Who is correct and why?

•A. Kevin is correct. Amy did not regroup properly.

•B. Amy is correct. Kevin did not regroup properly.

•C. Kevin is correct. Amy did not line up the decimals correctly.

•D. Amy is correct. Kevin did not line up the decimals correctly.

The correct inequality that represents the given scenario is, x + 4 ≤ 16. Hence option A is true.

Used the concept of inequality,

A relation by which we can compare two or more mathematical expressions is called an inequality.

Given that,

Joanne volunteers 4 hours more per week than Richard does.

In a given week, they do not volunteer for more than a combined total of 16 hours.

Let x be the number of hours that Richard volunteers.

Then the correct inequality is,

x + 4 ≤ 16

Therefore, option A is true.,

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Answer:

x ( > or = ) 5/9

Step-by-step explanation:

● 2(1 + x) ( > or = ) 11 - 3x

● 2 + 2x ( > or = ) 11 - 3x

Add 3x to both sides

● 2 + 2x + 3x ( > or = ) 11 - 3x + 3x

● 2 + 5x (> or = ) 11

Substract 2 from both sides

● 2 + 5x -2 ( > or = ) 11 -2

● 5x (> or =) 9

Divide both sides by 5

● 5x/5 ( > or = ) 5/9

● x ( > or = ) 5/9

The causes of variation that can be identified and eliminated are called; Assignable Causes.

There are two primary causes of variation in the quality of a product or process. These two primary causes are called;

Now, Common causes of variation are defined as random causes that we cannot identify. However, Assignable causes of variation are those that can be identified and eliminated.

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The given expression is

To solve the product, we have to use the distributive property

Then, we move all the terms to the left side to combine like terms

Now, we use the quadratic formula to find the solutions

Where a = 1, b = -5, and c = -204. Let's replace these values

There are two solutions

The midpoint of AB has coordinates (9, -1.5), the gradient of line L is -3 and the point (100, -302) doesn't lie on L.

What is a coordinate?

Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space (3D). Mathematicians, physicists, and engineers employ a variety of coordinate schemes.

(a) Given point A (5, -4) and point B (13, 1)

Therefore, midpoint of AB is \((\frac{x1+x2}{2},\frac{y1+y2}{2})\)

                                          \(or,(\frac{5+13}{2},\frac{-4+1}{2})\)

                                          \(or, (\frac{18}{2},\frac{-3}{2} )\)

                                          \(or,(9, -1.5)\)

(b) In the equation \(y=2-3x\), -3 is the gradient of line L.  

(c) The point with coordinates (100, -302) doesn't lie on L as it doesn't satisfy the equation \(y=2-3x\)

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Answer:

5 feet

Step-by-step explanation:

By triangle inequality, the sum of lengths of any two sides has to be strictly greater than the length of the third side.

Let x feet be the length of the third side.

We have 3+x>7, x+7>3 and 3+7>x.

Solving these, we get x > 4, x > -4 and x < 10.

The solution is therefore 4 < x < 10 and the smallest whole number which satisfies the inequality is 5.

Therefore the answer is 5 feet.

Answer:

22320

Step-by-step explanation:

simple interest= p (deposit) × r (rate) × t (time)

=1550×7.2×2

=22320

Answer:

Step-by-step explanation:

volume of an oblique square pyramid V = 1/3 * b * H where;

b is the base area of the pyramid

H is the height of the pyramid

To determine the expression that represents area of the base of the pyramid, we will make the variable 'b' the subject of the formula from

V = 1/3 bH

\(V=\frac{bH}{3}\)

Cross multiplying we have;

\(3V = bH\\\)

Dividing both sides by H we have;

\(\frac{3V}{H} = \frac{bH}{H} \\b = \frac{3V}{H}units^{2}\)

This gives the correct expression for the base area of the pyramid

Answer:

A.

Step-by-step explanation:

Using the slope concept, it is found that:

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

Hence, for the mango tree, we have that:

tan(x) = 17/8

x = arctan(17/8)

x = 64.8º.

Which is the angle of elevation of the sun.

For the car, we have that:

tan(29º) = 125/d

d = 125/tan(29º)

d = 225.5.

Which is the distance.

For the stick, we have that:

tan(x) = 4/2

x = arctan(2)

x = 63.4º.

Which is the angle of elevation of the stick.

For the flagpole, we have that:

tan(49º) = h/4.

h = 4 x tan(49)

h = 4.6 m.

Which is the height of the flagpole.

For the lighthouse, we have that:

tan(38) = h/255.

h = 255 x tan(38)

h = 199 ft.

Which is the height of the lighthouse.

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17.83 is the average value of the function f(x) = x(x-1) over the interval [2, 7]

To find the average value of the function f(x) = x(x-1) over the interval [2, 7], we need to calculate the definite integral of the function over that interval and divide it by the width of the interval.

First, let's find the definite integral of the function f(x) = x(x-1):

∫[2, 7] x(x-1) dx

Integrating the function, we get:

∫[2, 7] (x^2 - x) dx = [1/3 x^3 - 1/2 x^2] evaluated from 2 to 7

Plugging in the upper and lower limits, we get:

\([1/3 (7)^3 - 1/2 (7)^2] - [1/3 (2)^3 - 1/2 (2)^2]\)

= [1/3 (343) - 1/2 (49)] - [1/3 (8) - 1/2 (4)]

Simplifying further, we have:

= (343/3 - 49/2) - (8/3 - 6/3)

= (539/6) - (2/3)

= (539/6) - (4/6)

= 535/6

Now, to find the average value, we divide the definite integral by the width of the interval:

Average value = (535/6) / (7 - 2)

= (535/6) / 5

= 535/30

= 17.83

Therefore, the average value of the function f(x) = x(x-1) over the interval [2, 7] is approximately 17.83.

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Answer: 40

Step-by-step explanation:

38+ 52=90

230-90=40

After 7 weeks, the plant's approximate height is 8.7 cm.

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the connection between two expressions on opposite sides of the sign. It generally consists of one variable and one equal to symbol.

Here,

You are given a a graph titled Plant Height that shows Number of Weeks on x axis and Height of Plant in cm on y axis. Plotting this and you will get an equation of y = 1.2792x - 0.1665 (I used excel using the given points from the above problem).

y = 1.2792x - 0.1665

y = 1.2792 (7) - 0.1665

y = 8.78 centimeters.

The most likely approximate height of the plant after 7 weeks is 8.7 centimeters.

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The volume of ball is 32.49 cubic centimeter.

What is volume ?

 Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area occupied within an object's three-dimensional bounds is referred to as its volume. The object's capacity is another name for it.

Here ,

The volume of a ball = 32490 cubic millimeters

To convert into cubic millimeter into cubic centimeter by dividing by 1000, Then,

=>  32490/1000

=> 32.49 cubic centimeter.

Hence the volume of ball in cubic centimeter is 32.49 .

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Answer:

3 hours and 30 minutes

Step-by-step explanation:

8:15+3=11:15

11:15+30=11:45

Answer:

15 hr 30 min

Step-by-step explanation:

8:15 - 9 am = 45 min

9 am to 11 pm = 14 hours

11pm - 11:45 pm = 45 min

90 min = 1 hr 30 min

14 hr + 1 hr 30 min = 15 hr 30 min

The boundaries of the critical region for a two-tailed test with a = 0.05 for each of the following df values are given below:a) df = 8 : t = ±2.306b) df = 15 : t = ±2.131c) df = 24 : t = ±2.064

The critical value of t is determined by the degrees of freedom (df) and the level of significance (α) for a two-tailed test.

When the level of significance is 0.05, the critical value of t is used to define the boundaries of the critical region.

The null hypothesis is accepted if the test statistic falls within the critical region, while the alternative hypothesis is accepted if it falls outside the critical region.

For the degrees of freedom (df) 8, the critical values of t are ±2.306. For df = 15, the critical values of t are ±2.131. And for df = 24, the critical values of t are ±2.064.

These values are calculated using a t-distribution table or statistical software like SPSS.

By comparing the calculated test statistic with the critical values of t, we can decide whether to accept or reject the null hypothesis.

If the test statistic is greater than the positive critical value or less than the negative critical value, we reject the null hypothesis.

If the test statistic is between the positive and negative critical values, we fail to reject the null hypothesis.

In conclusion, we can find the critical values of t for a two-tailed test with a = 0.05 by using a t-distribution table or statistical software, given the degrees of freedom.

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Given problem represent Fundamental Counting Theorem.

Fundamental Counting Theorem states that if an event can occur in m different ways, and another event can occur in n different ways, then the total number of occurrences of the events is m×n.

Here Taylor has 5 baskets and there are 6 balls in each basket.

That is m = 5 and n = 6

Therefore Taylor have m×n= 5×6 =30 balls

Hence here we use Fundamental counting theorem.

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Answer:

x = 3

Step-by-step explanation:

-5x + 10 = -5

       -10    -10

-5x = -15

divide by -5

x = 3

Answer:

\(x = 11\)

Step-by-step explanation:

\( - 5(x - 10) = - 5\)

\( - 5 \times x - 10 \times - 5 = - 5\)

\( - 5x + 50 = - 5\)

\( - 5x = - 5 - 50\)

\( - 5x = - 55\)

\( \frac{ - 5x}{ - 5} = \frac{ - 55}{ - 5} \)

\(x = 11\)

\( - 5(11 - 10) { = }^{?} - 5\)

\( - 5 \times 11 - 5 \times - 10 { = }^{?} - 5\)

\( - 55 + 50 { = }^{?} - 5\)

\( - 5 = - 5\)

Using sampling concepts, it is found that a sample that involves an equal proportion of boys and girls is representative of the population.

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.

The students of the seventh grade can be divided into boys and girls, hence, a sample that involves an equal proportion of boys and girls is representative of the population.

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Answer:

C) \(60^\circ+n360^\circ,120^\circ+n360^\circ\)

Step-by-step explanation:

\(sinx-\sqrt{3-3sin^2x}=0\)

\(sinx=\sqrt{3-3sin^2x} \)

\(sin^2x=3-3sin^2x\)

\(4sin^2x=3\)

\(sin^2x=\frac{3}{4} \)

\(sinx=\pm\sqrt{\frac{3}{4} } \)

\(sinx=\pm\frac{\sqrt{3}}{2} \)

\(x=\frac{\pi}{3}+2\pi n,\frac{2\pi}{3}+2\pi n \)

\(x=60^\circ+n360^\circ,120^\circ+n360^\circ\)

Therefore, the correct option is C

Answer:

\(Dom= R-\{-4\}\)

\(Range = R- \{0\}\)

Step-by-step explanation:

The declaration made indicates that Mabel left a $15.80 gratuity.

Percent, which is a relative number used to denote hundredths of any amount. Since one percent is equal to one tenth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage.

To find the amount of the tip that Mabel left, we can multiply the bill amount by the tip percentage, which is 20% or 0.2 in decimal form.

The amount of the tip is:

Tip = Bill Amount x Tip Percentage

Tip = $79 x 0.2

Tip = $15.80

Therefore, the tip that Mabel left was $15.80.

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value of x is 11.

hope this answer helps you dear....take care and may u have a great day ahead!

9514 1404 393

Answer:

  (1, 7)

Step-by-step explanation:

Fill in x=1 and do the arithmetic.

  h(1) = 4(1) +3 = 7

The coordinate pair is ...

  (x, h(x)) = (1, h(1)) = (1, 7)

(a) The differential equation that is satisfied by y is:

\(\frac{dy}{dt} = ky(1-y)\)

(b) To solve the differential equation, we separate the variables and integrate both sides:

\(\frac{dy}{y*(1-y)} = k*dt\)

Integrating both sides, we get:

\(\frac{lnly}{1-y} = k*t +c1\)

where C1 is an arbitrary constant of integration.

We can rewrite the equation in terms of y:

\(\frac{y}{1-y} = e^{(k*t+c1)}\)

Multiplying both sides by (1-y), we get:

\({y} = e^{(k*t+c1)} *(1-y)\)

\(y= \frac{C}{(1+(c-1)e^{-kt} }\)

where C = y(0) is the initial fraction of the population who have heard the rumor.

(c) In this case, the initial fraction of the population who have heard the rumor is y(0) = \(\frac{100}{1300}\) = 0.077. At noon, half the town has heard the rumor, so y(4) = 0.5.

Substituting these values into the equation from part (b), we get:

\(0.5= \frac{0.077}{1+(0.777-1) e^{-k4} }\)

Solving for k, we get:

\(k= ln(\frac{12.857}{4} )\)

Substituting this value of k into the equation from part (b), and setting y = 0.9 (since we want to find the time at which 90% of the population has heard the rumor), we get:

\(0.9= \frac{0.077}{1+(0.777-1) e^{-ln(12.857}*\frac{t}{4} }\))

Solving for t, we get:

t = 8.7 hours after the beginning (rounded to one decimal place)

A differential equation is a mathematical equation that relates a function to its derivatives. It is a powerful tool used in many fields of science and engineering to describe how physical systems change over time. The equation typically includes the independent variable (such as time) and one or more derivatives of the dependent variable (such as position, velocity, or temperature).

Differential equations can be classified based on their order, which refers to the highest derivative present in the equation, and their linearity, which determines whether the equation is a linear combination of the dependent variable and its derivatives. Solving a differential equation involves finding a function that satisfies the equation. This can be done analytically or numerically, depending on the complexity of the equation and the available tools.

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Answer:

C. -12-(-15) =3

Step-by-step explanation:

you subtract the two numbers to get the distance.

to get the equation of any straight line we simply need two points off of it, hmmm let's use the points in the picture below for "a".

\((\stackrel{x_1}{-4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-4)}}}\implies \cfrac{-6}{2+4}\implies \cfrac{-6}{6}\implies -1\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{-1}(x-\stackrel{x_1}{(-4)}) \\\\\\ y-3=-1(x+4)\implies y-3=-x-4\implies y=-x-1\)

Answer:

A. 10

Step-by-step explanation:

As we know that

The length of the major axis of the ellipse is 10

i.e

2 a = 10

Also, the ellipse is the curve that consists of 2 focal points  in order that the total of the distance to the 2 focal points would remain constant for each and every point displayed in the curve

Now we assume that P is the curve point

So,

PF1 + PF2

i.e

2 a (blue line) + (red line)

2 a = 10

Therefore the sum of the length is 10

Answer:

10

Step-by-step explanation:

\(\\ \bull\tt\longrightarrow T_n=n^2+2n+9\)

\(\\ \bull\tt\longrightarrow T_1=1^2+2(1)+9=1+2+9=12\)

\(\\ \bull\tt\longrightarrow T_2=2^2+2(2)+9=4+4+9=17\)

\(\\ \bull\tt\longrightarrow T_3=3^2+2(3)+9=9+6+9=24\)