Using distributive property, factor out the GCF and rewrite 54 + 90​

The inequality is -8/3 < c < 16/3

The correct option is (a)

Given:

In the question:

The inequality is :

l3c - 4l < 12

To solve the above inequality.

Now, According to the question:

l3c - 4l < 12

Convert the absolute inequality to standard inequality.

-12 < 3c - 4 < 12

Separate compound inequalities into system of inequalities

3c - 4 > -12

3c - 4 < 12

3c - 4 > -12

3c > -12 +4

3c > -8

c > -8/3

Similarly, 3c - 4 < 12

3c < 12 + 4

3c < 16

c < 16/3

Hence, The inequality is -8/3 < c < 16/3

The correct option is (a)

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Here is the final matching of multiplication expressions with their estimated products:

(80)(30) = 2,400

(30)(6) = 180

(30)(5) = 150

(60)(4) = 240

(50)(30) = 1,500

29.3 x 5.9 ≈ 173

81.4 x 32.1 ≈ 2,618

32.9 x 4.81 ≈ 158

46.7 x 31.7 ≈ 1,479

59.3 x 3.57 ≈ 212

Match each multiplication expression on the left with the best estimate of its product on the right:

(80)(30) = 2,400

(30)(6) = 180

(30)(5) = 150

(60)(4) = 240

(50)(30) = 1,500

29.3 x 5.9

81.4 x 32.1

32.9 x 4.81

46.7 x 31.7

59.3 x 3.57

Matching the expressions with their estimated products:

(80)(30) = 2,400

(30)(6) = 180

(30)(5) = 150

(60)(4) = 240

(50)(30) = 1,500

Estimates for the remaining expressions:

29.3 x 5.9 ≈ 173.27

81.4 x 32.1 ≈ 2,612.94

32.9 x 4.81 ≈ 158.05

46.7 x 31.7 ≈ 1,480.39

59.3 x 3.57 ≈ 211.46

Matching the expressions with their estimated products:

(80)(30) = 2,400

(30)(6) = 180

(30)(5) = 150

(60)(4) = 240

(50)(30) = 1,500

29.3 x 5.9 ≈ 173.27

81.4 x 32.1 ≈ 2,612.94

32.9 x 4.81 ≈ 158.05

46.7 x 31.7 ≈ 1,480.39

59.3 x 3.57 ≈ 211.46

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Scores between 23 & 59 will give Paul a C for the semester (an average between 70 and 79).

The sum of the scores on the first three, hundred point tests

= 82 + 88 + 87 = 257.

The total score required in four 100-point tests to get an average score of 70 = 70X4= 280.

The total score required in four 100-point tests to get an average score of 79 = 79X4= 316.

Therefore, the score on the fourth test should be between (280-257) & (316-57) i.e, 23 & 59 to get an average score of 70 & 79.

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The margin of error for this survey, expressed as a proportion to the nearest thousandth, is 0.021.

To calculate the margin of error for a survey, we need to use the formula:

Margin of Error = Critical Value * Standard Error

1. The critical value is determined based on the desired level of confidence. Since we want a 95% confidence level, we need to find the critical value associated with a 95% confidence interval.

2. For a 95% confidence interval, the critical value is approximately 1.96. This value corresponds to a standard normal distribution.

3. The standard error represents the standard deviation of the sample proportion. It can be calculated using the formula:

Standard Error = sqrt[(p * (1 - p)) / n]

where p is the sample proportion (proportion of respondents who preferred Candidate A) and n is the sample size.

4. In this case, the sample proportion is 350/1750 = 0.2 (or 20% in percentage terms). The sample size is given as 1750.

5. Plugging the values into the formula, we get:

Standard Error = sqrt[(0.2 * (1 - 0.2)) / 1750] = sqrt(0.00022857) ≈ 0.015.

6. Finally, we can calculate the margin of error:

Margin of Error = 1.96 * 0.015 ≈ 0.029.

Rounding the margin of error to the nearest thousandth, we get 0.029, which is equivalent to 0.021 when expressed as a proportion without the ± symbol.

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Answer:

  71

Step-by-step explanation:

The congruency statement tells you ...

  KL = NO

  5x -3 = 4x +7

  x = 10 . . . . . . . . add 3-4x to both sides

Then that longest side is ...

  4(10)+7 = 47

Corresponding sides are the same length in both triangles. The perimeter is the sum of side lengths:

  P = 14 + 10 + 47 = 71

The perimeter of ΔKLM is 71 units.

_____

Additional comment

A triangle with these side lengths cannot exist. The short sides are too short to connect to the ends of the long side. (The long side must be between 14 and 24 units.) I suggest you talk to your teacher about this problem.

Answer:

Step-by-step explanation:

The complete question in the attached figure

we know that

When two lines are crossed by another line (transversal), a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal, are called Alternate Interior Angles.

When the two lines being crossed are Parallel Lines the Alternate Interior Angles are congruent

In this problem

---> by alternate interior angles

we have

therefore

The perimeter of the figure is 4(π + 9)ft.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

Given is a 2 - D figure as shown in the figure attached.

We can write the perimeter as -

P = P{rectangle} + P{semicircle}

P = 2(10 + 8) + (4π)

P =  (4π) + (36)

P = 4(π + 9)

Therefore, the perimeter of the figure is 4(π + 9)ft.

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Answer:

the answer is 7

Step-by-step explanation:

7+(-3)=4

7-3=4

hence shown so missing number is 7

Answer (assuming it can be put in point-slope format):

\(y + 4 = 3(x-2)\)

Step-by-step explanation:

You can write an equation of a line when knowing its slope and a line it passes through using point slope formula, \(y-y_1 = m (x-x_1)\).

1) First, find the slope of the equation. We know it has to be parallel to y = 3x + 2. Lines that are parallel have the same slope, thus the slope of y = 3x + 2 is the slope of the answer as well. y = 3x + 2 is in slope-intercept format, or \(y = mx + b\). The coefficient of the x term, or \(m\), represents the slope - so, the slope must be 3.

2) Now, use point-slope formula,\(y-y_1 = m (x-x_1)\),  to write the equation. Substitute \(m\), \(x_1\), and \(y_1\) for real values.

The \(m\) represents the slope, so substitute 3 for \(m\). The \(x_1\) and \(y_1\) represent the x and y values of a point the line crosses through. The line crosses through (2, -4), so substitute 2 for \(x_1\) and -4 for \(y_1\). This gives the following answer:

\(y - (-4) = 3 (x-(2))\\y + 4 = 3(x-2)\)

Perimeter of the parallelogram = 210 in.

Area of parallelogram = 2,484 in.²

Perimeter of parallelogram = 2(a + b), where a and b are its sides.

Area of parallelogram = (b)(h), where h is its height and b is the length of one of its bases.

Given:

a = 51 in.

b = 54 in.

h = 46 in.

Perimeter of the parallelogram = 2(54 + 51) = 210 in.

Area of parallelogram = (b)(h) = (54)(46) = 2,484 in.²

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Answer:

-15

Step-by-step explanation:

The solution of expression for x = - 4 is,

⇒ - 15

We have to given that,

An expression is,

⇒ 2x - 7

Now, We can simplify the expression for x = - 4 as,

An expression is,

⇒ 2x - 7

Plug x = - 4;

⇒ 2 × - 4 - 7

⇒ - 8 - 7

⇒ - 15

Thus, The solution of expression for x = - 4 is,

⇒ - 15

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Answer:

220.00

-185.00

= 35.00 the difference of what was paid at the same prices.

if the ratio of two sample variances exceeds the critical value of f at a defined confidence level, then the level of confidence also exceeds the critical level.

All tests that make use of the F-distribution are collectively referred to as "F Tests." The F-Test to Compare Two Variances is often what is meant when the term "F-Test" is used. However, a number of tests, including regression analysis, the Chow test, and the Scheffe test, use the f-statistic. If we are conducting an F-Test, we might employ a variety of technological tools. since doing an F-test manually while accounting for variations is a difficult and time-consuming operation.

if the ratio of two sample variances exceeds the critical value of f at a defined confidence level, then the level of confidence also exceeds the critical level.

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Answer:

3zx-15z+12x-60

Step-by-step explanation:

first do parenthesis and distribute (z+4)(x-5) into zx-5z+4x-20

then distribute the 3 to get the answer

Answer: 1000

Step-by-step explanation: since the number next to it is a seven and seven is closer to ten and ten is the first two digits of the answer. The answer is 1000.

Round the integer number 973 nearest hundred will be 1000.

The action of forming anything into a circle. Mathematics. the act of substituting a number with one that is roughly equivalent in value but has fewer digits: To the closest dollar, rounding $27.68 results in $28. a comparable procedure that identifies one of several rules.

The integer is given below.

⇒ 973

Round the number 973 nearest hundred.

If the tens place is more than 5, then the hundred places will be increased by one.

In the tens place is 7, then the number 9 is increased by one that is 10.

Round the integer number 973 nearest hundred will be 1000.

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The function g(x) = x² + 4x has a: A. minimum.

The minimum value occur at x = -2.

The function's minimum value is -4.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function g(x) = x² + 4x, we have:

a = 1, b = 4, and c = 0

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(4)/2(1)

Axis of symmetry, Xmax = -2

Next, we would determine vertex as follows;

g(x) = x² + 4x

g(-2) = -(-2)² + 4(-2)

g(-2) = -4.

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Responses

y = 8

y, = 8

y = 3

y, = 3

y=−3

y equals negative 3

y=−8

y equals negative

The rate for 7 people to work to answer the same number of calls is 10 calls per hour.

From the information, the call centre has 5 people answering calls and to answer all of the calls, each person needs to work at a rate of 14 calls per hour.

Therefore, the rate for 7 people will be:

= (14 × 5) / 7

= 70 / 7

= 10 calls per hour.

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The probability of someone ordering a fish taco at the Mexican restaurant is 0.19 or 19%.

It is a number between 0 and 1, where 0 denotes the impossibility of the event and 1 denotes its certainty.

To find the probability of someone ordering a fish taco, we need to divide the number of people who ordered fish tacos by the total number of people surveyed:

Probability of ordering a fish taco = (number of people who ordered fish tacos) / (total number of people surveyed)

= (22 + 16) / 200

= 38 / 200

= 0.19

Therefore, the probability of someone ordering a fish taco at the Mexican restaurant is 0.19 or 19%.

For example, if we toss a fair coin, the probability of getting heads is 0.5, since there are two equally likely outcomes (heads and tails) and only one of them will occur.

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1.

6x - 16 = 14x + 8

the question above can be solved by simply collecting like terms and solve for x

step 1

collect like terms by carrying 6x to the right hand side and taking 8 to the left hand side

however, note that the sign changes when they cross equality sign

proceed to divide both sides by 8 to solve for x

2.

9y + 21 = 3y - 5

step 1

collect like terms

step 2

divide both sides by 6

3

5n + 7 + 3n = -8 + 3n

step 1

4

6d - 1 = -d + 20

5

3b + 8 - 5b = 2(4 - b)

step 1

open the bracket on the right hand side and collect like terms

6

-11 - 2p = 6p + 5(p + 3)

-11 - 2p = 6p + 5p + 15

10

h + 3(h - 2) = 2(2h -3)

step 1

simplify by opening the bracket

7

7w - 3(

The values of a, h and k for the function include the following:

a = 2

h = 3

k = -2

In Mathematics and Geometry, the general form of a logarithm function is represented by the following mathematical equation:

f(x) = alog(±x + h) + k

Where:

Based on the given logarithm function f(x) = 2log₄(x + 3) - 2, we can reasonably infer and logically deduce that the scale factor (a) used is equal to 2.

This ultimately implies that, the values of a, h and k for the function are 2, 3, and -2 respectively.

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On the given statement, the transitive property is applicable. Thus option A is correct option.

According to the statement

we have to find that the which statements are true in the form of given statement.

So, For this purpose, we know that the

A property is called transitive property, if x, y and z are the three quantities, and if x is related to y by some rule, and y is related to z by the same rule, then we can say x is related to z by the same rule.

And the given equation is

x=y and y = z

from this it is clear that the x= z.

then transitive property is perfect for this.

So, On the given statement, the transitive property is applicable. Thus option A is correct option.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

If x=y and y = z, which statement must be true

A. Transitive property applicable here

B . Associative property applicable here

C . Distributive property applicable here

D . Identity property applicable here

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\(\huge{ \mathfrak{  \underline{ Answer }\:  \:  ✓ }}\)

The given triangle is a right angled triangle,

therefore, by using trigonometry :

\( \boxed{ \cos(45) = \frac{6}{x} }\)

_____________________________

\(\mathrm{ ☠ \: TeeNForeveR \:☠ }\)

The amount (present value at age 60) that Sandro would neet in his retirement savings account in order to have a monthly income of $1,500 until he is 90 years old, compounded at 4.5% monthly is $296,041.74.

The present value is computed using an online fiance calculator that discounts the future withdrawals (monthly income) for a 360-months period.

End of withdrawal period = 90 years old

Beginning of withdrawal period = 60 years old

The number of years between 60 and 90 = 30 years

N (# of periods) = 360 months (30 years x 12)

I/Y (Interest per year) = 4.5%

PMT (Periodic Payment) = $-1,500

FV (Future Value) = $0

Results:

Present Value (PV) = $296,041.74

Sum of all periodic payments = $540,000 ($1,500 x 360 months)

Total Interest = $243,958.26

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Answer: It's a 80% increase

Step-by-step explanation:

ANSWER:

     43

Explanation:

A : B : C

     4 : 3  

          5 : 2

A × B → 4 × 5 = 20

B × B → 3 × 5 = 15

B × C → 3 × 2 = 6

  A : B : C

 20 : 15 : 6

B = 15 = 30

what of teams A and C together?

 If 15 = 30games, what about 26games?

Cross multiply.

   15 × 26          =13

      30

So, games won by Team B + games won by Teams A and C

        30games + 13games

               =43games.

Answer:

82

Step-by-step explanation:

The -2/5 means we go to the left 2/5 of a full unit. So we take 2 small little steps (going over 2 little tickmarks), then we move 4 small steps to the right due to the +4/5 portion. Ultimately, we end up at 2/5 as the answer

So -2/5 + 4/5 = 2/5

This can be thought of as -2+4 = 2, then you just stick 5 in the denominator for each term.