Simplify. 54+4(3/4−1/2)2

9514 1404 393

Answer:

  (b)  y = -2x +3

Step-by-step explanation:

Subtract the 2x term to get y by itself on the left.

  2x -2x +y = 3 -2x

  y = -2x +3 . . . . . . . matches slope-intercept form y = mx +b

Answer:

x = 8

Step-by-step explanation:

An Equilateral triangle is a triangle in which all three sides and angles are equal. The value of each angle of an equilateral triangle is 60 degrees therefore we get the equation 9x - 12 = 60

Add 12 from both sides to isolate the 9x leaving us with:

9x = 72

Divide both sides by 9 to give us x, which is

x = 8

Answer: If you want to live in a city with greater variability of temperature, you should look for cities with a continental climate. Continental climates are characterized by hot summers and cold winters, with large temperature fluctuations between day and night and between seasons.

Cities located in the interior of large landmasses, far from large bodies of water, are more likely to have a continental climate. Examples of cities with a continental climate include Moscow (Russia), Calgary (Canada), and Chicago (USA). These cities experience wide temperature swings throughout the year, with hot summers and cold winters.

On the other hand, cities located near large bodies of water tend to have a more moderate climate, with smaller temperature fluctuations. Examples of such cities include San Francisco (USA), Sydney (Australia), and London (UK). These cities experience mild summers and winters, with relatively constant temperatures throughout the year.

Step-by-step explanation:

Answer:

7/25 is a fraction

Step-by-step explanation:

7/25 is a fraction and 7/25 in decimal form is 0.28

To turn into decimal 7 divide by 25 =0.28

[RevyBreeze]

Answer:

7/25 supposed to be a fraction

Step-by-step explanation:

its decimal form is 0.28

Look at the picture below. Sorry if its hard to understand.

The results for the addition operation are obtained as  84⁵/₉,  6²/₉,  -23.24 and 131.87 respectively.

The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.

The given problem can be solved as follows,

(a) 45²/₉ + 39³/₉

⇒ 45 + 2/9 + 39 + 3/9

⇒ (45 + 39) + (2/9 + 3/9)  = 84⁵/₉

(b) -24⁵/₉ + 30⁷/₉

⇒ -24 - 5/9 + 30  + 7/9

⇒ (-24 + 30) + (7/9 - 5/9)

⇒ 6²/₉

(c) 28.98 + (-52.22)

⇒ 28.98 - 52.22

⇒ -23.24

(d) 56.75 + 75.12

⇒ 131.87

The given arithmetic operation can be matched in the form of table as,

    Sum                                    Result

45²/₉ + 39³/₉                             84⁵/₉

-24⁵/₉ + 30⁷/₉                            6²/₉

28.98 + (-52.22)                     -23.24

56.75 + 75.12                           131.87  

Hence, the given numbers are added to give result as 84⁵/₉,  6²/₉,  -23.24 and 131.87 respectively.

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If X and Y are any random variables with E(X) = 5, E(Y) = 6, E(XY) = 21, V(X) = 9 and V(Y) = 10, then the relationship between x and y is a strong negative relationship.

A simple random sample can be defined as a subset of items that are selected from a statistical population or larger data set, and each member of the subset has an equal or the same probability of being selected.

This ultimately implies that, each member of the subset are selected randomly and by chance, and as such a simple random sample is an unbiased representation of a statistical population.

By calculating the covariance using the following expression, we have:

Cov(X, Y) = E(XY) - E(X)E(Y).

E(X) = 5, E(Y) = 6 and E(XY) = 21.

In conclusion, we can infer and logically deduce that the relationship between x and y is a strong negative relationship.

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Complete Question:

If X and Y are any random variables with E(X) = 5, E(Y) = 6, E(XY) = 21, V(X) = 9 and V(Y) = 10, then the relationship between X and Y is a:

-strong positive relationship

-strong negative relationship

-weak positive relationship

-weak negative relationship

The given series Σ(-1)^(n+1)ln(n)/n from n=1 Upon examination, we can conclude that the series diverges. To understand why, let's consider the alternating series test and the behavior of the individual terms in the series.

The alternating series test states that if the absolute values of the terms in an alternating series decrease and approach zero, the series converges. However, in this case, the individual terms of the series do not approach zero as n increases. The natural logarithm function grows without bound as n approaches infinity, and dividing it by n does not change this fact.

As a result, the terms of the series do not satisfy the condition required for convergence, and the series diverges.

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Answer:

let, width be 'x'

perimeter of rectangle=2(length+width)

56=2(19+x)

56=38+2x

2x=56-38

x=18/2

x=9inches

so, the width of rectangle is 9 inches.

hope it helps.

Answer:

17

but it can be 18 too

cuz the q doesn't tell us that the value of x has to be a prime no.

Step-by-step explanation:

2+3+5+7+11+13+17=58

Option (a) 7+3•5

Step-by-step explanation:

\({ \purple{ \tt{6 + {2}^{4}}}} \)

\({ = \purple{ \tt{6 + 2 \times 2 \times 2 \times 2}}}\)

\({ = \purple{ \tt{6 + 16}}}\)

\({ = \purple{ \tt{22}}}\)

_________________________________

\({ \red{ \sf{7 + 3 \times 5}}}\)

\({ = \red{ \sf{7 + 15 }}}\)

\({ = \red{ \sf{22}}}\)

Therefore,

\({ \green{ \sf{6 + {2}^{4} = 7 + 3 \times 5}}}\)

\({ \green{ \sf{22 \: \: \: \: \: \: \: = \: \: \: \: \: \: 22}}}\)

A child weighing 19 pounds should receive approximately 432.7 milligrams of cough medicine in one day, assuming a dosage of 5.0 milligrams of medicine per kilogram of body weight.

Step 1: Convert the weight from pounds to kilograms.

To convert pounds to kilograms, we multiply the weight in pounds by the conversion factor 0.4536.

19 pounds × 0.4536 = 8.6184 kilograms

Step 2: Calculate the amount of cough medicine based on the dosage.

Multiply the weight in kilograms by the dosage per kilogram.

8.6184 kilograms × 5.0 milligrams/kg = 43.092 milligrams

Therefore, a child weighing 19 pounds should receive approximately 43.092 milligrams of cough medicine in one day, using the given dosage of 5.0 milligrams of medicine per kilogram of body weight.

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Explanation:

If some angle x is supplementary to \(128.9^{\circ}\), then we can say the following:

\(x+128.9 = 180\\\\x = 180-128.9\\\\x = 51.1\\\\\)

Therefore, the two angles \(51.1^{\circ}\) and \(128.9^{\circ}\) add to 180 degrees. The two angles can be glued together to form a straight line.

The remaining number of flires that Linda still not posted is 40.

According to the given question.

The total number of fliers Linda have = 84

Fraction of fliers Linda posted = 1/3

And, fraction of fliers Linda posted second time from the remaning fliers = 2/7

Now,

1/3 of 84 fliers = 1/3 × 84 = 28

So, the number of fliers are left with Linda after first posting = 84 - 28 = 56

Again she posted 2/7 fliers. The number of flires Linda posted second time is given by

⇒ 2/7 × 56 = 16

Thereore,  the number of fliers that Lindna still not posted  = 56 - 16 = 40

Hence, Linda still not posted 40 fliers.

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Answer:

C. -10,000

Step-by-step explanation:

As x approaches zero, f(x) approaches infinity or negative infinity.

Answer: C. -10,000

Answer:

-10,000

Step-by-step explanation:

Answer:

the motion of the object will stay the same

Step-by-step explanation:

The slope of the line that passes through the graph is 3

From the graph, the points are given as

(0, 0)  and (1, 3)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (0, 0)  and (1, 3)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (0, 0)  and (1, 3)

Substitute the known values in the above equation

So, we have the following equation

Slope = (3 - 0)/(1 - 0)

Evaluate

Slope = 3

Hence, the slope of the line is 3

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(a) The mathematical model describes the rate of dye change in the mixture as the difference between the input rate (0.6r kg/min) and the output rate (Q/(2+(10+r)) kg/min).

(b) To achieve a dye concentration of 0.2 kg/L in the outflow, the injection rate, r, must satisfy 0.6r = Q/(2+(10+r)).

(c) The time to reach within 1% of the desired concentration is determined by solving Q/(2+(10+r)) = 0.2 - 0.2*0.01 using the mathematical model.

(a) Mathematical model for the mixing process:

The rate of change of dye amount, dQ/dt, in the mixture can be described by the following equation:

dQ/dt = (rate of dye input) - (rate of dye output)

The rate of dye input is given by the concentration of the dye solution (0.6 kg/L) multiplied by the injection rate, r L/min. Therefore, the rate of dye input is 0.6r kg/min.

The rate of dye output is determined by the concentration of the mixture, Q/total volume, multiplied by the outflow rate (10+r L/min). Hence, the rate of dye output is Q/(2+(10+r)) kg/min.

Combining these terms, the mathematical model for the mixing process is:

dQ/dt = 0.6r - (Q/(2+(10+r))) kg/min.

(b) Injection rate to achieve equilibrium solution:

To obtain a dye concentration of 0.2 kg/L in the outflow mixture, we need to find the injection rate, r, that leads to this equilibrium solution. At equilibrium, the rate of dye input equals the rate of dye output.

Setting 0.6r = Q/(2+(10+r)) and solving for r gives the injection rate required to achieve the desired concentration.

(c) Time to reach within 1% of the desired concentration:

To determine the time it takes for the outflow concentration to reach within 1% of the desired concentration (0.2 kg/L), we can use the mathematical model from part (a) and solve for the time, t, that satisfies Q/(2+(10+r)) = 0.2 - 0.2*0.01.

Solving this equation will give the time required for the outflow concentration to be within 1% of the desired concentration.

Note: The presence of dye in the initial fluid in the chamber at t=0 would affect the equilibrium injection rate, as it would already contribute to the dye concentration. However, the time required to reach the desired concentration would still be determined by the mathematical model and would depend on the injection rate and the mixing process.

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Answer:

Listed

Please mark me as the brainliest and thanks

Given:

a.) A triangular prism has a base area of 43 square meters.

b.) Its volume is 645 cubic meters.

Recall: Formula in getting the volume of a triangular prism.

Where,

B = Base area of the prism.

H = Height of the prism.

Let's now determine the area of the prism:

Therefore, the height of the prism is 15 meters.

The solution to the inequality 6x + 3y ≤ 84 is the dark region shown and the point (9, 10) satisfies this inequality.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the number of rides Darren can ride and y represent the number of exhibits he can view. Hence:

6x + 3y ≤ 84

The solution to the inequality 6x + 3y ≤ 84 is the dark region shown and the point (9, 10) satisfies this inequality.

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It was A! I got it right on the Edmentum/Plato test!! YW!!!

Answer:

12

Step-by-step explanation:

32-20=12

(Correct me if i am wromg)

The width of the frame will be 6 inches.

The area of the rectangle is defined as the space occupied by the rectangle in two dimensional space.

Given that a rectangular picture is 9 inches wide and 12 inches long. the picture has a frame of uniform width. if the combined area of picture and frame is 180 in².

The area of the picture is calculated as:-

Area = L x W

Area =  12 x 9

Area = 108 square inches

The remaining area of the frame is,

Area = 180 - 108

Area = 72 square inches.

The width of the ram is calculated as:-

Area = L x W
72 = 12 x W
W = 72 / 12

W = 6 inches

Therefore, the frame will have a width of 6 inches.

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The total number of subjects (n) in the study is 30. This is because the researcher gathered 15 men and 15 women, which gives a total of 30 participants in the study. Each participant was given a memorization task to perform in two different environments, one with music and one without music.

Therefore, each participant performed the task twice, resulting in a total of 60 data points (30 participants x 2 environments).

It is important to note that the researcher is interested in the effect of two independent variables, gender and environment, on the dependent variable of memorization. By including both men and women in the study, the researcher can examine if there are any gender differences in memorization abilities.

By having two different environments, the researcher can examine if there are any environmental factors that may affect memorization. Multiple independent variables and measures of the dependent variable can provide a more complete understanding of the phenomenon being studied.

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If Jim has to run faster than 80% of adult then he need to run with speed 5.89 mph.

A Normal Distribution is defined as the distribution where the random variable values are distributed symmetrically.

In the Question it is given  that

mean (μ) = 5.3                                                   ...(i)

standard deviation (σ) = 0.7                             ...(ii)

and Jim runs faster than 80% of adult men,

and the group follows a normal distribution.

For Normal Distribution

Jim runs faster than 80% of adult men, is represented by

P(x<z)=0.80

z=φ(0.80)

z=0.842    ( from z table )                                  ...(iii)

we know that

\(z=\frac{x-\mu}{\sigma}\)                                         ...(iv)

Substituting the values of (i),(ii) and (iii)  in (iv) we get

\(0.842=\frac{x-5.3}{0.7} \\ \\ x-5.3=0.842*0.7\\ \\ x-5.3=0.5894\)

\(x=0.5894+5.3\\x=5.8894\)

x≅5.89

Therefore , if Jim has to run faster than 80% of adult then he need to run with speed 5.89 mph.

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Answer:

9

Step-by-step explanation:

Horizontal line from 4 to -5.

Distance formula is: \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

       \((x_{1},y_{1}) = (4,7)\\(x_{2},y_{2}) = (-5,7)\)

Thus let us plug in all the know values and solve:

      \(\sqrt{(-5-4)^2+(7-7)^2} =\sqrt{(-9)^2} =\sqrt{81} = 9\)

Thus the distance is 9

Hope that helps!

Answer:

-3

Step-by-step explanation:

Use slope formula to find the slope of the first road:

(y2 - y1) / (x2 - x1)

(1 - 5) / (-1 - 11)

-4 / -12

1 / 3

The slope of a line perpendicular to this line would just be the negative reciprocal of the slope:

-3 / 1 or just -3

Answer:

The number of

Quarters = q = 58 quarters

Nickels = n = 32 nickels

Step-by-step explanation:

It is important to note that:

A quarter is worth 25 cents = 0.25q

A nickel is worth 5 cents = 0.05n

George has only Quarters and nickels in his piggy bank.

Let the number of

Quarters = q

Nickels = n

He has a total of 90 coins.

Hence,

q + n = 90.... Equation 1

q = 90 - n

The value of the coins is $16.10.

Hence,

0.25q + 0.05n = 16.10....Equation 2

We substitute 90 - n for q in Equation 2

0.25(90 - n) + 0.05n = 16.10

22.5 - 0.25n + 0.05n = 16.10

Collect like terms

- 0.25n + 0.05n = 16.10 - 22.5

-0.2n = - 6.4

n = -6.4/-0.2

n = 32 nickels

Solving for q

q = 90 - n

q = 90 - 32

q = 58 quarters

Therefore, the number of

Quarters = q = 58 quarters

Nickels = n = 32 nickels

The set A ∩ B = {3}

The intersection of sets, denoted as A ∩ B, refers to the set that contains elements that are common to both sets A and B. In this case, set A consists of the elements {1, 2, 3, 6}, and set B consists of the elements {3, 4, 5}.

The intersection of A and B, written as A ∩ B, represents the set of elements that appear in both sets simultaneously.

To find the intersection of sets A and B, we examine each element of set A and check if it is also present in set B. In this case, the element 3 is the only element that exists in both sets.

Therefore, the intersection of sets A and B is {3}.

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The approximate area of the window that is not cleaned by the wiper is:

240 - 100.5 ≈ 139.5 square inches. Answer: \boxed{139.5}.

What is circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center.

To solve this problem, we need to find the area of the trapezoid and subtract the area of the semicircle.

The area of a trapezoid is given by the formula:

A = (a + b)h/2

where a and b are the lengths of the parallel sides, and h is the height (the perpendicular distance between the parallel sides).

In this case, we have:

a = 24 inches (the top parallel side)

b = 16 inches (the bottom parallel side)

h = 12 inches (the height)

Using the formula, we get:

A = (24 + 16) x 12/2

A = 240 square inches

The area of a semicircle is given by the formula:

A = πr²/2

where r is the radius of the circle.

In this case, the radius is half of the length of the wiper, so we have:

r = 16/2 = 8 inches

Using the formula, we get:

A = π(8²)/2

A ≈ 100.5 square inches

Therefore, the approximate area of the window that is not cleaned by the wiper is:

240 - 100.5 ≈ 139.5 square inches. Answer: \boxed{139.5}.

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