John went to the market. He had $30.00. He purchased apples for $1.29, oranges for $2.50, and milk for $2.99. What was his total?

Answer:

13 square feet × 7 feet = 91 cubic feet

Answer:

y = 2h + x

Step-by-step explanation:

Let x and y represent the different lengths of the legs, instead of b1 and b2.

The average length of the trapezoid is

x + y

---------

    2

and so the area is

x + y

--------- * h

    2

We are to solve this formula for y (which you have called b 2).

Multiplying both sides by yields x + y = 2h, and so

y = 2h + x

The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

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The area enclosed by the curves f(x) and g(x) is  1/12

Integral calculus can be used to compute the area between two curves, which is the region between two intersecting curves.

When we are aware of the equation for two curves and the locations of their intersections, integration can be utilized to determine the area under the curves.

Let our given curves be :

f(x) = x² and g(x) = x³ within the interval [0,1]

Formula to calculate area under these curves is

=> A = \(\int\limits^{c}_{a} {|f(x) - g(x)| \, dx\)

Interval is given from 0 to 1

Therefore ,

=> A = \(\int\limits^{1}_{0} {[x^2 - x^3]} \, dx\)

Integrating,

=> \([\frac{x^3}{3} - \frac{x^4}{4}]^{1}_{0}\)

=> 1/3 - 1/4

=> 1/12 is required area

The given question is incomplete So, I've answered the question in general

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A study based on a population sample that includes 2000 respondents would be the most reliable out of the given options.

In statistical analysis, the reliability of a study depends on the representativeness and size of the sample.

A larger sample size generally provides more reliable results as it reduces the sampling error and increases the precision of the estimates.

Given that the population contains 20,000 people, we need to consider which number of respondents would yield the most reliable study.

Option A: 200 respondents

This represents only 1% of the population.

While it is better than having just 2 respondents, it may not be sufficient to accurately capture the characteristics of the entire population.

Option B: 20 respondents

This represents only 0.1% of the population.

With such a small sample size, the study would likely suffer from a high sampling error and may not provide reliable results.

Option C: 2000 respondents

This represents 10% of the population.

While it is a larger sample size compared to the previous options, it still only captures a fraction of the population.

The study may provide reasonably reliable results, but there is room for potential sampling error.

Option D: 2 respondents

This represents an extremely small sample size, accounting for only 0.01% of the population.

With such a small sample, the study would be highly susceptible to sampling bias and would likely yield unreliable results.

Based on the options provided, option C with 2000 respondents would be the most reliable study.

Although it does not include the entire population, a sample size of 2000 respondents provides a larger representation of the population and reduces the potential for sampling error.

However, it's important to note that the reliability of a study depends not only on sample size but also on the sampling method, data collection techniques, and other factors that ensure representativeness.

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Answer: the correct answer is No, her exponent should be a negative value

Step-by-step explanation:

Answer:

C) No, her exponent should be a negative value

Step-by-step explanation:

Got it right on the assignment EDGE 2022

Answer:

A = (1/4)√(4 + 11 + 14)√(-4 + 11 + 14)√(4 - 11 + 14)√(4 + 11 - 14)

A = (1/4)√29√21√7

= about 16.32 mm²

Answer:

  16.27 mm²  (see comment)

Step-by-step explanation:

You want the area of a triangle with side lengths 11 mm and 14 mm, and the angle between them 12.2°.

The area is given by the formula ...

  A = 1/2ab·sin(C)

  A = 1/2(11 mm)(14 mm)·sin(12.2°) ≈ 16.27 mm²

The area of the triangle is about 16.27 square millimeters.

__

Additional comment

If you use Heron's formula for the area from the three side lengths, you find it is about 16.32 mm². That's the trouble with over-specified geometrical figures. The result you get depends on which of the given values you use. (To get the area accurate to 4 sf, the angle needs to be specified to 4 sf: 12.24°.)

  s = (4 +11 +14)/2 = 14.5

  A = √(s(s -a)(s -b)(s -c))

  A = √(14.5(14.5 -4)(14.5 -11)(14.5 -14)) = √(14.5·10.5·3.5·0.5) = √266.4375

  A ≈ 16.32

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1/10 to get your answer

10÷100=

0.1=1/10

Answer:

The cost per pound of the ham is $5.89.

Step-by-step explanation:

Given that a 4kg ham cost $13/kg, in order to find the cost per pound the following calculation has to be made:

1 kg = 2.20462 pounds

2.20462 = 13

1 = X

((1 x 13) / 2.20462) = X

13 / 2.20462 = X

5.89 = X

Therefore, the cost per pound of the ham is $5.89.

Answer:

We are given that The valve was tested on 150 engines and the mean pressure was 7.7 lbs/square inch.

We are also given that the valve was designed to produce a mean pressure of 7.6 lbs/square inch

So,  

Null hypothesis:  

Alternate hypothesis :  

Since n > 30 and population standard deviation is given

So, We will use z test

Formula :  

Substitute the values

refer the z table for p value

so, p value is 0.9927

Since it is a two tailed test So, p = 2(1-  0.9927) = 0.0146

α = 0.1

p value< α

So, we reject null hypothesis

Hence There is  sufficient evidence at the 0.1 level that the valve does not perform to the specifications

Step-by-step explanation:

No, there is insufficient evidence at the 0.02 level that the valve does not perform to the specifications.

Step-by-step explanation:

We are given that an engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 170 engines and the mean pressure was 7.5 pounds/square inch (psi). Assume the population variance is 0.36 and the valve was designed to produce a mean pressure of 7.4 psi.

We have to test if there sufficient evidence at the 0.02 level that the valve does not perform to the specifications.

Let, NULL HYPOTHESIS, H_0H

0

: \muμ = 7.4 psi {means that the valve perform to the specifications}

ALTERNATE HYPOTHESIS, H_1H

1

: \mu\neqμ



= 7.4 psi {means that the valve does not perform to the specifications}

The test statistics that will be used here is One-sample z-test;

T.S. = \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }

n

σ

X

ˉ

−μ

~ N(0,1)

where, \bar X

X

ˉ

= sample mean pressure = 7.5 psi

\sigmaσ = population standard deviation = \sqrt{Variance}

Variance

= \sqrt{0.36}

0.36

= 0.6

n = sample of engines = 170

So, test statistics = \frac{7.5-7.4}{\frac{0.6}{\sqrt{170} } }

170

0.6

7.5−7.4

= 2.173

Now, at 0.02 significance level z table gives critical value of 2.3263. Since our test statistics is less than the critical value of z so we have insufficient evidence to reject null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the valve perform to the specifications and there is not sufficient evidence at the 0.02 level that the valve does not perform to the specifications.

Answer:

\( \tt \: true\)

Step-by-step explanation:

\(The \: ordered \: pair \: (1, \: 0) \: is \: a \: solution \: to \: the \: inequality \: y.\)

Answer:

52.5 inch square

Step-by-step explanation:

Area of pentagon: A = 1/2 × p × a;

where 'p' is the perimeter of the pentagon and 'a' is the apothem of the pentagon.

A = 1/2 x (6 x 5) x 3.5 = 1/2 x 30 x 3.5 = 15 x 3.5 = 52.5

The area of the regular pentagon with apothem 3.5 and side 6 is 52.5

In Mathematics, a pentagon is a polygon with 5 sides. A pentagon can be classified as a regular pentagon and irregular pentagon. When all the sides and the angles of a pentagon are of equal measure, then it is called a regular pentagon.

Given the question, we need to find the area of the regular pentagon with apothem 3.5 and side 6.

In order to find the area, the formula to calculate the area of the regular pentagon is given by:

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)

Now,

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times s \times a\)

\(\text{Area of pentagon} =\sf \huge \text(\dfrac{5}{2}\huge \text) \times 6 \times 3.5\)

\(\text{Area of pentagon} =52.5\)

Therefore, the area of the regular pentagon with apothem 3.5 and side 6 is 52.5

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Answer:

Step-by-step explanation

Okay so lets solve step by step/

15% can be written as a  fraction: 15/100

The of in the equation means multiplying.

15/100= 3/20

3/20*9= 270/20

27/2 is answer

Answer: 84 seconds

Step-by-step explanation:

The vertex of the parabola is located at the point \((-b/2a, c - b^2/4a).\)

The equation of a parabola can be written in standard form as:

\(y = ax^2 + bx + c\)

where 'a' is the coefficient of the squared term, 'b' is the coefficient of the linear term, and 'c' is the y-intercept.

If we want the y-intercept to appear as a constant, we can rearrange the standard form to get:

\(y - c = ax^2 + bx\)

where 'c' is the y-intercept. This form is known as the vertex form of the parabola.

We can further manipulate the equation to obtain the vertex coordinates of the parabola. To do this, we complete the square by adding and subtracting \((b/2a)^2\) inside the parentheses:

\(y - c = a(x^2 + (b/2a)x + (b/2a)^2 - (b/2a)^2)y - c = a(x + b/2a)^2 - a(b/2a)^2y - c = a(x + b/2a)^2 - (b^2/4a)\)

The vertex of the parabola is located at the point \((-b/2a, c - b^2/4a).\)

In summary, if we want the y-intercept to appear as a constant, we can use the vertex form of the parabola, which can be obtained by manipulating the standard form. The vertex form can be useful for quickly identifying the vertex coordinates of the parabola.

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Answer:

(7,0)

Step-by-step explanation:

By Multiplying 4 and 7 (aka x), it will equal 28.

Multiplying 9 and y, (aka 0) , it will equal to 0

4(7)+9(0)=28

multiplying -4 by 7 will equal to -28 ,minus y which is 0, total will be -28

[~S & (R V S)] ≡ (Q ⊃ S) is true when A = T, S = F, R = F, and Q = T by substituting the propositional variables.

A truth table is a table used to determine the truth values of a compound proposition, which is a logical statement made up of simpler propositions using logical operators such as "and" (represented by "&"), "or" (represented by "V"), "not" (represented by "~"), conditional (represented by "⊃"), and biconditional (represented by "≡").

Let's substitute the given truth values for the propositional variables in the given statement:

[~F & (F V F)] ≡ (T ⊃ F)

Using the truth table for conjunction (represented by "&") and disjunction (represented by "V"), we can simplify the left-hand side of the equivalence:

[T & F] ≡ (T ⊃ F)

Using the truth table for conditional (represented by "⊃"), we can simplify the right-hand side of the equivalence:

F ≡ F

Since both sides of the equivalence have the same truth value, the statement is true.

Therefore, [~S & (R V S)] ≡ (Q ⊃ S) is true when A = T, S = F, R = F, and Q = T.

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Answer:

the last one

Step-by-step explanation:

there is no rhythm

Answer:

91in^2

Step-by-step explanation:

SA of base =  7x7 = 49in^2

SA of each triangle = 1/2 x 7 x 3 = 10.5in^2

SA of all 4 triangles = 10.5 x 4 = 42in^2

SA Total = 49 + 42.= 91inch^2

Jack and Jill went for a walk separately. Jack’s total distance in blocks, x, was thirty blocks fewer than twice Jill’s total distance in blocks, y. The difference between five times Jack’s total distance and twice Jill’s total distance is ten blocks. 10 blocks did Jack and Jill each walk. This can be solved by solving equations.

An equation is an algebraic statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 6x + 11 = 14, for instance, the two expressions 6x + 11 and 14 are separated by the symbol "equal (=)"

x= 2y -30 ............. (1)

5x-2y=10 ............. (2)

substitute x= 2y-30 into the 2nd equation

or, 5(2y-30)-2y = 10

or, 10y-150-2y=10

or, 10y -150-2y= 10

or, 8y-150=10

After adding 150 on both sides we get:

or, 8y = 160

so, y = 20  

substitute y=20 into x = 2y-30

so, x = 40-30

so x = 10 & y = 20

thus, 10 blocks did Jack and Jill each walk.

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Answer:

-8(-x-5)-2 = -2 (x+1)

8x + 40 -2 = -2x -2

8x + 2x = -2 -40 +2

10x = -40

x = -40/10

x = -4

The measure of the minor arc m∡rv = 111°

Recall that according to the principle of angle of intersecting secants, (a-b)/2 = c

Where a = ∡RV
b = ∡SU = 37°:

and c = ∠T (the angle between intersecting secants.

Thus, if (a-b)/2 = c, and b = c = 37 degrees, then we can substitute these values into the equation to get:

(a - 37) / 2 = 37

Multiplying both sides by 2 gives:

a - 37 = 74

Adding 37 to both sides gives:

a = 111

Therefore, a is equal to  m∡rv = 111°.

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Answer:

x=30o+n90on∈Z

Step-by-step explanation:

cos2x=sin(90o−2x)=sin(2x−30o)

Which mean 90o−2x=2x−30o+n360o

or 90o−2x+2x−30o=(2n+1)180o

The later cannot be true.

so x=30o+n90on∈Z

\(▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ { \huge \mathfrak{Answer}}▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ \)

The value of tan x is :

solution is in attachment !

If Athlete J continues at that speed, it will take 12 minutes to run 1 mile

It will take Athlete J 60 minutes to run 5miles

Since the speed of Athlete H is greater than that of J, hence Athlete H runs faster.

The formula for calculating the speed of the athlete is expressed as:

Speed = Distance/Time

1) If Athlete J runs 2/3 of a mile in 8 minutes, this can be expressed as:

2/3 miles = 8 minutes

If the athlete runs for 1 mile, then;

1 mile = x

Divide both expressions

2/3 = 8/x

2x = 24

x = 12 minutes

Hence If Athlete J continues at that speed, it will take 12 minutes to run 1 mile

2) if athlete J run 5 miles, the time taken will be expressed as;

2/3(5) = 8/x

2/15 = 8/x

2x = 120

x = 60minutes

Hence it will take Athlete J 60 minutes to run 5miles

3) If Athlete H runs 2 3/4 miles in 1/2 hour, then the speed of athlete H will be expressed as:

Speed = (2 3/4)/0.5

Speed = 2.75/0.5

Speed = 5.5miles/hr

For Athlete J;

Speed = 5/1

Speed = 5 miles/hr

Since the speed of Athlete H is greater than that of J, hence Athlete H runs faster.

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