found as;

[tex]\rm x+c^2 \geq 0 \ x\neq 0 \\\\ x\geq-c^2 \ x\neq 0[/tex]

The domain of the function is,

[tex]\rm x \geq -c^2 \ x\neq0[/tex]

To find the function is continuous or not, we have to find the continuity;

[tex]\rm f(x) = \frac{\sqrt{ x+c^2-c}}{x} ,c > 0[/tex]

At x= 0 the function is undefined. So that the function is discontinuous at x=0.

Hence, The domain of the function is, [tex]\rm x \geq -c^2 \ x\neq0[/tex] and the function is discontinuous at x=0.

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Answer:

It's 8 yuan per hour in company A and 9 yuan per hour in company B

Answer:

Step-by-step explanation:

AB = 6

BC = 4

just sum

6 + 4 = 10

AC = 10

Step-by-step explanation:

Divide the two numbers.

5/2 / 1/4

Flip the 2nd fraction and multiply:

5/2 * 4/1

20/2

10

So the marathon runner travels at a unit rate of 10 MPH.