Find the indicated critical value. z 0.03

The fencing needed to enclose the garden is equal to the perimeter of the rectangle and it will be 5x + 56.

The perimeter of the rectangle: The sum of all the sides of the rectangle will be known as the perimeter of the rectangle.

Let L be the length and W be the width of the rectangle.

Then the perimeter of the rectangle will be

The perimeter of the rectangle = Sum of all the sides

If the gardener fences in the total rectangular area shown in the illustration instead of just the square area, he will need twice as much fencing to enclose the garden.

From the diagram, the length is 28 + x. And the width is x. Then the perimeters of the rectangle will be

P = 28 + x + 28 + x + x + x + x

P = 56 + 5x

The fencing needed is equal to the perimeter and will be 5x + 56.

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Answer:

Step-by-step explanation:To determine which store charges the least amount per bottle, you need to calculate the price per bottle for each store. You can do this by dividing the total price of the cases by the number of bottles in each case.

For Super Buy, the price per bottle is $3.96 / 12 bottles = $0.33 per bottle.

For Fresh Grocers, the price per bottle is $2.08 / 8 bottles = $0.26 per bottle.

For Saveway, the price per bottle is $5.52 / 24 bottles = $0.23 per bottle.

For Shop and Go, the price per bottle is $7.56 / 36 bottles = $0.21 per bottle.

Based on these calculations, it looks like Shop and Go charges the least amount per bottle at $0.21.

The months when both of these plans would pay off the same amout of money for the new phone is 8 months.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario

Let the number of months be x

You can pay a one-time charge of 200$ and then an additional $15 per month. This will be 200 + 15x. The second option is not paying any money at this time and having a monthly bill of 40$ a month. This will be 40x.

The equation will be

200 + 15x = 40x

Collect like terms

40x - 15x = 200

25x = 200

Divide

x = 200/25

x = 8

The number of months is 8.

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Dorothea needs 2.4 kilograms of filo pastry to make on pan of baklava.

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b.

Given that,

The quantity needed of filo pastry to make one pan of baklava = 400 grams

To find the quantity of pastry to make 6 pans of baklava

Use ratio property,

1 pan of baklava needed = 400 grams

6 pans of baklava needed = 400 x 6 = 2400 grams

Since, 1000 gram = 1 kilogram

2400 gram = 2.4 kilograms

Hence, Dorothea needs 2.4 kilograms of filo pastry.

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Answer:

63 =  EHF

Step-by-step explanation:

We know that EHG is a right angle which is 90 degrees

FHG is 27 degrees

EHG = FHG + EHF

90 = 27+  EHF

90-27 = EHF

63 =  EHF

A Polygon is a closed figure made up of line segments (not curves) in a two-dimensional plane. Polygon is the combination of two words, i.e. poly (meaning many) and gon (meaning sides). Usually , a minimum of three line segments is required to connect end to end, to make a closed figure. In terms of geometry, a polygon is a plane figure that is described by a finite number of straight line segments (greater than 3) connected to form a closed polygonal chain.

A regular polygon is a polygon with sides equal in length and angles equal in measure. For example, a square has all four sides equal and all four angles equal to 90 degrees. Hence, it is a regular polygon.

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Answer:

Step-by-step explanation:

Given,

[tex]P = $400 find I\\R = 9%\\\\T = 0.25 years[/tex]

[tex]T=0.25[/tex](Remember 9% = .09 in decimal form)

So We convert it into a decimal form

[tex]\frac{9}{100} =0.09[/tex]

Now we find the Interest,

[tex]I=PRT\\[/tex][tex]I = 400X0.09X0.25\\I=36X0.25\\I=9$[/tex]

9$ is the answer

The probability that less than 2 people will return the purchased items on the web be, 0.52822

Given, a research claims that 30% of people, who purchase items on the web of a specific store, return it.

Now, if we pick 5 people who purchase via the web,

then we have to find the probability that less than 2 will return their purchase

we have to find, P(X < 2)

Now, n = 5

p = 0.3

q = 0.7

P(X < 2) = P(X = 0) + P(X = 1)

P(X < 2) = C(5 , 0)(0.3)^0(0.7)^5 + C(5 , 1)(0.3)^1(0.7)^4

P(X < 2) = (0.16807) + (0.2401)(0.3)(5)

P(X < 2) = 0.16807 + 0.6015

P(X < 2) =  0.52822

So, the probability that less than 2 will return be, 0.52822

Hence, the probability that less than 2 will return be, 0.52822

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Answer:

6 7/12

Step-by-step explanation:

"12 1/4 - 5 2/3" is an expression.  It is not said to equal anything.  The "=" sign makes it an equation.  But we can evalute an expression by simplyfying it.  Let's do the subtraction.  We first need to convert one of the fractions so that it has the same denominator as the other.

12 1/4 - 5 2/3 can be written as (12 - 5)+(1/4 - 2/3)

(12 - 5)+(1/4 - 2/3)

(7)+(1/4 - 2/3)        Let's convert both fractions to have denominators of 12 [since 4*3 = 12]

7 + 1/4 - 2/3

7 + (1/4)*(3/3) - (2/3)*(4/4)   [Multiply the tqo fractions by (3/3) and (4/4), repectively.  This is OK since both are the equivalent of multiply by 1.  But it converts the denominators so that we can now add or subtract.

7 + (3/12) - (8/12)

7 - (5/12)

or 6 7/12

If you have two main effects, and one main effect is significant, this means that d. The other main effect and the interaction effect may or may not be significant

A statistically significant result indicates that it is unlikely to be explained solely by chance or random factors. In other words, if there is no true effect in a research study, a statistically significant result has a very low chance of occurring.

The significance level is the threshold at which one can accept whether an event is statistically significant. Researchers use the p-value to determine statistical significance: if the p-value is less than the significance level, the result is statistically significant.

If you have two main effects and one of them is significant, the other one and the interaction effect may or may not be significant.

In conclusion, based on the information illustrated, the correct option is D.

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The absolute value for |4 - 5i| =[tex]\sqrt{41}[/tex].

Without taking into account direction, absolute value describes how far a number is from zero on the number line. A number's absolute value can never be negative. Look at some illustrations. 5 is the sum of its absolute values. There are 5 units between 5 and 0. A negative number has a positive absolute value, too. If x 0, then |x| = -x gives the absolute value of the supplied number.

For illustration, |-2| = 2. No matter what the numerical value's sign, the absolute value is always positive.

Here complex number form =|a+ib|

= |4-5i| Here a=4, b=(-5).

[tex]|a+ib| = \sqrt{a^{2}+b^{2} } \\\\\sqrt{4^{2}+5^{2} } \\\\\sqrt{16+25} \\\\\sqrt{41} \\[/tex]

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Answer: $552

Step-by-step explanation:

Let x be the number of year and y is the total amount

We have the equation

y= 6.5x + 500

Then put 8 in for the x

y= 6.5(8) + 500

y= $552

Answer:

Step-by-step explanation:

Stop Cheating.

13+16 are the numbers that equals to 19.

The equal sign in the  mathematics describes by  equality between the values,. Of the  equations, or expressions are the  written on both sides. There symbol for equal to is two be the  small horizontal lines placed to parallelly. We place the to the  'equal to' sign is between two things that are to the same or equal.

As we know,

If two things are equal or if one thing is equal to the  another, they are the same or  in the size, number, standard, or values .

As per the question we have to find equal number of 19.

So 13+6 are the equal number that equals to 19.

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Answer:

9

Step-by-step explanation:

3(x-4)=15

Use distributive property with the 3 (multiply 3 times x and 3 times -4)

3x-12=15

Add the 12 to both sides.

3x=27

divide 27 by 3.

x=9

Answer:

Step-by-step explanation:

How do you solve 3(x−4)=15?

3(x − 4) = 15

divide both side by 3

x - 4 = 5

x = 5 + 4

x = 9

----------------

check

3(9 - 4) = 15

9 - 4 = 5

5 = 5

the answer is good

The equation is shown in the graph as (C) g(x) = (1/7)^x - 4.

A relationship between two terms on either side of an equal sign is described by a straightforward equation.

Additionally, addition, basic arithmetic, multiplication, and division are one or more of the four arithmetic calculations that simple equations undertake.

The system of equations can be expressed in three different ways: in point-slope form, standard form, and slope-intercept form.

So, the parent function is therefore known to be:

f(x) = (1/7)^x

Observe that the y-intercept results from evaluating this in zero:

f(0) = (1/7)^0 = 1

The graph's y-intercept is located at y = -3.

As a result, the function was translated downward by 4 units, bringing it to a point 4 units below the y-intercept of the parent function.

Thus, the graphed function is as follows:

g(x) = f(x) - 4

g(x) = (1/7)^x - 4

Therefore, the equation is shown in the graph as (C) g(x) = (1/7)^x - 4.

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Complete question:
What is the equation of the function shown in the graph, given that the equation of the parent function is f(x)=(1/7)^x ?

A. g(x)=(1/7)^x−3

B. g(x)=(1/7)^x−2

C. g(x)=(1/7)^x−4

D. g(x)=(1/7)^x+3

The simplified form of the expression 2/5 + 5/20 is 13/20

The expression is

2/5 + 5/20

The expression is the mathematical statement that consist of different variables, numbers and mathematical operator. The mathematical operators are addition, subtraction, division and multiplication

The expression is

2/5 + 5/20

Cross multiply the terms in the expression

2/5 + 5/20 = (2×20) + (5×5) / (5 × 20)

Multiply the terms in the numerator and denominator

= (40 + 25) / 100

Add the terms in the numerator

= 65 /100

Simplify the terms by dividing 5 on the both numerator and denominator

= 13/20

Therefore, the simplified form is 13/20

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Using  Pythagoras triple, the side lengths 6, 9 and 12 are not the sides of a triangle

Pythagorean triples are a2+b2 = c2 where a, b and c are the three positive integers. These triples are represented as (a,b,c). Here, a is the perpendicular, b is the base and c is the hypotenuse of the right-angled triangle.

In this problem, we are going to determine is 6, 9 and 12 are Pythagoras triple.

Taking the largest number and assuming it's the hypothenuse of the triangle;

12² = 6² + 9²

144 = 117

144≠117

The side lengths 6, 9 and 12 can't form a right angle triangle.

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Answer:

an outcome

Step-by-step explanation:

All veterinarians that responded to the questionnaire were included in the sample.

Complete Question : Veterinarians often use non-steroidal anti-inflammatory drugs to treat lameness in horses. A group of veterinary researchers wanted to find out how widespread the practice was in the United States. They obtained a list of all veterinarians treating large animals, including horses. They sent questionnaires to all the veterinarians on the list. Such a survey is called a census. The response rate was 40%. Which of the following statement is correct?

a. The sample consisted of all veterinarians on the list and therefore equaled the target population.

b. The sample consisted of all veterinarians who returned the questionnaire.

c. The sample consisted of all veterinarians who treat horses with NSAIDs.

d. None of the choices are correct.

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The height of the pole will be 3m (approx.)

We have the ground located 4 m from a pole, its upper part can be seen with an elevation angle of 37°.

We can write the height of the pole as -

h = 4 tan(37°)

h = 4 x 0.75

h = 3 m (approx.)

Therefore, the height of the pole will be 3m (approx.)

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[Question in english -

From a point on the ground located 4m from a pole, its upper part can be seen with an elevation angle of 37°. What is the height of the pole?]

Therefore , the solution of the given problem of triangle comes out to be

Orthocentre (0, - 5 ).

Triangles are polygons with three sides and three vertices. The triangle's angles are created by joining its three sides end to end at a single point. The triangle has three angles, and the sum of them is 180 degrees.

Here,

We need the lengths of the triangle's three sides in order to identify which of the aforementioned cases the triangle fits into.

Make the length calculations using the distance formula.

d = [tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}[/tex]

L(0, 5) and M(3, 1)

LM =d = [tex]\sqrt{(3-0)^{2}+(1-5)^{2}}[/tex]  = 5

L(0, 5) and (N(8, 1)

LN = d = [tex]\sqrt{(8-0)^{2}+(1-5)^{2}}[/tex]   = √80

M(3, 1) and (N(8, 1)

MN = [tex]\sqrt{(8-3)^{2}+(1-1)^{2}}[/tex]  = 5

If a triangle has three sides, a, b, and c, and side c is the longest, then

• Right triangle formed by a2 + b2 = c2

• a2 + b2 c2 - acute triangle

Triangle with angles a2, b2, and c.

A, B, and C are equal to five in this instance.

a² + b² = 5² + 5² = 25 + 25 = 50

c² = (4 )² = 80

A triangle is obtuse and the orthocentre lies outside the triangle because a2 + b2 c2.

The place where the triangle's three altitudes converge is known as the orthocentre.

For the orthocentre's coordinates, we only need to simultaneously solve

the equations for two of the altitudes.

A line drawn at a right angle from a vertex to the other side is known as an altitude.

Altitude from M to LN

Calculate the slope of LN using the slope formula

m =  (y2 - y1 )/ (x2- x1 ) = 1-5/8-0   ⇒  = 2

Equation of altitude

y - 1 = 2(x - 3)

y - 1 = 2x - 6

y = 2x - 5 → (1)

Altitude between M and LN

Utilize the slope formula to determine LN's slope.

m = (y2 - y1)/ (x2- x1) = 1-5/8-0 ⇒ = 2

formula for altitude

y - 1 = 2(x - 3) (x - 3)

y - 1 = 2x - 6

y = 2x - 5 → (1) (1)

Altitude between N and LM

m = (y2 - y1)/ (x2- x1) = 1-5/3-0 ⇒ -3/4

formula for altitude

y - 1 = (x - 8) (x - 8)

y - 1 = x - 6

y = x - 5 → (2) (2)

Adding (1) to (2)

2x - 5 Equals x - 5 ( multiply through by 4 ) ( multiply through by 4 )

8x - 20 = 3x - 20

5x - 20 = - 20 ( add 20 on both sides ) ( add 20 to both sides )

5x = 0 ⇒ x = 0

Place x = 0 in place of (1)

y = 0 - 5 = - 5

It is the orthocentre (0, - 5 )

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Answer: 2x + 2

Step-by-step explanation:

The composition of two functions f and g, denoted g(f(x)), is a new function that is obtained by substituting the function f(x) into the function g(x) in place of x.

In this case, f(x) = x + 1 and g(x) = 2x. Substituting f(x) into g(x) in place of x gives us g(f(x)) = 2(x + 1) = 2x + 2.

Therefore, the final expression for g(f(x)) is 2x + 2. The coefficient of x is 2, and the constant term is 2.

Using system of linear equations he will require 20kg of 15% copper and 30kg of 70% copper to produce an alloy of 48% in 50kg

The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables.

To solve this problem, we need to write a system of linear equations and find the equivalent amount of the metal required to make the desired amount of the alloy.

0.15x + 0.7y = 0.48(50) ..eq(i)

0.15x + 0.7y = 24 ...eq(i)

x + y = 50 ...eq(ii)

solving equation (i) and (ii)

x = 20, y = 30

He needs 20kg of 15% copper and 30kg of 70% copper to get 48% of 50kg of alloy.

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David's speed in still water 2 mile per hour , using downstream and upstream concept in river .

What is downstream and upstream in river?

Downstream : Towards the river where flow ends

In this river speed get added in rowing boat speed.

Upstream : Opposite to the flow of river

In this river speed gets subtracted from rowing boat speed.

In given que , one time boat is rowed by David in upstream and got back to original place i.e. case of downstream.

Speed of river = 1mile per hour

Let speed of David = x mile per hour.

Total time taken = 4 hour

As we know time = total distance / speed

Total distance covered by David = 3+3 = 6 miles

In upstream speed = x-1

In downstream speed = x+1

So, time = 3/(x-1 )+ 3/(x+1)

            4/3 = 1/x-1  + 1/x+1

Solving this we get,

2x^2 - 3x - 2 = 0

Solution for this eq will be

x  = 2, -1/2

But speed can't be negative.

So, x= 2mile per hour.

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If a caterer made a sandwich 6feet 6inches long for a party and 3 feet 8 inches added to the sandwich The total length of the sandwich is 122 inches

The height of the sandwich = 6 feet 6 inches

Convert to the inches

We know 1 feet = 12 inches

6 feet 6 inches = 6 × 12 + 6

= 72 + 6

= 78 inches

The height added to sandwich = 3 feet 8 inches

Convert to inches

3 feet 8 inches = 3 × 12 + 8

= 36 + 8

= 44 inches

The new height of the sandwich = 78 + 44

= 122

Therefore, the final height of the sandwich is 122 inches

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Answer:

$47.25

Step-by-step explanation:

When the price goes down by 30%, you pay 70% of the original price.

When the price goes down by 10%, you pay 90% of the original price.

0.9 × 0.7 × $75 = $47.25

The probability that at least 15 in the sample are among the group of athletes who have been told by coaches to neglect their studies is approximately 0.0998.

Probability can be used to make predictions or decisions in a variety of situations, such as in gambling, finance, and science. In these situations, probabilities can be calculated based on statistical data or by using mathematical models.

To find the probability that at least 15 in the sample are among the group of athletes who have been told by coaches to neglect their studies, we can use the binomial cumulative distribution function. This is given by:

$$P(X \ge 15) = \sum_{k=15}^{50} \binom{50}{k} (0.4)^k (0.6)^{50-k}$$

We can calculate this probability using a calculator or computer, or we can approximate it using the normal distribution. To do this, we can use the continuity correction and compute:

$$P(X \ge 15) \approx P\left(\frac{X-n p}{\sqrt{n p (1-p)}} \ge \frac{15 - 50 \cdot 0.4}{\sqrt{50 \cdot 0.4 \cdot 0.6}}\right) = P(Z \ge 1.28)$$

Where $Z$ is a standard normal random variable. Using a standard normal table or calculator, we find that $P(Z \ge 1.28) \approx 0.0998$.

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On solving the provided question, we got to know that, Blenders sold as a percentage of food processors sold is 30/20, or 3/2.

Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics. From straightforward algebraic equations that just require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity.

Compared to mixers, the dealer sold twice as many food processors.

Let M be the quantity of mixers sold.

Therefore, 2M is the quantity of food processors sold.

A total of 60 of the three appliances were sold by the dealer.

M + 2M = 3M

Thus, 3M is a representation of the whole sales of mixers and food processors.

60 appliances were purchased in total, thus 60 - 3M equals the quantity of blenders purchased.

Everything was sold by the merchant for a total of $4,200.

We get: (30)(M) + (120)(2M) + (50)(60 - 3M) = 4,200

30M + 240M + 3000 - 150M = 4200

130M + 3000 = 4200

120M = 1200

M = 10

The retailer so sold 10 mixers.

This indicates that the vendor sold 20 food processors and 30 food processors.

Blenders sold as a percentage of food processors sold is 30/20, or 3/2.

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The function that provides a model for the function p(t) for the population of a city is

The given problem is solved using,  f(x) = a (b)^x

the starting = a

the base = b

the exponents = x

considering the given problem

p(t) = a (b)^t

a = 1250

rate, r = 25%

r = 25 / 100

r = 0.25

for increasing rate, b = 1 + r = 1 + 0.25 = 1.25

substituting known variables

p(t) = 1250 (1.25)^t

the equation that models the population of a city is p(t) = 1250 (1.25)^t

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