If 30% of a number is 42 and 70% of the same number is 98, find 40% of that number.

Newington's budget in the "previous year" is $119.2 million

The term "budget" refers to a financial plan for a given period that outlines expected expenses and revenues. The previous year's budget for Newington is the financial plan that the town had for the previous fiscal year.

Assuming the previous year's budget refers to the fiscal year that ended just before the current fiscal year, we can find the amount by looking at the town's financial statements for that period. These statements will show the town's revenues and expenses for that fiscal year, and the difference between the two will be the budget.

If the town had $100 million in revenues and $95 million in expenses in the previous fiscal year, then the budget for that year would be $5 million. This means that the proposed $124.2 million budget for the upcoming year is a 4.7% increase from the $119.2 million budget of the previous year.

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Answer:

I believe Edgar payed $84 for the tickets.

Step-by-step explanation:

12(4)=48

6(6)=36

48+36=84

The final result is: 30x^3 - 6x^2 + 15x^2 - 3x + 40x - 8 = 30x^3 + 9x^2 + 40x - 8

The box method, also known as the FOIL method, is a way of multiplying two polynomials by using the distributive property.

Given the expression (5x - 1)(6x^2 + 3x + 8), we can use the box method to multiply the terms as follows:

Therefore., the final result is:

30x^3 - 6x^2 + 15x^2 - 3x + 40x - 8 = 30x^3 + 9x^2 + 40x - 8

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Answer: 44, -14, 4

Step-by-step explanation:

plug the f(x) into the x and solve itself.

(5)^2 + 3(5) + 4 = 44

(-3)^2 + 3(-3) + 4 = -14

(0)^2 + 3(0) + 4 = 4

The algebraic expression G x C, where G represents the total number of gallons needed and C represents the cost per gallon.

In mathematics, an expression is a combination of one or more numbers, variables, and/or operators that represent a quantity or a mathematical relationship.

To calculate the total cost of gasoline, we first need to determine how many gallons of gasoline will be needed for the entire trip. This can be done by dividing the total distance traveled by the car's miles per gallon (MPG) rating. Let's use "G" to represent the total number of gallons needed.

G = Total Distance Traveled / MPG

To find the total cost of gasoline, we can multiply the number of gallons needed by the cost per gallon. Let's use "T" to represent the total cost of gasoline.

T = G x C

Using the expression we developed earlier, we can now find the total cost of gasoline for the full-size car:

=> T = G x C

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Complete Question:

Four friends plan to rent a car to go on a camping trip. They will drive a total of 450 miles. The cost of gasoline is $2.20 per gallon Type of Car SUV Full size Compact Rental Cost $283 $215 $183 Insurance Cost $120 $108 $95 Miles per Gallon 24 25 33 Total Gas Cost $ $ $ Cost per Person.

Write an algebraic expression for the total cost of the gasoline.

Answer:

hope this helps!

Step-by-step explanation:

Answer:

150

Step-by-step explanation:

5/6= ?/180

We can use cross-products to solve.

5 * 180 = 6 * ?

Divide each side by 6.

5 * 180/6 = ?

5 * 30 = ?

150

The missing number is 150.

Answer:

150/180

Step-by-step explanation:

Solution by Cross Multiplication;

The equation:

[tex]\frac{5}{6} = \frac{x}{180}[/tex]

The cross-product is:  

5(180)  =  6(x)

Solving for x:

x = [tex]\frac{5(180)}{6} \\[/tex]

x = 150

In all, Cameron removed 6 tiles (3 consonant vowels and 4 vowel consonants). Take that amount, 6, then divide it by the 24 vowels in total. 24/6=4. It provides you four. Then you multiply that number, 4, by the number of consonant vowels he removed, which is 3, for a total of 6, or 4*2. your response is six vowels.

The five distinct vowel letters are A, E, I, O, and U. The English language has vowels in practically every word and phrase, making them incredibly prevalent. Any letter of the alphabet that isn't a vowel is referred to as a consonant (a, e, i, o, u).All of the non-vowel sounds in the English alphabet are consonants. Vowels, the loud sounds that make up each syllable's core and are separated by consonants. Letters A and O stand in for vowels, whereas B, C, D, F, J, K, M, N, P, Q, S, T, V, X, and Z stand in for consonants.

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Answer:

Below

Step-by-step explanation:

 strawberries to plums  9:1       then total would be 10 parts  of which 1 is plums    so    1 : 10

In the illustration given above, the length and the diameter of the shaft would be = 21.8 in and 7/8 in respectively.

The total length of the shaft can be calculated through the addition of the various given lengths along the shaft such as follows:

= 5⅛ + 5 + 7⅝ + 4 1/16

First convert all the mixed fraction into single fraction;

= 41/8 + 5/1 + 61/8 + 65/16

= 82+80+122+65/16

= 349/16

= 21.8 in.

The diameter of the shaft can be calculated as follows;

= 7¼ - (3 3/16 + 3 3/16 )

First convert all the mixed fraction into single fraction;

= 29/4 - (51/16 + 51/16)

= 29/4 - 102/16

= 116-102/16

= 14/16

= 7/8 in.

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Is that all of the question?

The lower and upper bounds of the given confidence interval of 95% with sample size= 1,555 , sample mean = 2.938 and standard deviation 2.837 is equal to ( 2.797 , 3.079 ).

Upper and lower bounds of the confidence interval is :

= Sample mean ± Margin of error

And Margin of error is :

=  Z-critical × ( σ/√(n ) )

Standard deviation 'σ ' = 2.837

Sample size 'n' = 1,555

Sample mean 'μ' = 2.938

Z-critical for 95% confidence interval

= Zα/2

= 1.96

Margin of error

= 1.96 × (2.837/√1,555)

= 1.96 × (2.837/ 39.43 )

= 0.1410

Confidence interval:

Upper boundary

= 2.938 + 0.1410

= 3.079

Lower boundary

= 2.938 - 0.1410

= 2.797

Therefore, for the given confidence interval of 95% the lower and upper bounds of the interval are ( 2.797 , 3.079 ).

The above question is incomplete , the complete question is:

find the 95% confidence interval for the mean number of hours of tv watched each day by adults in the us. report the upper and lower bounds of the interval:

Sample size      Sample mean      Standard deviation

1,555                  2.938                    2.837

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The expression used to calculate the sale price is given as follows:

S(p) = 0.65p.

The expression used to calculate the sale price is obtained applying the proportions in the context of the problem.

The price was 35% off, meaning that there was a discount of 35%, meaning that a percentage of 100 - 35 = 65% of the total price was paid, hence the expression used to calculate the sale price is given as follows:

S(p) = 0.65p.

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Answer:

just 150x2 = 300 minutes or just 150 minutes to cook

Step-by-step explanation:

The cooking time of a turkey depends on its weight, so a 16-pound turkey will take longer to cook than an 8-pound turkey. However, without additional information such as the cooking method, temperature, and the shape and size of the turkeys, it's not possible to determine the exact cooking time for the 16-pound turkey.

The measurement of the angle 1 in the given parallel lines is 35° whereas the value of x is 15.

Parallel lines are those straight lines that are always the same distance apart from each other.

Given that, two lines RS and TU are parallel, and ∠ 7 = 3x-10 and ∠ 3 = 2x+5,

We need to find ∠ 1

Since, ∠ 7 and ∠ 3 are corresponding angles between two parallel lines therefore, both are congruent,

Therefore,

3x-10 = 2x+5

x = 15

Now, ∠ 1 = ∠ 3 as they are vertically opposite angles,

Therefore,

∠ 1 = 2(15)+5

∠ 1 = 35°

Hence, the measurement of the angle 1 in the given parallel lines is 35° whereas the value of x is 15.

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The figure was not given so the figure is attached.

Answer: 38 degrees

Step-by-step explanation:

HZJ and FZG are congruent angles so then that means that they are the same 38 degrees.

On solving the provided question, we can say that by fractions,  the space from the edge of the wall to the picture = 17/4*1/2 = 17/8

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

Simply subtract the length of the image from the length of the wall to get the total area below and above the picture from the edge of the wall. So.

[tex]14\frac{1}{2} - 10\frac{1}{4}[/tex]

29/2 - 41/2

17/2

the space from the edge of the wall to the picture = 17/4*1/2 = 17/8

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In the given case the set of 56 students who returned surveys is an example of a sample

A sample would be the 56 students who responded to the surveys. A sample is a portion of the population that is chosen for a study in research. American college students would be the population in this scenario. The 56 students who returned the surveys were chosen at random for the sample by the researcher.

The researcher is attempting to guarantee that the sample is representative of the greater population of American college students by utilising a random selection process. The researcher discovered that these students spend an average of 4.1 hours per week working on course material outside of class based on the data collected from the sample. This is an example of a descriptive statistic that provides a summary of the information gleaned from the sample.

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Step-by-step explanation:

the zeros are the x-intercepts. because these are x values, when y (= f(x)) = 0.

a quadratic equation has 2 zeros (even if they are equal or complex numbers).

a quadratic equation

ax² + bx + c = 0

can always be solved by

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (-14 ± sqrt(14² - 4×2×20))/(2×2) =

= (-14 ± sqrt(196 - 160))/4 =

= (-14 ± sqrt(36))/4 = (-14 ± 6)/4

x1 = (-14 + 6)/4 = -8/4 = -2

x2 = (-14 - 6)/4 = -20/4 = -5

these are the 2 zeros (x-intercepts).

if you need the explicit points :

(-5, 0) and (-2, 0)

the y-intercept is the y-value when x = 0

y = 2×0² + 14×0 + 20 = 20

the explicit point : (0, 20)

15 ounces of herbs should be mixed to produce a mixture of costing $2.50 per ounce.

What is meant by addition?

In mathematics, addition is the process of fusing two or more integers. The numbers being added are known as addends, while the outcome of the addition process, or the final response, is known as the sum. It is one of the fundamental mathematical operations we employ on a daily basis. We add numbers in many different contexts.

Given that, an herbalist has 15 ounces of herbs costing $3 per ounce.

Let the ounces of herbs costing $2 per ounce that should be added to the above herbs be 'x'

Cost of total mixture is 15*3 + x*2 = (x+15)*2.5

15*(3-2.5) = x*(2.5-2)

15*0.5 = x*0.5

x = 15

Therefore, 15 oz of herbs for $2 should be added.

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The barn with shadow height, 70 feet, having the the height which is equals to the 30 feet, that is barn is 30 feet tall.

The height of farmer Cole = 6 feet

The height of shadow of farmer Cole = 14 feet

The height of shadow of barn = 70 feet

Let the height of barn be ' x feet '. We have to determine the value of x. Now, we the above figure, AB and CD represents height of barn and Cole respectively. Similarly BE and CE represent the shadow height of barn and Cole respectively.

Let angle BAE made here be equals to θ. Also angle BAE = angle CDE = θ. Now, consider right angled triangle, CDE with sides. Using triganomertric functions, tanθ = height/base

=> tanθ = CE/CD = 14/6

simplify, tanθ = 7/3 --(1)

Also, consider right angled triangle ABE,

tanθ = height/base = BE/AB

=> tanθ = 70 / x

=> x tanθ = 70

from equation (1), x (7/3) = 70

=> 7x/3 = 70

=> 7x = 210

=> x = 210/7

=> x = 30

Hence, required value of x is 30 feet.

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There is no real solution to the given equation s = 4 + sqrt(s+2) with value of s = 2, s = 7, s = 2 or s = 7.

To solve the equation:

s = 4 + sqrt(s+2)

We can start by isolating the square root term on one side:

s - 4 = sqrt(s+2)

Then, we can square both sides to eliminate the square root:

(s - 4)^2 = s + 2

Expanding the left side:

s^2 - 8s + 16 = s + 2

Bringing all terms to one side:

s^2 - 9s + 14 = 0

We can solve for s using the quadratic formula:

s = (9 ± sqrt(9^2 - 4(1)(14))) / 2(1)

s = (9 ± sqrt(49)) / 2

s = (9 ± 7) / 2

So the two possible solutions are:

s = 8/2 = 4

s = 2/2 = 1

However, we need to check if these solutions satisfy the original equation.

If we plug s=4 into the equation, we get:

4 = 4 + sqrt(4+2)

4 = 4 + sqrt(6)

This is not true, since the right-hand side is greater than the left-hand side.

If we plug s=1 into the equation, we get:

1 = 4 + sqrt(1+2)

1 = 4 + sqrt(3)

This is also not true.

Therefore, there is no real solution to the equation s = 4 + sqrt(s+2).

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Answer:

B

Step-by-step explanation:

The statement "the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring." is false.

What is meant by probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

The given statement is:

"the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring."

This is a false statement.

The probability of the union of two events is the probability of individual events without considering the probability of the intersection of the events.

When the events do not have an intersection, then the probability of a union of events is greater than the probability of an intersection of events.

The chance of both occurrences occurring together is given by the union of two events, but the probability of both events occurring simultaneously is given by the intersection of two events, which is smaller than probability of union of events.

Therefore the statement "the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring." is false.

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The area of the shaded region in each of the following figures are the same, that is, 94.5cm²

(i) Area of the shaded region in the first figure:

= (Area of the square with side 21m) - (Area of the circle with diameter 21m)

we know the diameter of the circle is 21 cm, therefore we can say that the radius of the circle is 10.5 cm

we need to find the area of the shaded region = (21 × 21)

([tex]\frac{22}{7}[/tex]×[tex]\frac{21}{2}[/tex]×[tex]\frac{21}{2}[/tex]) cm² = 441 - 346.5

= 94.5cm²

(ii) Area of the shaded region in the second figure:

(Area of the square with side 21 cm) - (4×Area of the sector)

= (21 - 21) - (4×[tex]\frac{90}{360}[/tex]×[tex]\frac{22}{7}[/tex]×[tex]\frac{21}{2}[/tex]×[tex]\frac{21}{2}[/tex])

(21 - 21) = (4 - [tex]\frac{1}{4}[/tex]×[tex]\frac{22}{7}[/tex]×[tex]\frac{21}{2}[/tex]×[tex]\frac{21}{2}[/tex])

= (441−346.5) cm²

=94.5 cm²

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The number of choices for all the possible passwords are 43,056,000

Given, we have to make a password which includes 4 characters and 4 even digits. And none of the characters or digits can be used more than once. So, For the first character we have 26 choices as we can use any character from the alphabet. For the 2nd character we get 25 choices as we cant choose the first character already twice. Similarly, for 3rd character we get 24 choices and for 4th character we get 23 choices.

Now for the digits, we can only use even digits 0,2,4,6,8 with no repetition allowed. Therefore, for first digit we can choose any digit so we get 5 choices. For the 2nd digit we get 4 choices. For the 3rd digit we get 3 choices. For the 4th digit we get 2 choices.

Noe, to find all the possible combinations , we just need to multiply all the choices :

⇒ 26 x 25 x 24 x 23 x 5 x 4 x 3 x 2

⇒ 43,056,000

Therefore, the total number of all the possible combination of passwords according to the given condition is 43,056,000.

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you do not give the answer choice in this picture, but I assume it is along the lines of this

The scatter plot shows a negative association between variable X and Y

The measures of angle possible for of an isosceles triangle when one angle given is 140° then other two angles is 20°.

In an isosceles triangle, two of the angles have the same measure. Let's call this measure x. Since the sum of the angles of a triangle is 180 degrees, we can set up an equation:

x + x + 140° = 180°

Simplifying the equation, we get:

2x + 140° = 180°

Subtracting 140° from both sides, we get:

2x = 40°

Dividing both sides by 2, we get:

x = 20°

So the other two angles in the isosceles triangle each measure:

x = 20°

Therefore, the measures 28°, 22°, 26° are not possible for the other two angles of the isosceles triangle, but the measure 20° degrees is possible.

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The angle that completes the law of cosines is 62°.

Option D is the correct answer.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

The law of cosines in a triangle states that,

c² = a² + b² - 2ab cos C

Where c is the side opposite to ∠C.

Similarly,

a² = b² + c² - 2bc cos A

b² = a² + c² - 2ac cos B

Now,

289 + 64 - 272 cos __ = 15²

17² + 8² - 2 x 17 x 8 cos 62 = 15²

289 + 64 - 272 cos 62 = 15²

Thus,

The angle that completes the law of cosines is 62°.

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The complete question.

289 + 64 - 272 cos __ = 15²

Answer:

  ±1.007%

Step-by-step explanation:

You want the relative error in the computed value of 1/P -1/Q when P=1.80 and Q=2.91.

Each of P and Q is specified to the hundredths place, so the errors in each of P and Q will be half of a hundredth, or 0.005. The maximum value of P or Q will be 0.005 more than the given value, and the minimum will be 0.005 less.

The maximum and minimum of the computation will be had when P and Q are at their opposite extremes: one is a maximum when the other is a minimum.

Max difference = 1/1.795 -1/2.915 ≈ 0.21404

Min difference = 1/1.805 -1/2.905 ≈ 0.20978

The relative error in the computed value can be found a couple of ways. One is to compare the maximum and minimum computed values with the nominal computed value.

Here, we choose to compare half the difference in the computed values to the average of the computed values. That way, we can describe the error as symmetrical about that average;

  ((0.21404 -0.20978)/2) / ((0.21404 +0.20978)/2) = relative error

  = (0.21404 -0.20978) / (0.21404 +0.20978) ≈ 0.01007

The relative error is about ±1.007%.

__

Additional comment

Another way to compute the error is by looking at the derivatives. The relative error found that way is ...

  RE = -∆P(Q/P(Q -P)) +∆Q(P/Q(Q -P))

where ∆P and ∆Q are ±0.005.

The maximum relative error found this way is about ±1.00686% compared to the ±1.00685% computed above.

If you compare the possible error to the nominal value, it is not symmetrical: -1.00532% to 1.00841%.

Looking at the above expression for RE, you see that the multiplier of the relative error in P is Q/(Q-P), while the multiplier of the relative error in Q is P/(Q-P). That is, errors in P have a much larger effect than errors in Q.