Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of wood, and accommodates 300 sailors. She receives a delivery of 4 tons of wood each day. The deliveries can continue for 100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?

Answer:

[tex] \boxed{\sf (3x - 2)(2x + 1)} [/tex]

Step-by-step explanation:

[tex] \sf Factor \: the \: following: \\ \sf \implies 6 {x}^{2} - x - 2 \\ \\ \sf The \: coefficient \: of \: {x}^{2} \: is \: 6 \: and \: the \: constant \\ \sf term \: is \: - 2. \: The \: product \: of \: 6 \: and \: - 2 \\ \sf is \: - 12. \\ \sf The \: factors \: of \: - 12 \: which \: sum \: to \\ \sf - 1 \: are \: 3 \: and \: - 4. \\ \\ \sf So, \\ \sf \implies 6 {x}^{2} - 4x + 3x - 2 \\ \\ \sf \implies 2x(3x - 2) + 1(3x - 2) \\ \\ \sf \implies (3x - 2)(2x + 1)[/tex]

Answer:

Step-by-step explanation:

[tex] \mathsf{ {6x}^{2} - x - 2}[/tex]

Write -x as a difference

[tex] \mathsf{6 {x}^{2} + 3x - 4x - 2}[/tex]

Factor out 3x from the expression

[tex] \mathsf{3x(2x + 1) - 4x - 2}[/tex]

Factor out -2 from the expression

[tex] \mathsf{3x(2x + 1) - 2(2x + 1)}[/tex]

Factor out 2x + 1 from the expression

[tex] \mathsf{(2x + 1)(3x - 2)}[/tex]

[tex] \mathcal{Hope \: I \: helped!}[/tex]

[tex] \mathcal{Best \: regards!}[/tex]

[tex]2x \times x + 2x \times 5 - 9 \times x - 9 \times 5[/tex]

[tex] {2x }^{2} + 10x - 9x - 45 [/tex]

[tex] {2x}^{2} + x - 45 [/tex]

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Hi my lil bunny!

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[tex]\boxed{x=14}[/tex]

Reorder the terms:

[tex]-9 + 2x = 5 + x[/tex]

Solving

[tex]-9 + 2x = 5 + x[/tex]

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1x' to each side of the equation.

[tex]-9 + 2x + -1x = 5 + x + -1x[/tex]

Combine like terms: [tex]2x + -1x = 1x[/tex]

[tex]-9 + 1x = 5 + x + -1x[/tex]

Combine like terms: [tex]x + -1x = 0[/tex]

[tex]-9 + 1x = 5 + 0\\-9 + 1x = 5[/tex]

Add '9' to each side of the equation.

[tex]-9 + 9 + 1x = 5 + 9[/tex]

Combine like terms: [tex]-9 + 9 = 0[/tex]

[tex]0 + 1x = 5 + 9\\1x = 5 + 9[/tex]

Combine like terms: [tex]5 + 9 = 14[/tex]

[tex]1x = 14[/tex]

Divide each side by '[tex]1[/tex]'.

[tex]x = 14[/tex]

Simplifying

[tex]x = 14[/tex]

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Have a great day/night!

❀*May*❀

Answer:b

Step-by-step explanation:

Rocket science

Answer:

Answer: D : Median, because there is 1 outlier that affects the center

Step-by-step explanation:

Mean and median terms are use to measure the central tendency in a data set.

Mean is the best measure of center if there is no outlier present in the data otherwise median is the best measure of center if there is outlier present because outliers effects the means value of a data but not the median value.

In the third period, there is an outlier present as 8 that affects the center, then the best measure of center for third period must be Median.

Answer:

aₙ = 30 - 5n

Step-by-step explanation:

25,20,15,10, ...

We see from the given series that it is AP with:

Then formula is:

ANSWER IS ATTACHED

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                              PEACE!

The vertical distance through which the car rises is 16.7 m

"It is a triangle whose one of the angle is 90°."

In right triangle, for angle 'x',

sin(x) = (opposite side of angle x)/hypotenuse

For given example,

Consider the following figure for given situation.

A car travels 120 m along AC.

ΔABC is right triangle with hypotenuse AC.

∠C = 8°

Consider sine of angle C,

[tex]\Rightarrow sin(C)=\frac{AB}{AC}\\\\\Rightarrow sin(8^{\circ})=\frac{AB}{120}\\\\ \Rightarrow 0.1392=\frac{AB}{120}\\\\ \Rightarrow AB = 0.1392\times 120\\\\\Rightarrow AB = 16.70~ m[/tex]

Therefore, the vertical distance through which the car rises is 16.7 m

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Answer:

m∠C = 102°

Step-by-step explanation:

The above diagram is a cyclic quadrilateral

Step 1

First we find m∠B

The sum of opposite angles in a cyclic quadrilateral is equal to 180°

m∠D + m∠B = 180°

m∠B = 180° - m∠D

m∠B = 180° - 80°

m∠B = 100°

Step 2

Since we have found m∠B

We can proceed to find the Angle outside to circle

m∠CDA = 2 × m∠B

m∠CDA = 2 × 100°

m∠CDA = 200°

m∠CDA = m∠CD + m∠DA

m∠DA = m∠CDA - m∠CD

m∠DA = 200° - 116°

m∠DA = 84°

Step 3

Find m∠DAB

m∠DAB = m∠DA + m∠AB

m∠DAB = 84° + 120°

m∠DAB = 204°

Step 4

Find m∠C

It you look at the cyclic quadrilateral properly,

m∠DAB is Opposite m∠C

Hence

m∠C = 1/2 × m∠DAB

m∠C = 1/2 × 204

m∠C = 102°

Therefore ,m∠C = 102°

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]6x^2-8x+k=0\\\\\text{We compute the discriminant.}\\\\\Delta = b^2-4ac=8^2-4*6*k=8*8-8*3*k=8*(8-3k)[/tex]

And the we know that if the discriminant is

***** [tex]\Delta[/tex] < 0, meaning 8-3k<0, meaning

[tex]\boxed{k>\dfrac{8}{3}}[/tex]

then, there is no real solution.

***** [tex]\Delta = 0[/tex], meaning

[tex]\boxed{k=\dfrac{8}{3}}[/tex]

There is 1 solution.

***** [tex]\Delta[/tex] > 0, meaning

[tex]\boxed{k<\dfrac{8}{3}}[/tex]

There are 2 solutions.

Thank you

PS: To give more details...

[tex]8-3k=0\\\\\text{Add 3k}\\\\8=3k\\\\\text{Divide by 3}\\\\k=\dfrac{8}{3}[/tex]

Answer: Hi!

Alll of the follow are true except option 4, which states the absolute value of -93 is -93. This is not true! Absolute value will always be positive.

Hope this helps!

All of the given statements are true except |-93|=-93.

We need to identify the false statement from the given options.

The absolute value of a number is defined as its magnitude irrespective of the sign of the number. To find the absolute value of a real number, we consider only the number and remove the sign. It can only be a non-negative value. The absolute value of a positive number is the number itself, that of a negative number is the number without a negative sign, and the absolute value of 0 is 0.

From option (A):

|93|=93 is true.\

From option (B):

-|93|=-93 is true

From option (C):

|-93|=93 is true

From option (D):

|-93|=-93 is false

Therefore, all of the given statements are true except |-93|=-93.

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Answer:

[tex]\large \boxed{4}[/tex]

Step-by-step explanation:

[tex]\sf The \ sum \ of \ -5, \ -10, \ and \ -9 \ is \ divided \\ by \ the \ product \ or \ multiplication \ of \ 2 \ and -3.[/tex]

[tex]\displaystyle \frac{-5+-10+-9}{2 \times -3}[/tex]

[tex]\displaystyle \frac{-24}{-6}[/tex]

[tex]=4[/tex]

Answer:

4

Step-by-step explanation:

-5+(-10)+(-9)/2*(-3)

=-5-10-9/-6

=-24/-6

=4

Answer:

hey good

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

[tex]3m - 12 > 30 \text{ and } -6m\geq 24[/tex]

[tex]\boxed{3m - 12 > 30 \wedge -6m\geq 24}[/tex]

[tex]m>14 \wedge m\leq -4[/tex]

There's no solution. It is the first one already. There is no number that is both greater than 14 and less than or equal to -4. That is no solution because there's no [tex]m[/tex] that satisfy the compound inequality.

Note: the signal change because we divided by negative number.

Answer:

3m - 12 > 30 and -6m >= 24

Step-by-step explanation:

A. 3m - 12 > 30 and -6m >= 24

3m > 42  and m < = -4

m > 14 and m < = -4

This has no solution

B. -6m >= 12 and m + 5 -18

cannot solve since missing inequality

C. -5m < 20 and 6m > -18

m > -4   and m > -3

solution m > -3

D. -4m - 10 <= -22 and 6m - 8 >= 22

-4m < = -12  and 6m > = 30

m > = 3   and m > =5

m > = 5

Answer:

x = 1/2

Step-by-step explanation:

Let's represent this in a mathematical way,

(x+1)^2 - x^2 = 2

Ok now we expand,

x^2 + 2x + 1 -x^2 = 2

rearrange,

x^2 - x^2 + 2x + 1 = 2

subtract,

2x + 1 = 2

subtract 1 from both sides,

2x + 1 - 1 = 2 - 1

2x = 1

Now divide 2 from both sides and get your answer,

x = 1/2

Answer:

[tex](x + 1) { }^{2} - x {}^{2} = 2[/tex]

[tex]x {}^{2} + 2x + 1 - x {}^{2} = 2[/tex]

[tex]2x + 1 = 2[/tex]

[tex]x = 1 \div 2[/tex]

Answer:

c) Slope;-7;y-intercept:2

Step-by-step explanation:

Answer:

acceleration [tex]\approx 2.78\,\,\frac{m}{s^2}[/tex]

Step-by-step explanation:

The acceleration is the change in velocity per unit of time.

Therefore to have this rate in appropriate units that can combine, we re-write the change from 0 to 70 km/h in meters per second using:

[tex]70 \frac{km}{h} = \frac{70000}{3600} \frac{m}{s}[/tex]

so in this case the acceleration becomes:

[tex]accel=\frac{change\,\,vel}{change\,\,time} =\frac{70000m}{3600\,*7\,s^2} \approx 2.78\,\,\frac{m}{s^2}[/tex]

Answer:

Step-by-step explanation:

The standard form of writing a scientific notation is expressed as [tex]a.b*10^n[/tex] where a, b and n are integers. Note that a, b and n cannot be a fraction. When writing in scientific notation, the value of 'a' must not be equal to zero and it must not be a 'two digits values' but just 'a digit value'.

Based on the above conclusion, the following numbers are correctly written in scientific notation.

1×10⁻⁴ and 9.8×10⁵

- The expression 10.8×10 −3 is not correctly written because the value of a on comparison is a two digits number i.e 10.

- Also, 0.54×10^6 is not correctly written because a is zero on comparison

- 7.6×10 2.5 is not correctly written because the power is a decimal number i.e 2.5. We must only have an integer as the degree.

Answer:  D

Step-by-step explanation:

To find how much time she need on each project divide the time by 3 because there are 3 projects and to get to 1 project you will need to divide by 3.

16 3/4 =  67/4

[tex]\frac{67}{4}[/tex] ÷ [tex]\frac{3}{1}[/tex]  = [tex]\frac{67}{12}[/tex]   = 5 7/12

Answer:

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , thus

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7\sqrt{2} }{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

x = 7[tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] = 7 × 2 = 14

Answer:

Step-by-step explanation:

[tex]Hypotenuse = x \\Opposite = 7\sqrt{2} \\\alpha = 45\\\\\Using \: SOHCAHTOA\\Sin \alpha = \frac{Opposite}{Hypotenuse}\\ \\Sin 45 = \frac{7\sqrt{2} }{x} \\\\\frac{\sqrt{2} }{2} = \frac{7\sqrt{2} }{x} \\\\\sqrt{2x} = 14\sqrt{2} \\\\\frac{\sqrt{2x} }{2} = \frac{14\sqrt{2} }{2} \\x = 14[/tex]

Answer:

x + y + z = 4

Step-by-step explanation:

Give equations are,

2x + 3y - z = 5 --------(1)

x - 3y + 2z = -6 --------(2)

3x + y - 4z = -8 --------(3)

By adding equations (1) and (2),

(2x + 3y - z) + (x - 3y + 2z) = 5 - 6

3x + z = -1 -------(4)

By multiplying equation (3) by 3, then by adding to equation (2)

(9x + 3y - 12z) + (x - 3y + 2z) = -24 - 6

10x - 10z = -30

x - z = -3 --------- (5)

By adding equation (4) and (5),

(3x + z) + (x - z) = -1 - 3

4x = -4

x = -1

From equation (5),

-1 - z = -3

z = 2

From equation (1),

2(-1) + 3y - 2 = 5

-2 + 3y - 2 = 5

3y = 5 + 4

y = 3

Therefore, x + y + z = -1 + 3 + 2

x + y + z = 4

Answer:

V = 60 m³

Step-by-step explanation:

Volume of Triangular Pyramid: V = 1/3bh

Area of Triangle: A = 1/2bh

b = area of bottom triangle (base)

h = height of triangular pyramid

Step 1: Find area of base triangle

A = 1/2(8)(5)

A = 4(5)

A = 20

Step 2: Plug in known variables into volume formula

V = 1/3(20)(9)

V = 1/3(180)

V = 60

[tex]f(x)[/tex] passes through origin, i.e. $(0,0)$

if you move 5 units up, it should pass through $(0,5)$

so you'll add 5 to $y$ i.e. $y+5=x^2$ this satisfies $(0,5)$

and to move right, it should pass through $(7,0)$ so you'll subtract $7$ from $x$ i.e. $y=(x-7)^2$

now combine both translations

$g(x)=(x-7)^2-5=x^2-14x+45$

Work Shown:

1 pound = 16 ounces

100/16 = 6.25

100 ounces = 6.25 pounds

100 ounces = 6 pounds + 0.25 pounds

-------

1 pound = 16 ounces

0.25*1 pound = 0.25*16 ounces

0.25 pounds = 4 ounces

------

100 ounces = 6 pounds + 0.25 pounds

100 ounces = 6 pounds + 4 ounces

100 ounces = 6 pounds, 4 ounces

It depends on how b approaches 0

If b is positive and gets closer to zero, then we say b is approaching 0 from the right, or from the positive side. Let's say a = 1. The equation a/b turns into 1/b. Looking at a table of values, 1/b will steadily increase without bound as positive b values get closer to 0.

On the other side, if b is negative and gets closer to zero, then 1/b will be negative and those negative values will decrease without bound. So 1/b approaches negative infinity if we approach 0 on the left (or negative) side.

The graph of y = 1/x shows this. See the diagram below. Note the vertical asymptote at x = 0. The portion to the right of it has the curve go upward to positive infinity as x approaches 0. The curve to the left goes down to negative infinity as x approaches 0.

Answer:

x = 36

Step-by-step explanation:

To obtain the value of x, we must first obtain the value of y and z as shown in the attached photo.

i. Determination of y

2x + y = 180 (angle on a straight line)

Rearrange

y = 180 – 2x

ii. Determination of z.

z + 4x = 180 (angle on a straight line)

Rearrange

z = 180 – 4x

iii. Determination of x

x + y + z = 180 (sum of angles in a triangle)

But:

y = 180 – 2x

z = 180 – 4x

Therefore,

x + y + z = 180

x + 180 – 2x + 180 – 4x = 180

Collect like terms

x – 2x – 4x = 180 – 180 –180

– 5x = – 180

Divide both side by – 5

x = – 180 / – 5

x = 36

Therefore, the value of x is 36.

Answer:

x = 28

Step-by-step explanation:

12/x = 3/7

Using cross products

3x = 12*7

3x = 84

Divide by 3

x = 28

Answer:

29 divided by 5

quotient is 5 4/5

Step-by-step explanation:

I just took that test from school

Answer: 29 divided by 5. 5 4/5

Step-by-step explanation:

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Answer:

A. unbiased estimator.

Step-by-step explanation:

In Statistics, an estimator is a statistical value which is used to estimate a parameter. Parameters are the determinants of the probability distribution. Therefore, to determine a normal distribution we would use the parameters, mean and variance of the population.

A function of random variables used to estimate a parameter of a distribution is an unbiased estimator.

An unbiased estimator is one in which the difference between the estimator and the population parameter grows smaller as the sample size grows larger. This simply means that, an unbiased estimator captures the true population value of the parameter on average, this is because the mean of its sampling distribution is the truth.

Also, we know that the bias of an estimator (b) that estimates a parameter (p) is given by; [tex]E(b) - p[/tex]

Hence, an unbiased estimator is an estimator that has an expected value that is equal to the parameter i.e the value of its bias is equal to zero (0).

Generally, in statistical analysis, sample mean is an unbiased estimator of the population mean while the sample variance is an unbiased estimator of the population variance.

Answer: B statistic

Step-by-step explanation:

it just is trust me

Answer:

The amount the school pays is £32.40

Step-by-step explanation:

The cost of each pen = 15 pence

The cost of each ruler = 20 pence

The number of pens bought by the school = 150

The number of rulers bought by the school = 90

The cost reduction (discount) on the items bought = 1/5

Therefore, we have;

The total cost of the pens bought by the school = 150 × 15 = 2250 = £22.50

The total cost of the rulers bought by the school = 90 × 20 = 1800 = £18.00

The total cost of the writing materials (rulers and pens) bought by the school = £22.50 + £18.00 = £40.50

The discount = 1/5 total cost reduction = 1/5×£40.50  = $8.10

The amount the school pays = The total cost of the writing materials - The discount

The amount the school pays = £40.50 - $8.10 =  £32.40

The amount the school pays =  £32.40.

Answer:

4 1/3

Step-by-step explanation:

3 + 5 + 4 + 3 + 5 + 6 = 26

26/6 = 4 2/6 (4 1/3)

Answer:

13/3

Step-by-step explanation:

To find the mean, add up all the numbers and divide by the number of terms

( 3+5+4+3+5+6) /6

26/6

Divide top and bottom by 2 to simplify the fraction

13/3