equation [tex] - 3 - 4x \leqslant 21.[/tex]solve..........

The mixed fraction 4 3/8 + 7 3/4 is equivalent to the fraction to 12 1/8

An equation shows the relationship between two or more numbers and variables.

The mixed fraction 4 3/8 is equivalent to the fraction (4 * 8 + 3)/8 = 35/8

The mixed fraction 7 3/4 is equivalent to the fraction (4 * 7 + 3)/4 = 31/4

Hence:

4 3/8 + 7 3/4

Substituting:

= 35/8 + 31/4

Simplifying:

= 97/8 = 12 1/8

4 3/8 + 7 3/4 is equal to 12 1/8

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From the given table, it is found that:

1. The linear regression equation is: y = 16.96x + 3.

2. The meaning of the slope is that he hiked an average of 16.96 miles a day.

3. In 52 days, Sean had hiked 885 miles.

4. In 22 days, Sean had hiked 377 miles.

To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.

In the context of this problem, the points are given as follows:

(0,0), (19,308), (34, 578), (67, 1070), (91, 1715), (112, 1902), (134, 2200).

Using a calculator, the equation is given as follows:

y = 16.96x + 3.

The input of the function and the output of the function are given as follows:

The slope is the rate of change, that is, change in the output divided by change in the input. Hence the slope of 16.96 means that he hiked an average of 16.96 miles a day.

In 52 days, the number of miles hiked is:

y = 16.96(52) + 3 = 885 miles.

The number of days is took to hike 377 miles is found as follows:

377 = 16.96x + 3

x = 374/16.96

x = 22 days.

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The equation b=-a is the correct equation.

What is an equation?

An equation is a statement in maths that demonstrates the equivalence of two factors by linking them with the equivalent symbol =. Equations are used to define geometric patterns in Euclidean geometry. Because the equations beneath consideration, such as implicitly equations or descriptive equations, contain an unlimited variety of solutions, the goal has started to shift: instead of directly stating the alternatives or collecting them, which again is unattainable, one utilizes equations to analyze the features of figures. This is the fundamental concept of elementary algebra, a significant mathematics discipline. Differential equations is equations in which 1 or more polynomials and its implications are involved. They are addressed by locating a functional expression that doesn't employ derivatives. Differential equations are utilized to analyze rate-related phenomena.

The equation b=-a is the correct equation.

Hence, option (a) b=-a is correct.

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Using the z-distribution, the 95% confidence interval for the proportion of male respondents that agree that a working mother does not hurt children is:

(0.1439, 0.2161).

The bounds of a confidence interval of proportions is given according to the following rule:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the parameters are described as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The values of the other parameters are given as follows:

[tex]\pi = 0.18, n = 435[/tex]

Hence the lower end of the interval is calculated as follows:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.18 - 1.96\sqrt{\frac{0.18(0.82)}{435}} = 0.1439[/tex]

The upper end of the interval is calculated as follows:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.18 + 1.96\sqrt{\frac{0.18(0.82)}{435}} = 0.2161[/tex]

The problem asks for the 95% confidence interval for the proportion of male respondents that agree that a working mother does not hurt children is:

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Answer:

45%

Step-by-step explanation:

x * 29 = 13

x = 13/29

x = 0.448

45%

Given the function:

Answer:

$850.14

Step-by-step explanation:

7.75% as decimal: 0.0775

788.99 x 0.0775 = 61.146725

788.99 + 61.146725 = 850.136725

850.136725 rounded to nearest cent is 850.14

So the total price of the camera with sales tax included is $850.14

The probability that a sum of 9 on the 2 die will occur at least once is 217/729.

Sum of 9 in a pair of dice can occur in the following 4 ways.

3 + 6

4 + 5

5 + 4

6 + 3

Also, total number of ways = 6*6 = 36

Hence, probability of getting a sum of 9  = 4/36 = 1/9.

We know that,

Probability of getting a sum of 9 + Probability of not getting a sum of 9 = 1

Hence, we can write,

1/9 +  Probability of not getting a sum of 9 = 1

Probability of not getting a sum of 9 = 8/9

Also,

Probability of getting the sum of 9 atleast 1 + probability of getting the sum 9 none of the times = 1

Hence, we can write,

Probability of getting the sum of 9 atleast once =  1 - probability of getting the sum 9 none of the times/

Probability of getting the sum of 9 atleast 1 = 1 - (8/9)*(8/9)*(8/9) = 1 - 512/729 = 217/729.

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Answer:

  (a) expression: (6 yd)²; area: 36 yd²

  (b) expression: (10 yd)²; area: 100 yd²

  (c) Jones: 18; Evansbee: 50

  (d) Jones: $89.82; Evansbee: $249.50

Step-by-step explanation:

You want the area, number of plants that can be placed, and the cost of plantings for gardens that are 6 yards square and 10 yards square. Each plant takes 2 square yards and costs $4.99.

The formula for the area of a square of side length s is ...

  A = s²

The area of a square garden with a side length of 6 yards is ...

  A = (6 yd)² . . . . . expression for the area

  A = 36 yd² . . . . . the area of the garden

The area of a square garden with a side length of 10 yards is ...

  A = (10 yd)² . . . . . expression for the area

  A = 100 yd² . . . . . the area of the garden

The area used by the plants is the product of their number and the area taken by each.

For Jones' garden, the number of plants that can be placed is ...

  n(2 yd²/plant) = 36 yd²

  n = (36 yd²)/(2 yd²/plant) = 18 plants

Mr. Jones can place 18 plants in his garden.

For Evansbee's garden, the number of plants that can be placed is ...

  n(2 yd²/plant) = 100 yd²

  n = (100 yd²)/(2 yd²/plant) = 50 plants

Mr. Evansbee can place 50 plants in his garden.

At $4.99 each, the cost of plantings will be $4.99 times the number of plants.

Plants for Jones' garden cost 18($4.99) = $89.82.

Pants for Evansbee's garden cost 50($4.99) = $249.50.

Answer: 1, 2, 3, 4,6 12

Step-by-step explanation:

every single number can be divided by the answer numbes

Answer:

  1) CW 270° or CCW 90°

Step-by-step explanation:

In each case, you want to identify two transformations that will map the preimage to the image.

We note the transformation maps ...

  A(-7, 0) ⇒ A'(0, -7) . . . . . . CCW 90° or CW 270°

  B(-4, -1) ⇒ B'(1, -4)

  C(-7, 3) ⇒ C'(-3, -7)

These can be described by ...

  (x, y) ⇒ (-y, x)

This transformation is equivalent to either of the two transformations ...

As above, rotation about the origin by 90° in one direction is the same as rotation 270° about the origin in the other direction. The attached graph shows the result either way. The two equivalent transformations are ...

The coordinate transformation is ...

  (x, y) ⇒ (y, -x)

Answer:

A''(3, 2), B''(-1, 4), C''(2, 0)

Explanation:

For the first step, negate the y coordinate.

For the second step, add 4 to the x coordinate and 5 to the y coordinate.

[tex]A(1,-3) \longrightarrow A'(-1, -3) \longrightarrow A''(3, 2) \\ \\ B(5,-1) \longrightarrow B'(-5,-1) \longrightarrow B''(-1, 4) \\ \\ C(2, -5) \longrightarrow C'(-2, -5) \longrightarrow C''(2, 0)[/tex]

Answer:

B

Step-by-step explanation:

(120 - 50 b/m) / 5 b / m^2 = 14 minutes    

Answer:

y = -13

Step-by-step explanation:

a) Subtract y from both sides.

2y + 6 − y = y − 7 − y

y + 6 = −7

b) Subtract 6 from both sides.

y + 6 − 6 = −7 − 6

y = -13

Answer:

13 + 13 = 26

13/26 * 12/25 = 6/25 = 0.24

The decimal form of this rational number is 0.27, where 27 in decimal is recurring.

What are the steps to solve a rational number?
The steps to solve a rational number problem are:
(a) Let 'a/b' be a rational number. From the sentence, we deduce that denotes the denominator of a rational integer, while represents the numerator. Consequently, is 3 and is 11.
(b) The decimal form is achieved by dividing by, and we described the procedure required to do so:
(i) Ten times the numerator:
Dividend is 30, and the result is known to be zero. Remainder: N/A
ii) Dividend less the dividend multiplied by the divisor by two:
Known outcome: 0.2; residuals: 8
iii) 10 times the residue:
Known outcome: 0.2; residuals: 80
iv) Divide the residue by the divisor and multiply it by 7:
0.27 as known result; 3 as residue
v) Ten times the residue:
0.27 as known result; 30 as residue
vi) Divide the divisor by two and deduct the result from the sum:
Results known: 0.272/Residue: 8
vii) 10 times the residue:
The known outcome is 0.272/Residue: 80.
viii) Divide the divisor by 7 and deduct the result from the sum:
A known outcome is 0.2727/Residue: 3.

Therefore, we can see that is a periodic decimal number in its decimal form.
As a result, we deduce that the decimal representation of this rational number is 0.27, where 27 is a regular integer.

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Answer:

7

Step-by-step explanation:

42 divided by 3 = 14 = total of triangle XYZ

14 divided by 2 = 7

line X/Y = 7

The main goal is 140 percent i.e., 21 members.

What is meant by percentage?

In mathematics, a percentage (from Latin: percentage , "by a hundred") may be a number or ratio expressed as a fraction of 100. it's often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" also are used. A percentage may be a dimensionless number (pure number); it has no unit of measurement. The term "percent" springs from the Latin per centum, meaning "hundred" or "by the hundred". The Italian word per cento, which means "for a hundred," gradually shrank to become the symbol for "percent." The "per" was often abbreviated as "p."—eventually disappeared entirely. The "cento" was contracted to 2 circles separated by a horizontal line, from which the fashionable "%" symbol is derived.

140 percent of 15 = 15x140/100 = 21 members

Hence, the main goal is 21 members.

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The covid strain will take 17.33 weeks to infect 800,000 people.

To solve the given problem, we only need to utilize the exponential function formula, which is stated as

[tex]A = Pe^{rt}[/tex]

Where A is the final value,

P denotes the starting value

The rate is r and time is given by t.

Given:

The rate of spread of the new strain of covid = 12% a week

Currently the number of people infected with the virus = 100,000

To determine how long will it take before the virus has infected 800,000 people, substitute the values in the formula

[tex]A = Pe^{rt}[/tex]

[tex]800000 = 100000e^{0.12*t}[/tex]

[tex]8 = e^{0.12*t}[/tex]

[tex]ln 8 = {0.12*t}[/tex]

[tex]t = ln 8/0.12[/tex]

[tex]t = 17.33 weeks[/tex]

Therefore, the covid strain will take 17.33 weeks to infect 800,000 people.

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The area of a parallelogram can be determined by multiplying its base and height, the formula is

The area of a triangle is equal to half the product between the base and the height, following the formula:

The area of a trapezoid is equal to the product of half the sum of its bases and its height following the formula:

Function:

A function is a relation in which every input x has a different output value y.

If there is more than 1 outputs for the same input then it doesn't represent a function.

Let us analyze each of the given options.

Option A:

{(2, -1), (4, -2), (6, -3), (8, -4)}

As you can see, each input x has a different output value y.

Therefore, it is a function

Option B:

{(0, 0), (1, 1), (1, 0), (2, 1)}

As you can see, the input (1) has two different outputs (1 and 0)

Therefore, it is not a function.

Option C:

{(3, 3), (3,4),(4,3),(4,4)}

We have

probability of B occurs is 5/8

probability that event A occurs given B occurs is 5/8

We have the next formula, that is the conditional probability formula

where

P(A|B)= probability of A given B

P(B)= probability of B

P(A∩B)=probability of A and B

so we need to isolate the P(A∩B) in order to obtain the probability that events A and B both occur

04) The complementary angles are the angles whose sum is 90° thus { 26°,54°,48°,29°,22°} will be the corresponding angles.05)The supplementary angles are the angles whose sum is 180° thus {54°,48°,12°,135°,91°} will be the corresponding angles.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

If m∠A + m∠B = 90° then A and B will be the complimentary angle.

The complementary of 64° = 90° - 64° = 26°

The complementary angle of 36° = 90° - 36° = 54°

The complementary angle of 42°= 90° - 42° = 48°

The complementary angle of 51°= 90° - 51° = 29°

The complementary angle of 68°= 90° - 68° = 22°

If m∠A + m∠B = 180° then A and B will be the supplementary angle.

The supplementary of   = 180° - 126°  = 54°

The supplementary of   = 180° -  132° = 48°

The supplementary of   = 180° - 178°  = 12°

The supplementary of   = 180° -   45° = 135°

The supplementary of   = 180° -  89°  = 91°

Hence " { 26°,54°,48°,29°,22°} will be the corresponding complementary angle and {54°,48°,12°,135°,91°} will be the corresponding supplementary angles".

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ANSWER:

D. x = 9/k

STEP-BY-STEP EXPLANATION:

We have the following equation:

We solving for x:

The correct answer is D. x = 9/k

An event can be said to be a set of possible outcomes which results from an experiment.

An individual can be said to create a theory after he observes events.

A theory is said to be a set of ideas that explains the results from an experiment.

Therefore, an individual creates a theory after he observes an event.

ANSWER:

Theory

To solve the equation

we are going to use the general formula for quadratic equations:

In our case a=2, b=-24 and c=54. Then

Then x is:

Given:-

Using the future value formula, it is found that:

a) You will have $301,355 in the account after 30 years.

b) You will have put $108,000 in the account.

c) You will have earned $193,355 in interest.

The future value formula  is given by:

[tex]V(n) = P\left[\frac{(1 + r)^n - 1}{r}\right][/tex]

In which the parameters are described as follows:

Considering the $300 deposits, the interest rate of 6% and the monthly compoundings for 30 years, the values of the parameters are given as follows:

P = 300, r = 0.06/12 = 0.005, n = 12 x 30 = 360.

Hence the balance of the account after 30 years will be given by:

[tex]V(30) = 300\left[\frac{(1.005)^{360} - 1}{0.005}\right][/tex]

V(30) = $301,355.

The amount placed into the account is given by:

360 x 300 = $108,000.

The remaining amount is earned in interest, hence:

301355 - 108000 = $193,355.

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The  savings plan balance after 15 months with an APR of 6% and monthly payments of $200 is $3,123.

Given data :

The APR = 6% coincides with a .06/12 = .005 monthly interest rate

Now let determine or find the total after 15 months

Total after 15 month :

Total after 15 month = 200 [ (1 +.005^ 16) - (1 + .005] /(.005)

Total after 15 month = 200 [( 1.005 ^ 16 - 1.005] /(.005)

Total after 15 month = 200 (15.614)

Total after 15 month = $3,122.8

Total after 15 month = $3,123 (Approximately)

Therefore we can conclude that the total sum is the amount of $3,123.

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Answer

Options C and F are correct.

x² + 6x + 9 = 25

(x + 3)² = 25

are both equivalent to

x² + 6x = 16

Explanation

The equations that are equivalent to x² + 6x = 16 will all have to reduce to this exact equation on simplification.

x² + 6x + 9 = 0

Option A is not correct as this equation isn't equal to the equation given in the question.

x² + 6x + 9 = 16

x² + 6x = 16 - 9

x² + 6x = 7

Option B is not correct as this equation isn't equal to the equation given in the question.

x² + 6x + 9 = 25

x² + 6x = 25 - 9

x² + 6x = 16

This option C is corect as it matches the equation given in the quesion.

(x + 3)² = 0

x² + 6x + 9 = 0

Option D is not correct as this equation isn't equal to the equation given in the question.

(x + 3)² = 16

x² + 6x + 9 = 16

x² + 6x = 16 - 9

x² + 6x = 7

Option E is not correct as this equation isn't equal to the equation given in the question.

(x + 3)² = 25

x² + 6x + 9 = 25

x² + 6x = 25 - 9

x² + 6x = 16

This option F is corect as it matches the equation given in the quesion.

Hope this Helps!!!