a machine makes 36 trophies every hour. The machine makes trophies for 8 and a half hours each day, on 5 days of the week. The trophies are pack into boxes. Each box holds 8 trophies.
How many boxes are needed for all the trophies made each week?

Using Z- distribution it is found that the mean length of jail time has increased because the test statistics is greater than the critical value.

Z- distribution: It is a special normal distribution where the mean is 0 and standard deviation is 01.

                             z = (x -μ) / σ

At the Null hypothesis, it is tested if the mean length of jail time is still of 2.5 years.,          

            i.e.,  H₀ :μ = 2.5

Null hypothesis : It refers to a hypothesis that states that there is no relationship between two population parameters.

At the alternative hypothesis, it is tested if it has increased

                 i.e., H₁ :μ>2.5

Alternative Hypothesis:   The alternative hypothesis states the research prediction of an effect or relationship.

we have the standard deviation for population thus the z- distribution is used.  The test statistics is :

                 z= ⁻ₓ -μ /σ /√n

where, x is the sample mean

           μ is the value tested at the null hypothesis.

           σ is the standard deviation of sample.

           n is the sample size.

For this problem the values of parameter are:

         x= 5 ,σ =1.4 ,μ = 2.5 and n = 27

hence the value is :

              z= ⁻ₓ -μ /σ /√n

                 = 5 - 2.5 / 1.4 ÷ √27

                 = 2.5 × √27 /1.4

                 = 9.27

The critical value for a right tailed test as we are testing if the mean is greater than a value with a significance level of 0.05 is of 2*= 1.645.

since, the test statistics is greater than the critical value, it can be concluded that the mean length of jail time has increased.

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Answer:

y= [tex]\frac{5}{9}[/tex]x - 2

Step-by-step explanation:

You want to get y alone so divide both sides by -9 to get: y = [tex]\frac{5}{9}[/tex]x- 2

this is because 2 negatives (-5x and -9) make a positive

The two numbers whose sum is 2 and product is -24 are 6 and -4

A quadratic equation is a second-order polynomial equation in a single variable x

a[tex]x^{2}[/tex]+bx+c=0

with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

Let the two numbers be x and y

so that

x + y = 2 ----------------1

xy = -24 -----------------2

from equation 1 make x the subject of the equation, so that it becomes

x = 2 - y ---------------3

substitute x in equation 3 in equation 2

y(2-y) = - 24

multiply out the bracket

2y - [tex]y^{2}[/tex] = -24

taking all terms to one side of the equation, it becomes

[tex]y^{2}[/tex] -2y -24 = 0

factorizing the equation

[tex]y^{2}[/tex] -6y + 4y - 24 = 0

y(y - 6) +4(y - 6) = 0

taking the terms outside bracket and putting them in a new bracket we have

(y + 4) (y - 6) = 0

so y + 4 = 0 or y - 6  = 0

y = -4 or y = 6

using y = -4 and substituting in equation 3

x = 2 - - 4

x = 6

In conclusion the two numbers are 6 and -4

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The total surface are of cuboid is 304 cm square.

What is total surface area of cuboid?

The area of a cuboid refers to the surface area as the cuboid is a three dimensional solid. Thus, the area of cuboid can be calculated using the formula of area of rectangle, since the faces of a cuboid are in a rectangular shape.

The Total surface area of a cuboid (TSA) is equal to the sum of the areas of it’s 6 rectangular faces, which is given by:

Total Surface Area of a Cuboid (TSA) = 2 (lw + wh + lh) square units

The above formula gives the total surface area of a cuboid having all six faces.

Given, length = 10cm , width = 6 cm , height = 7cm

Total surface area = 2[10(6)+6(7)+10(7)]

=2(60+42+70)

=2(152)

=304.

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Answer:

14x + 8 for the first column and the second one is i think its 2 (7x + 4)

Step-by-step explanation:

sorry if this is not what your looking for

[tex]\boldsymbol{\sf{\dfrac{5}{3}x+4=\dfrac{2}{3}x }}[/tex]

Subtract 2/3x on both sides.

[tex]\boldsymbol{\sf{\dfrac{5}{3}x+4-\dfrac{2}{3}x=0 }}[/tex]

Combine 5/3x and -2/3x to get x.

[tex]\boldsymbol{\sf{x+4=0 }}[/tex]

Subtract 4 from both sides. Any value subtracted from zero results in its negative value.

[tex]\boldsymbol{\sf{x=-4 }}[/tex]

Answer:

x = - 4

Step-by-step explanation:

[tex]\frac{5}{3}[/tex] x + 4 = [tex]\frac{2}{3}[/tex] x ( multiply through by 3 to clear the fractions )

5x + 12 = 2x ( subtract 2x from both sides )

3x + 12 = 0 ( subtract 12 from both sides )

3x = - 12 ( divide both sides by 3 )

x = - 4

Answer:

I'm not sure, but it could be "inverse"

Step-by-step explanation:

The approximate value of the account after 5 years will be $6778.

Given that,

Mario put $6,000 into a savings account that accrues interest at a rate of 5% per year.

The amount is given by,

A= p(1 + r)^t

P = 6000

R = 5%

T= 2.5 years

R = Rate of Interest

T= Time

P = Principal Amount

By substituting we get,

A= p(1 + r)^t

A = 6000(1 + 0.05)^2.5

A = 6000(1.05)^2.5

A = 6000 * 1.129

A = 6778.35

As a result, the account will roughly be worth $6778 after five years.

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Answer:

Step-by-step explanation:

no because (-2X1, Y1), and-2X3, y3), arent congruent so the whole problem is not congruent

The point(0,3) is not a part of any quadrant. option D is the correct answer

The points on the x-axis and the y-axis are not a part of any quadrant.

From the question, we have

The point(0,3) is not a part of any quadrant.

Cartesian Coordinate System:

A point in a plane can be found using the coordinate system by connecting two perpendicular lines. In two dimensions, points are represented as coordinates (x, y) with respect to the x- and y-axes. We will study the Cartesian Coordinate System in this article. Axes and quadrants make up a plane. The coordinate axes are the name of the axes. Axes and quadrants make up a plane. The coordinate axes are the name of the axes. A rectangular system's reference lines, the vertical and perpendicular axes, are used to measure distances.

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Answer:

m<T = 60°

m<U = 60°

TS = 13

SU = 13

Step-by-step explanation:

Triangle TSU is an equilateral triangle.

All interior angles has equal measures and each = 60° since the sum of interior angles in a triangle is equal to 180 and this divided by 3 = 60

all side lengths are also equal to one another, TU is given as 13 cm so the length of TS and SU is also = 13

According to the area of triangle, the value of x is 8.6 and the value of y is 10.5

Area of triangle:

The area of the triangle is defined as the region enclosed by its perimeter or the three sides of the triangle.

Given,

Here we have the triangle with side values and height.

Now, we have to find the value of x and y in the triangle.

We know the formula of the triangle is,

A = 1/2 b x h

Here the value of b is x + 9 and the value of h = 6

So, the area of the triangle is,

=> [(x + 9) x 6]/2

=> 2 = 6x + 54

=> 6x = 52

=>  x = 52/6

=> 8.6

Now, the value of y is calculated by using the Pythagoras theorem,

=> y² = (8.6)² + 6²

=> y² = 73.96 + 36

=> y² = 109.96

=> y = √109.96

=> y = 10.5

Therefore, the value of y is 10.5

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Weight of water will a 55 gallon tank hold 440 lbs.

If a 45 gallon hot water tank holds 360 lbs.

45 gal⇒  360 lb

55 gal ⇒ x lb?

Ratio

45 : 360 = 55 : x

Ratios are used to compare two numbers by dividing them. If you want to compare one data point (A) to another (B), your formula would be A/B. This signifies that you are dividing data A by data B. If A is five and B is ten, your ratio will be 5/10.

Here,

do the relation

[tex]\frac{45}{360} = \frac{55}{x}[/tex]

solve the x

[tex]x = \frac{55 * 360}{45} \\ = 440[/tex]

Hence weight of water will a 55 gallon tank hold 440 lbs.

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The exponential number 7⁴ we get expression as 2401.

Given that,

The exponential number is 7⁴.

We have to find the expression.

A number's exponent tells us how many times it has been multiplied by itself.

Exponent-related issues are resolved utilising exponentiation rules or exponentiation attributes.

How many times we must multiply the reciprocal of the base is indicated by a negative exponent is the exponential with negative symbol

A fractional exponent is one where the exponent of a number is a fraction.

Take the exponential number.

7⁴

7×7×7×7

2401

Therefore, The exponential number 7⁴ we get expression as 2401.

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Answer:

Only the third one is incorrect. First 2 and last 1 are correct.

Answer:

= 27

Step-by-step explanation:

36×3/4

36 × 3

--

4

9 × 3

= 27

Answer:

Step-by-step explanation:

75 = 64 + 8 + 2 + 1 = 1*2^6 + 1*2^3 + 1*2^1 + 1*2^0

There is no power 5, 4, or 2 so zeros go in those slots.

75 = 1001011 (Base 2)

The P(a, b and c)  is 0.0432 when P(a) = 0.90, p(b) = 0.96, p(c) = 0.05.

From the given question, we know that

Probability of event 'a' occurring, P(a) = 0.90

Probability of event 'b' occurring, P(b) = 0.96

Probability of event 'c' occurring, P(c) = 0.05

We have been told that these three events are independent.

Thus, we can use the multiplication rule of probability, which states that the probability of three independent events a, b, and, c occurring is equal to the products of the probability of each individual event occurring.

p(a, b and c) = p(a) × p(b) × p(c)

                    = 0.90 × 0.96 × 0.05

                    = 0.0432

Hence, the probability(a, b, and c) is 0.0432.

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Answer:

25%

Step-by-step explanation:

cause i did marh

The new volume of the container will be 120 ft³

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Given a container with dimensions 3ft by 4ft by 5ft

Its volume need to be twice.

Volume of container = length*width*height

Original volume = 3*4*5 = 60 ft³

After doubling = 60*2 = 120 ft³

New dimensions are = 4ft by 5ft by 6ft

Hence, The new volume of the container will be 120 ft³ and New dimensions are 4ft by 5ft by 6ft

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Answer:

k=297.54

Step-by-step explanation:

i can't really explain it

The value of k that satisfies the equation k/34.2 = 8.7 is approximately 297.54. So, correct option is B.

To determine the value of k in the equation k/34.2 = 8.7, we can solve for k by isolating it on one side of the equation.

We can start by multiplying both sides of the equation by 34.2 to eliminate the denominator:

k/34.2 * 34.2 = 8.7 * 34.2

This simplifies to:

k = 8.7 * 34.2

Evaluating the right side of the equation:

k ≈ 297.54

The correct option from the given choices is 297.54. So, correct option is B.

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The scale factor for a a pair of corresponding sides will be;

⇒ 3 / 2

What is Proportional?

The equality between two ratio is called Proportional.

Given that;

DEFG has been dilated to D'EF'G'.

Now,

Let the coordinates of DEFG are for side DG are;

D = (- 6, 3)

G = (- 3, 3)

And, The coordinates of D'E'F'G' are for side D'G' are;

D' = (- 4, 2)

G' = (- 2, 2)

So, The length of side DG is;

DG = √ (- 3 - (-6))² + (3 - 3)²

     = √ 3²

     = 3

And, The length of side D'G' is;

D'G' = √ (- 2 - (-4))² + (2 - 2)²

     = √ 2²

     = 2

Thus, The scale factor for a a pair of corresponding sides will be;

⇒ DG / D'G' = 3 / 2

Therefore, The scale factor for a a pair of corresponding sides will be;

⇒ 3 / 2

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Answer: 33 pages in 1 hour

Step-by-step explanation:

You could cross multiply

[tex]\frac{11}{1/3}[/tex] = [tex]\frac{x}{1}[/tex]

11=1/3x

x=33

Answer: y= -2/4x - 3

Step-by-step explanation:

b=y-intercept

Equation for slope-intercept form: y=mx+b

Locate the y-int/b: -3=b

Identify the slope/m: -2/4= 2 down, 4 to the right

Insert slope and y-int into slop-intercept form: y= -2/4x - 3

The marked price of the wrist watch after the trader sold a wrist watch for $3150 after giving a 10% discount is $3500.

First, let us understand the percentage:

A percentage is a fraction of a whole expressed as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent.

To determine a percentage, we need to divide the portion of the whole by the whole itself and multiply by 100.

Let the marked price be x.

So,

According to the question;

x - x * 10% = 3150

x - x * 10/100 = 3150

100x - 10x / 100 = 3150

90x = 3150 * 100

x = 3150 * 100 / 90

x = 3500

So, the marked price is $3500.

Thus, the marked price of the wrist watch after the trader sold a wrist watch for $3150 after giving a 10% discount is $3500.

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The simplified expression is 11 (1/6).

A fraction is a part of the whole represented by a/b, where a and b are any integers.

The given expression is 7 (5/12) - (-3 (3/4)).

Simplify the expression as follows:

7 (5/12) - (-3 (3/4))

= 89/12 +15/4

= (89+45)/12

= 134/12

= 11 (1/6)

Hence, the simplified expression is 11 (1/6).

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The degree of a function has no effect by the dilation of the function.

and the degree of the dilated function is same as the degree of the original function.

Dilation is defined as, when a function is multiplied by any number, the graph of the function retain a new shape, either by stretch or by compression in different directions.

Now, when a function is dilated it is either stretched or compressed in upward or downward direction.

It does not affect the degree of the function as the number of roots will be same as original function.

So, the degree of the dilated function is same as the degree of the original function.

Hence, the degree of the dilated function is same as the degree of the original function.

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The number of bottles of soda purchased are 4 and the number of bottles of juice purchased are 10.

Given,Parker went to the grocery store and bought bottles of soda and bottles of juice.

Each bottle of soda has 50 grams of sugar and each bottle of juice has 10 grams of sugar.

Parker purchased a total of 14 bottles of juice and soda which collectively contain 300 grams of sugar.

we are asked to determine  the number of bottles of soda purchased,x, and the number of bottles of juice purchased, y.

So, the total number of bottles:x+y=14

x=14-y ...eq(1)

As, Each bottle of soda has 50 grams of sugar and each bottle of juice has 10 grams of sugar.

50x+10y=300

Substituting the value of x from eq(1)

⇒ 50(14-y) + 10y = 300

⇒ 700 - 50y + 10y = 300

⇒ -40y = 300 - 700

⇒ -40y =-400

y = 400/40

y = 10

The number of juice bottles = 10.

Now, to get the number of bottle of soda by substituting the value of y  in equation (1):

x = 14-y

x = 14 - 10

x = 4

The number of soda bottles = 4.

Therefore, the number of bottles of soda purchased are 4 and the number of bottles of juice purchased are 10.

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a)  no solution

b) only one solution

c) only one solution

d) infinite many solution.

e)  only one solution

f) no solution

g) infinite many solution.

h)  infinite many solution.

i)  no solution

j) only one solution

k) infinite many solution.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

We know depending upon the types of lines there are different type of solution

if there are two equations

[tex]a_1 x+ b_1 y+ c_1= 0[/tex] and [tex]a_2 x+ b_2 y+ c_2= 0[/tex]

For Intersecting Lines

[tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]

and, have only one solution

For parallel lines:

[tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] ≠ [tex]c_1/c_2[/tex]

and, have no solution

For co- incident line

[tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]

and, have infinite many solution.

a) y= -5x + 4  --> 5x + y = 4

5x+y= -3

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] ≠ [tex]c_1/c_2[/tex]

and, have no solution

b) y=3/4 x+5

y= 4/3 x + 5

so, [tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]

and, have only one solution

c) y= -3/4x+5

y=3/4x+5

[tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]

and, have only one solution

d) y= 3/4 x + 5

y= 5+ 3/4x

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]

and, have infinite many solution.

e) y= 3/4x +5

y=  x + 2

So, [tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]

and, have only one solution

f) y= 3/4x + 5

y= 3/4x + 2

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] ≠ [tex]c_1/c_2[/tex]

and, have no solution

g) 6x -y = 5

-6x + y= -5

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]

and, have infinite many solution.

h) 2x- y +5 =0

2x- y+ 5 =0

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]

and, have infinite many solution.

i) 4x- y+ 5 =0

4x- y +3 = 0

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] ≠ [tex]c_1/c_2[/tex]

and, have no solution

j) 3x- y +5 = 0

2x -y +5 =0

So, [tex]a_1/a_2[/tex] ≠ [tex]b_1/b_2[/tex]

and, have only one solution

k) 2x+ y -1 = 0

2x + y- 1= 0

So, [tex]a_1/a_2[/tex] = [tex]b_1/b_2[/tex] = [tex]c_1/c_2[/tex]

and, have infinite many solution.

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Answer:

45mi/h

Step-by-step explanation:

4 to 8 = 4 hours

v = space / time

v = 180/4 = 45 mi/h