A store has x packages of 4 markers and y packages of 12 markers. The store has a total of 192 markers in
stock. If there are 21 packages of 4 markers in the store, how many packages of 12 markers are there?

Answer:

1.33 < 2.67 ; Fail to reject H0 at 0.05

Step-by-step explanation:

Given the data :

Men:

n1= 11

s1= 6.1

Women:

n2= 14

s2= 5.3

The hypothesis :

H0 : σ1² = σ2²

H1 : σ1² > σ2²

To calculate the test statistic ; we use th Ftest statistics ;

F statistic = Larger sample variance / Smaller sample variance

Fstatistic = s1² / s2² = 6.1² / 5.3² = 37.21/28.09 = 1.325

The F critical value at :

df numerator = n - 1 = 11 - 1 = 10

df denominator = n - 1 = 14 - 1 = 13

Using the F distribution table :

F critical = 2.671

Since

F statistic < F critical ; Fail to reject H0 at 0.05

We fail to reject the null hypothesis at significance level of H0 : s1² = s2²

For the men, we have:

For the women, we have:

The null and the alternate hypotheses are:

The numerator and the denominator degrees of freedom are calculated as:

[tex]\mathbf{df = n -1}[/tex]

So, we have:

[tex]\mathbf{df_1 = 11 -1}[/tex]

[tex]\mathbf{df_1 = 10}[/tex] ----- numerator

[tex]\mathbf{df_2 = 14 -1}[/tex]

[tex]\mathbf{df_2 = 13}[/tex] ----- denominator

The test statistic of the f test is:

[tex]\mathbf{t = \frac{s_1^2}{s_2^2}}[/tex]

So, we have:

[tex]\mathbf{t = \frac{6.1^2}{5.3^2}}[/tex]

[tex]\mathbf{t = \frac{37.21}{28.09}}[/tex]

[tex]\mathbf{t = 1.325}[/tex]

The critical values at [tex]\mathbf{t = 1.325}[/tex] and the degrees of freedom is:

[tex]\mathbf{F= 2.671}[/tex]

By comparison, 1.325 is less than 2.671.

Hence, we fail to reject the null hypothesis at H0 : s1² = s2²

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Answer:

0.9 = 90% probability that the suspect actually committed the crime.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Charged

Event B: Committed the crime.

16% of crimes of this type end up in a criminal charge.

This means that [tex]P(A) = 0.16[/tex]

Probability of being charged and committing the crime:

90% of 16%, so:

[tex]P(A \cap B) = 0.9*0.16[/tex]

What is the chance that the suspect actually committed the crime?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.9*0.16}{0.16} = 0.9[/tex]

0.9 = 90% probability that the suspect actually committed the crime.

Step-by-step explanation:

yo

so sorry I can't

really answer it

Answer:

Step-by-step explanation:

D

Answer:

∠J ≅ ∠V

Step-by-step explanation: I took the same test (:

Answer:

90 days

Step-by-step explanation:

b= number of days til  her birthday

s = number of days til summer

b+s =135

b = 2s

2s+s = 135

3s = 135

Divide by 3

3s/3 =135/3

s =45

b = 2s = 2(45) = 90

Answer:

The FitnessGram™ Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly, but gets faster each minute after you hear this signal. [beep] A single lap should be completed each time you hear this sound. [ding] Remember to run in a straight line, and run as long as possible. The second time you fail to complete a lap before the sound, your test is over.ep explanation:

Answer:

115

Step-by-step explanation:

Since the lines are parallel, PWX+WXR=180, WXR=65. So PWX=(180-65)=115

Answer:

The graph of y = f(x) will shift down 11 units

Step-by-step explanation:

Answer:

The answer is "720"

Step-by-step explanation:

The amount of different slates candidates:

[tex]n=\frac{N!}{(N-k)!}\\\\[/tex]

   [tex]=\frac{10!}{(10-3)!}\\\\=\frac{10!}{7!}\\\\=\frac{10\times 9 \times 8 \times 7! }{7!}\\\\=10\times 9 \times 8\\\\=90\times 8\\\\=720[/tex]

Answer:

Radius on it's own is enough

Step-by-step explanation:

you could get the radius from the other informations, but after all you will calculate the volume with it and not the otheds, so just take radius. a sphere is, in terms of information, the simplest 3D-body to describe, like with a circle in 2D

The dimensions would you need to calculate the volume of a basketball is Radius on its own is enough

We have given that,

radius and height

length, width, and slant height

radius

length, width, and height

We have to determine the dimensions would you need to calculate the volume of a basketball.

Dimensions in mathematics are the measure of the size or distance of an object or region or space in one direction.

you could get the radius from the other information, but after all, you will calculate the volume with it and not the others, so just take the radius.

A sphere is, in terms of information, the simplest 3D body to describe, like a circle in 2D.

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Answer:

38 percent of the Cocoa is produced in the ivory coast, with thousands being produced in Ghana, so Ghana is the main production rate of the cocoa, with the ivory coast producing less than half.

Step-by-step explanation:

Let the two equal angles each be x

Let the third angle be x + 48

Then ATQ

x + x + x + 48 = 180

3x + 48 = 180

3x = 180 - 48 (Angle Sum Property)

3x = 132

x = 132/3

x = 44

Now the two angles are each 44

And the largest angle = 44 + 48

= 92

Answered by Gauthmath must click thanks and mark brainliest

Largest angle in the triangle is [tex]92^{0}[/tex]

"A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry."

"Angle sum property of triangle states that the sum of interior angles of a triangle is 180°."

Let us assume the two equal angles be '[tex]x[/tex]'

According to the question,

Two equal angles = [tex]x[/tex]

Third angle = [tex]x+48^{0}[/tex]

We know the angle sum property

[tex]x+x+x+48^{0} =180^{0}[/tex]

⇒[tex]3x+48^{0}=180^{0}[/tex]

⇒[tex]3x=180^{0}-48^{0}[/tex]

⇒[tex]x=\frac{132^{0} }{3}[/tex]

⇒[tex]x=44^{0}[/tex]

Two equal angles  [tex]x[/tex] = [tex]44^{0}[/tex]

Largest Angle = [tex]44^{0} +48^{0}[/tex]

∴  Largest Angle = [tex]92^{0}[/tex]

Hence, Largest Angle = [tex]92^{0}[/tex]

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Answer:

12

Step-by-step explanation:

Range is the subtraction of the largest number and the smallest number.

The largest number is: 23

The smallest number is: 11

Now subtract:

23 - 11 = 12

Hope this helped.

Answer:

the lowest is 11 and the highest is 24 then subtract it you are going to have 13

Answer:

x = 35

Step-by-step explanation:

We can use the Pythagorean theorem since this is a right triangle

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

x^2 + 12^2 = (x+2)^2

FOIL

x^2+144=x^2+4x+4

Subtract x^2 from each side

144= 4x+4

Subtract 4 from each side

140 = 4x

Divide by 4

35 =x

Answer:

2.5+2.5+45+45

=95.0m

therefore area of the square= 95.0m

45m×0.5=45.5÷95=

Step-by-step explanation:

2.5m

2.5 m tiles are required

[tex]area = 2.5 \times 45 = 192.5 \: squared \: cenimetre \\ \\ no \: of \: tiles = 0.5 \times 0.5 = 0.25 \\ 192.5 \div 0.25 = 770tiles[/tex]

9514 1404 393

Answer:

  4·10 +4·5 = 6·12 -6·2

Step-by-step explanation:

Each outside factor multiplies each inside term.

  4(10 +5) = 6(12 -2)

  4·10 +4·5 = 6·12 -6·2

Answer:

Answer: Option A.

Step-by-step explanation:

Hey there!

Given; The Line BC contains points B (4, -5) and C (3, 2).

And the Line DE contains points D (2,0) and E (9, 1)

Note: Use double point formula for finding the equation and then find slopes of both then put the condition for perpendicular lines and parallel lines.

From line BC;

The points are B (4, -5) and C (3, 2).

Using double point formula;

[tex](y - y1) = \frac{y2 - y1}{x2 - x1}(x - x1) [/tex]

Keep all the value;

[tex](y + 5) = \frac{2 + 5}{3 - 4} (x - 4)[/tex]

Simplify it;

[tex]y + 5 = - 7x + 28[/tex]

Therefore, the equation is y = -7x+23........(I)And slope(m1) is -7 {comparing the equation (I) with y=Mx+c}

Again;

The points D (2,0) and E (9, 1)

Using double point formula;

[tex](y - y1) = \frac{y2 - y1}{x2 - x1} (x - x1)[/tex]

Keep all values;

[tex](y - 0) = \frac{9 - 2}{1 - 2} (x - 2)[/tex]

[tex]y = - 7x + 14[/tex]

Therefore, the equation is y = -7x+14......(ii)And the slope (m2) is -7. {comparing the equation (ii) with y= mx+c}

Check:

For parallel lines:

m1= m2

-7 = -7 (true)

Therefore, the lines are parallel.

Hope it helps!

Answer:

a) To show that we can use the 1 proportion z-interval, we know that 250 ( size sample) is big enough to approximate the binomial distribution ( tolerance-intolerance) to a normal distribution.

b) See step by step explanation

CI 90 %  =  (  0,296 ; 0,392)

c) We can support that with 90 % of confidence we will find the random variable between this interval ( 0,296 ; 0,392)

d) the CI 95 % will be wider

Step-by-step explanation:

Sample Information:

Sample size n  =  250

number of people with milk intolerance  x = 86

p₁  =  86 / 250    p₁ = 0.344    and   q₁ =  1  - p₁   q₁ = 0,656

To calculate 90 % of Confidence Interval   α = 10%  α/2 = 5 %  

α/2 = 0,05     z(c) from z-table is:  z(c) =  1.6

Then:

CI 90 %  =  (  p₁  ±  z(c) * SE )

SE =  √ (p₁*q₁)/n   =  √ 0,225664/250

SE = 0,03

CI 90 %  =  (  0,344  ±  1,6* 0,03 )

CI 90 %  =  (  0,344 - 0,048 ;  0,344 + 0,048)

b) CI 90 %  =  (  0,296 ; 0,392)

a) To show that we can use the 1 proportion z-interval, we know that 250 ( size sample) is big enough to approximate the binomial distribution ( tolerance-intolerance) to a normal distribution.

c) We can support that with 90 % of confidence we will find the random variable between  this interval (  0,296 ; 0,392) .

d) CI 95 %      then significance level α = 5 %   α/2 = 2.5 %  

α/2  =  0,025      z(c) = 1.96   from z-table

SE = 0,03

And  as 1.96 > 1.6    the CI 95 % will be wider

CI 95% =  ( 0,344 ±  1.96*0,03 )

CI 95% =  (  0,344 ± 0,0588 )

CI 95% =  ( 0,2852 ; 0,4028 )

Answer:

B.  [tex]f^{-1}(x)=\frac{x-4}{5}[/tex]

Step-by-step explanation:

To find the inverse of a function/equation:

I hope this helps!!

gl!

Answer:

D

Step-by-step explanation:

I explained why 5 minutes ago on a different question

Answer:

5y + 6x = 40

Step-by-step explanation:

hope it is well understood?

Answer:

Shawn earns $11 per hour.

Step-by-step explanation:

When looking at the x axis (hours), and find where 1 hour intersects with the y axis It intersects with the point labeled at $11. This means after working for 1 hour, Shawn earned $11.

Answer:

7/12

Step-by-step explanation:

total: 12 roses

white roses: 5

pink roses: 7

fraction of pink roses = 7/12

Answer:

2

Step-by-step explanation:

g(x) = 2x - 6

g(4) = 2*4 - 6

g(4) = 2

f(x) = x - 2

f(3) = 3 - 2

f(3) = 1

Thus g (4) / f (3) = 2 / 1 = 2

The value of the function g (4) / f (3) is 2.

Function is a type of relation, or rule, that maps one input to specific single output.

We are given the function as;

f(x)=x-2 and g(x)=2x-6, then we need to find g(4)/f(3)

Therefore, g(x) = 2x - 6

g(4) = 2*4 - 6

g(4) = 2

Similalry,

f(x) = x - 2

f(3) = 3 - 2

f(3) = 1

Thus we have the value of function as

g (4) / f (3) = 2 / 1

g (4) / f (3) = 2

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Answer:

The third side is increasing at an approximate rate of about 0.444 meters per minute.

Step-by-step explanation:

We are given a triangle with two sides having constant lengths of 13 m and 19 m. The angle between them is increasing at a rate of 2° per minute and we want to find the rate at which the third side of the triangle is increasing when the angle is 60°.

Let the angle between the two given sides be θ and let the third side be c.

Essentially, given dθ/dt = 2°/min and θ = 60°, we want to find dc/dt.

First, convert the degrees into radians:

[tex]\displaystyle 2^\circ \cdot \frac{\pi \text{ rad}}{180^\circ} = \frac{\pi}{90}\text{ rad}[/tex]

Hence, dθ/dt = π/90.

From the Law of Cosines:

[tex]\displaystyle c^2 = a^2 + b^2 - 2ab\cos \theta[/tex]

Since a = 13 and b = 19:

[tex]\displaystyle c^2 = (13)^2 + (19)^2 - 2(13)(19)\cos \theta[/tex]

Simplify:

[tex]\displaystyle c^2 = 530 - 494\cos \theta[/tex]

Take the derivative of both sides with respect to t:

[tex]\displaystyle \frac{d}{dt}\left[c^2\right] = \frac{d}{dt}\left[ 530 - 494\cos \theta\right][/tex]

Implicitly differentiate:

[tex]\displaystyle 2c\frac{dc}{dt} = 494\sin\theta \frac{d\theta}{dt}[/tex]

We want to find dc/dt given that dθ/dt = π/90 and when θ = 60° or π/3. First, find c:

[tex]\displaystyle \begin{aligned} c &= \sqrt{530 - 494\cos \theta}\\ \\ &=\sqrt{530 -494\cos \frac{\pi}{3} \\ \\ &= \sqrt{530 - 494\left(\frac{1}{2}\right)} \\ \\&= \sqrt{283\end{aligned}[/tex]

Substitute:

[tex]\displaystyle 2\left(\sqrt{283}\right) \frac{dc}{dt} = 494\sin\left(\frac{\pi}{3}\right)\left(\frac{\pi}{90}\right)[/tex]

Solve for dc/dt:

[tex]\displaystyle \frac{dc}{dt} = \frac{494\sin \dfrac{\pi}{3} \cdot \dfrac{\pi}{90}}{2\sqrt{283}}[/tex]

Evaluate. Hence:

[tex]\displaystyle \begin{aligned} \frac{dc}{dt} &= \frac{494\left(\dfrac{\sqrt{3}}{2} \right)\cdot \dfrac{\pi}{90}}{2\sqrt{283}}\\ \\ &= \frac{\dfrac{247\sqrt{3}\pi}{90}}{2\sqrt{283}}\\ \\ &= \frac{247\sqrt{3}\pi}{180\sqrt{283}} \\ \\ &\approx 0.444\text{ m/min}\end{aligned}[/tex]

The third side is increasing at an approximate rate of about 0.444 meters per minute.

9514 1404 393

Answer:

  0.444 m/min

Step-by-step explanation:

I find this kind of question to be answered easily by a graphing calculator.

The length of the third side can be found using the law of cosines. If the angle of interest is C, the two given sides 'a' and 'b', then the third side is ...

  c = √(a² +b² -2ab·cos(C))

Since C is a function of time, its value in degrees can be written ...

  C = 60° +2t° . . . . . where t is in minutes, and t=0 is the time of interest

Using a=13, and b=19, the length of the third side is ...

  c(t) = √(13² +19² -2·13·19·cos(60° +2t°))

Most graphing calculators are able to compute a numerical value of the derivative of a function. Here, we use the Desmos calculator for that. (Angles are set to degrees.) It tells us the rate of change of side 'c' is ...

  0.443855627418 m/min ≈ 0.444 m/min

_____

Additional comment

At that time, the length of the third side is about 16.823 m.

__

c(t) reduces to √(530 -494cos(π/90·t +π/3))

Then the derivative is ...

  [tex]c'(t)=\dfrac{494\sin{\left(\dfrac{\pi}{90}t+\dfrac{\pi}{3}\right)}\cdot\dfrac{\pi}{90}}{2\sqrt{530-494\cos{\left(\dfrac{\pi}{90}t+\dfrac{\pi}{3}}}\right)}}}\\\\c'(0)=\dfrac{247\pi\sqrt{3}}{180\sqrt{283}}\approx0.443855...\ \text{m/min}[/tex]

Answer:

rhe

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end

Step-by-step explanation:

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Answer:

Part A: y = 25x + 30

Part B: $180

Step-by-step explanation:

for part A, 25 is the constant so that goes with the x, and you just add 30 because it is the extra fee. slope intercept form is y = mx + b

for part B you just plug 6 into the slope intercept equation

y = 25(6) + 30

y = 150 + 30

y = 180

$180

Answer:

C. The volume of the square prism is equal to the volume of the cylinder.

Step-by-step explanation:

I took the test and it was right

Answer:

3:7

Step-by-step explanation:

i hope this helps